Article
Reputations for Resolve
and Higher-Order
Beliefs in Crisis
Bargaining
Allan Dafoe1,2, Remco Zwetsloot1,2, and Matthew Cebul3
Abstract
Reputations for resolve are said to be one of the few things worth fighting for, yet
they remain inadequately understood. Discussions of reputation focus almost
exclusively on first-order belief change— Astands firm, Bupdates its beliefs about A’s
resolve. Such first-order reputational effects are important, but they are not the
whole story. Higher-order beliefs—what Abelieves about B’s beliefs, and so on—
matter a great deal as well. When Acomes to believe that Bis more resolved, this
may decrease A’s resolve, and this in turn may increase B’s resolve, and so on.
In other words, resolve is interdependent . We offer a framework for estimating
higher-order effects, and find evidence of such reasoning in a survey experiment on
quasi-elites. Our findings indicate both that states and leaders can develop potent
reputations for resolve, and that higher-order beliefs are often responsible for a
large proportion of these effects (40 percent to 70 percent in our experimental
setting). We conclude by complementing the survey with qualitative evidence and
laying the groundwork for future research.
Keywords
bargaining, belief structure, conflict, game theory, survey experiment
1Centre for the Governance of AI, University of Oxford, Oxford, United Kingdom
2Department of Politics and International Relations, University of Oxford, Oxford, United Kingdom
3Weiser Center for Emerging Democracies, University of Michigan, Ann Arbor, MI, USA
Corresponding Author:
Remco Zwetsloot, Manor Rd, Oxford OX1 3UQ, United Kingdom.
Email: remcozwetsloot@gmail.comJournal of Conflict Resolution
1-27
ªThe Author(s) 2021
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/0022002721995549
journals.sagepub.com/home/jcr

[In bargaining situations], each party’s strategy is guided mainly by what he expects the
other to accept or insist on; yet each knows that the other is guided by reciprocal
thoughts. The final outcome must be a point from which neither expects the other to
retreat; yet the main ingredient of this expectation is what one thinks the other expects
the first to expect, and so on. Somehow, out of this fluid and indeterminate situation
that seemingly provides no logical reason for anybody to expect anything except what
he expects to be expected to expect, a decision is reached.
—Thomas Schelling (Schelling 1960, 70)
Can both sides simultaneously have images of high resolve or is there a zero-sum
element involved?
—Robert Jervis (Jervis 1978, 199)
Introduction
Navigating an international crisis can require incredibly complex inferences. Even
seemingly straightforward strategies can backfire dramatically. Suppose that per-
sons AandBare playing Chicken, the game in which two cars race toward each
other and the goal is to get the opponent to swerve first. One popular strategem
says that Ashould throw her steering wheel out of the window in order to convince
Bthat she cannot swerve, thereby compelling Bto do so.1Yet suppose that B
incorrectly believes that Ahid a spare steering wheel under her seat. If Adoes not
know that Bbelieves this, she may surrender her ability to swerve without actually
becoming committed in B’s eyes, raising the chances of a tragic crash. Or suppose
thatAincorrectly believes that Bbelieves that Ahas a spare steering wheel. This
belief might prevent Afrom using a tactic that would have improved her odds of
victory.
Much of the complexity in international crisis bargaining is attributable to higher-
order beliefs —beliefs about beliefs (Schelling 1960; O’Neill 1999). While these
complications are perhaps most apparent in hypothetical games like Chicken, exam-
ples abound in real-world international crises as well. For instance, in the years prior
to the Berlin crisis, Premier Khrushchev had deliberately exaggerated the Soviet
Union’s capabilities, and widely-discussed American concerns about a “missile gap”
had convinced him that the Americans had fallen for the ruse. “[O]n the assumption
that the Americans believed the Soviets were ahead in the arms race,” Khrushchev
chose to escalate tensions over Berlin (Kaplan 1983, 304). Khrushchev was forced to
back down, however, when he learned that US policymakers did not believe this at
all—a fact that the Americans purposely signaled via intelligence leaks to NATO
units that the US knew to be compromised by Soviet agents (Schlosser 2014, 284).
Higher-order beliefs thus played a critical role in both the onset and resolution of one
of the most significant crises of the Cold War.2 Journal of Conflict Resolution XX(X)
In this article, we examine the theoretical and empirical import of higher-order
belief dynamics for two crucial phenomena in international relations: resolve and
reputations for resolve. Reputations, especially for resolve, have been a long-
standing topic of scholarship, but most studies consider only first-order beliefs:
whether and how Bupdates his beliefs about Aon the basis of A’s behavior. We
argue that taking higher-order beliefs into account substantially amplifies the impor-
tance of reputations for resolve. This is because resolve is interdependent : one side’s
(perceived) resolve can affect the other side’s (perceived) resolve, meaning that
small initial changes in beliefs can spiral into large overall changes, with potentially
decisive consequences.
We evaluate our theory using a survey experiment conducted on a sample of
quasi-elites recruited through Stephen Walt’s Foreign Policy blog. We begin by
corroborating reputation scholars’ core assertion: states that behaved resolutely in
the past are perceived to be more highly resolved in the present. We find that the
effect of reputation on perceived resolve is larger than any other experimental
manipulation, including the effect of material capabilities, and persists across a
range of informational conditions and subgroups.
We then go a step further, advancing scholarship on reputations for resolve by
demonstrating that respondents also form higher-order beliefs in line with our argu-
ment. Exogenous increases in A’s perceived resolve, induced by providing informa-
tion about A’s behavior in disputes with states other than B, produce decreases in B’s
perceived resolve, even though respondents learned nothing about the usual factors
said to affect B’s resolve. The size of the parameter estimates we obtain suggest that
higher-order beliefs can account for as much as 70 percent of the reputational
manipulation’s effect on the balance of resolve, with a lower bound of roughly 40
percent. We thus answer Robert Jervis’s longstanding but still open question: there is
indeed a strong zero-sum element to resolve.
Our design also permits a direct test of a competing hypothesis linking higher-
order beliefs to resolve, which Jervis has referred to as the “domino theory paradox”
and Daryl Press as the “never again theory”: if Abacked down in a recent dispute, B
will believe that Awill expend extra effort to restore its tarnished reputation for
resolve, and therefore that Awill be more rather than less resolved in subsequent
disputes (Jervis 1991; Press 2005). Our evidence is contrary to these hypotheses.
Our results reinforce recent studies demonstrating the importance of reputation in
the domains of conflict, finance, and alliance politics, among others (see Crescenzi
2017, for a review). These studies all focus on the first-order effects of reputation.2
We show, however, that the story does not stop there. In doing so, we join a number
of others who place higher-order beliefs at the center of international relations
specifically (Schelling 1960; O’Neill 1999; Morrow 2014) and social, economic,
and political life more broadly (Kuran 1995; Chwe 2001). These beliefs are what
make resolve interdependent, and are therefore crucial to the onset and resolution of
crises and wars.Dafoe et al. 3
Resolve, Reputation, and Higher-Order Beliefs
Much of international politics pivots around perceptions. A state’s ability to per-
suade, deter, and compel depends in large part on how that state is perceived—
whether others consider its military capable, its threats credible, its promises reli-
able. As a result, states and leaders are motivated to act in ways that favorably shape
others’ perceptions and expectations, i.e. to cultivate reputations for desirable qua-
lities or behavioral tendencies.
One of the most important kinds of reputation in international politics is a rep-
utation for resolve . We define resolve as follows:
Resolve: the probability that an actor is willing to stand firm in a crisis, given
its beliefs about the world at that time.
We briefly explain how this behavioral definition relates to other common con-
ceptualizations of resolve. Formalized mathematical models of crisis bargaining
often define resolve as a state’s “value for war,” which is said to be a function of
material factors such as military capabilities, the issue under dispute, and domestic
audiences (see, e.g. Morrow 1989; Powell 1990; Fearon 1994; Sartori 2016). Psy-
chological accounts of resolve instead emphasize internal traits such as dispositional
determination, willpower, or “sticktoitiveness” (Kertzer 2016, 8-9). Here, we define
resolve in terms of states’ behavior in a crisis, in which states may either back down
or stand firm.3In this sense, a state’s “value for war” and its dispositional traits are
important factors that affect resolve—the probability that an actor stands firm—but
they may not be the only ones, so they do not define resolve.4
Understanding resolve in behavioral terms has several benefits.5By clearly spe-
cifying what kind of behavior is (in)consistent with being resolved, our definition
makes resolve measurable and facilitates empirical analysis. More importantly, our
definition allows scholars to directly incorporate another essential determinant of
whether Aw i l ls t a n df i r mi nac r i s i sw i t h B:A’s beliefs about B’s resolve. As
exemplified by Chicken, that A’s crisis behavior depends on her beliefs about B’s
resolve is what makes interstate crises complex strategic interactions. This relation-
ship also speaks to the literature on reputations for resolve, which we briefly review
below.
Building Reputations for Resolve
International crises can often be understood as “contests of resolve” (Morrow 1989,
941-42) in which the outcome is determined by one side’s ability to convince the
other that it will not back down. In such contests, a history of resolute past behavior
can be a valuable asset. We say that actors have a reputation for resolve when
observers have formed beliefs about that actor’s tendency to stand firm in a certain
class of disputes on the basis of that actor’s past behavior (Dafoe, Renshon, and
Huth 2014).64 Journal of Conflict Resolution XX(X)
The effect of a reputation for resolve remains a subject of debate. Proponents
contend that reputations offer a path to successful commitment, deterrence, and
compellence (Huth 1997), as costly past actions can corroborate threats and pro-
mises that might otherwise be dismissed as “cheap talk” (Fearon 1995; Trager 2017).
These scholars argue that an “undesired image can involve costs for which almost no
amount of the usual kinds of power can compensate” (Jervis 1970, 6), and so
reputations are “one of the few things worth fighting over” (Schelling 1966, 124).
In support of this position, a number of recent studies find evidence that states’ past
behavior shape how other states act toward it.7
Others, however, dispute the link between past actions and present behavior. For
instance, Mercer argues that the desirability of an action conditions how people
interpret the disposition of its initiator, concluding that “people do not consistently
use past behavior to predict similar behavior in the future” (Mercer 1996, 45-47,
212). Similarly, Press claims that “blood and wealth spent to maintain a country’s
record for keeping commitments are wasted,” since opponents form assessments of
credibility largely based on their perceptions of states’ interests and capabilities, not
their past behavior (Press 2005, 10). Detractors also aver that evidence of reputa-
tional effects is largely observational and often indirect, and is therefore
inconclusive.
Thus, one contribution of our article is to bring experimental methods to bear on a
basic question: do observers use a state’s past behavior to predict what it is likely to
do today?8
HREP: Perceptions of a state’s resolve will (a) increase if it stood firm in past
crises and (b) decrease if it backed down in past crises.9
In addition, we also seek to advance the reputation debate beyond HREPtoward a
discussion of higher-order beliefs. Note that HREPfocuses purely on how first-order
beliefs —beliefs about an actor’s traits or behavioral tendencies—change in response
to past behavior. Such arguments are at the center of most theoretical accounts of
reputational dynamics. First-order beliefs are, however, not the only kinds of beliefs
that matter. In the next section, we contend that reputations can also affect higher-
order beliefs —beliefs about beliefs (about beliefs, etc.)—with important conse-
quences for state behavior.
Reputational Effects and Higher-Order Beliefs
Consider a hypothetical dispute between states AandB, in which Bis considering
whether to escalate. Initially, Bhas some sense of how likely Awould be to stand
firm ( A’s resolve), though he cannot be sure. Bthen observes Abehaving resolutely
in some other dispute, and after considering that Amight, say, be more militarily
capable than Boriginally thought, Bupdates his beliefs about A’s resolve accord-
ingly. We can call this a first-order reputational effect , in which one side updates itsDafoe et al. 5
beliefs about its opponent’s characteristics or behavioral tendencies solely on the
basis of that opponent’s past behavior.
In many cases, however, higher-order reasoning further complicates the story.
For example, Amight know that Bwas paying careful attention to her behavior in the
other dispute. If so, Amight conclude that, since she stood firm, Bhas become less
resolved, and this could further embolden Ato also stand firm against B.I fBexpects
Ato be thinking along these lines, he might conclude that there is little he can do to
make Aback down, further reducing B’s resolve. If actors make inferences in this
way, the first-order reputational effect will be joined by higher-order effects. These
two effects together make up the total reputational effect , i.e. the full shift in the
balance of resolve between two actors due to a single initial reputational shock (see
Section “Do Higher-Order Beliefs Contribute to Reputational Effects?” for a for-
malization). Indeed, higher-order beliefs can theoretically produce large substantive
effects, as relatively small first-order reputational effects cascade through higher-
order belief chains into large changes in the balance of resolve.
Put another way, our argument is that resolve is a function of not just the material
factors emphasized in the modeling literature or the internal traits emphasized in
psychological accounts, but also states’ beliefs about their opponents’ resolve— A’s
resolve is decreasing in (her beliefs about) B’s resolve, and vice versa. In short,
resolve is interdependent . Furthermore, that resolve is interdependent implies that
higher-order beliefs may play a central, albeit under-appreciated, role in interna-
tional crises— A’s beliefs about B’s resolve (which dictate A’s own resolve) are
themselves a product of A’s higher-order beliefs about B’s beliefs about A’s resolve,
and vice versa. To express our arguments in terms of reputations, we contend not just
that states and leaders can possess reputations for resolve, but also that these actors
are aware that such a reputation may decrease the likelihood that their opponents
stand firm during crises, and so update their own resolve accordingly. In short, states
may expect that their reputations precede them.
HINT: Perceptions of a state’s resolve will (a) increase when there is a decrease
in perceptions of its opponent’s resolve, and (b) decrease when there is an
increase in perceptions of its opponent’s resolve.
There are two principal reasons why we may not expect this hypothesis to hold.
First, states may not form higher-order beliefs if they lack the ability to do so.
Kertzer, for example, argues that in many situations with higher-order uncertainty
about resolve “the complex nature of the decision-making environment actors face
stretches far beyond the limits of human cognition” (Kertzer 2016, 149; see also
Mercer 2012). And even if they have the ability, states may be insufficiently confi-
dent in their higher-order beliefs to in corporate them into their assessments of
resolve. If this were the case, we would expect to see no evidence of interdependence.
Second, HINTis not the only possible relationship between higher-order reason-
ing and reputational effects. HINTimplies that higher-order reasoning magnifies6 Journal of Conflict Resolution XX(X)
first-order effects—states that stand firm earn larger reputational bonuses, whereas
states that back down suffer larger penalties. In what Jervis labels the “domino
theory paradox” and Press “never again theory,” however, higher-order effects run
counter to the first-order effect (Jervis 1991; Press 2005). Domino theory, which
undergirded much of US foreign policy during the Cold War, holds that if a state
backs down in one situation, observers will infer that it is more likely to do so in
other situations as well. The paradox is that the corresponding higher-order beliefs
may be “self-defeating” (Jervis 1991, 36-37):
An actor who has had to back down once will feel especially strong incentives to
prevail the next time in order to show that the domino theory is not correct, or at least
does not apply to him. In other words, an actor who believes the domino theory—or
who believes that others accept it—will have incentives to act contrary to it. Indeed,
statesmen sometimes respond to a defeat by warning others that this history will make
them extremely resistant to retreating again. Furthermore, if others foresee this, they
will expect a defeated actor to be particularly unyielding in the next confrontation.
In short, the domino theory paradox pred icts that, in certain circumstances,
higher-order reasoning can mitigate or even reverse first-order reputational effects.
HDTP: Perceptions of a state’s resolve will increase when it backed down
recently and has a prior reputation to recover.
Research Design
The scientific study of reputations is limited by their inaccessibility. Reputations
consist of perceptions, which exist in people’s minds and are not directly observable.
Even records of private deliberations, free of any incentives to dissemble, may lead
us astray. To the extent that an opponent’s reputation is a constant during a crisis and
is common knowledge among decisionmakers, discussions are likely to focus on
new information such as troop movements even if reputation matters (Weisiger and
Yarhi-Milo 2015). Reputational inferences, given their evolutionary importance,
may also be so automatic that they are made subconsciously (Bowles and Gintis
2011). These difficulties were acknowledged by Snyder and Diesing, who noted that
their inability to find much evidence of reputational inferences in case histories
“may be only an artifact of the record” (Snyder and Diesing 1977, 496).
To overcome these challenges, we employ a scenario-based survey experiment.
Respondents are told about a scenario, features of which are randomly varied or
omitted, and then asked about their opinions or beliefs. Survey experiments are
especially suitable for research questions about how people incorporate, interpret,
and act on particular types of information (Mutz 2011), and these are precisely the
questions in which scholars of reputation are interested. Below, we review the
survey design and the sample in more detail.Dafoe et al. 7
Survey Vignette
Respondents read an abstract scenario about two countries ( AandB) engaged in a
serious territorial dispute. The features of the scenario are presented in a bullet list
format, each assigned with some probability independent of each other (a full fac-
torial design). Each feature has several different levels, including its omission. For
the full text of the survey and treatment allocations, see Online Appendix B.
Respondents were first informed of each country’s regime type, either democracy
or dictatorship (some received no information on regime type). Respondents then
learned about the military capab ilities of each country, with Ahaving either
“substantially stronger military forces” than B, being “about equally strong,” or B
being substantially stronger (again, some received no information about capabil-
ities). In all conditions except no information, respondents are also told that neither
country has nuclear weapons.
The respondent then reads the reputational feature of the scenario, State A’s
history of crisis interactions. This bullet involves two variables: whether Astood
firm or backed down in past crises, and whether A’s previous conflicts were against
Bor other countries.10
According to most impartial observers, of the three most recent major international
crises that Country A has faced against [ other countries /Country B ], Country A [ did not
back down and Country A achieved its aims /backed down in each crisis and failed to
achieve its aims ].
There is also a special Domino Theory Paradox version of this manipulation, in
which Astood firm in three past crises, but then backed down in a fourth, most recent
crisis. In all conditions except no infor mation, respondents are also informed
whether A’s past crises occurred under the current or a previous leader.
Lastly, the vignette includes several other experimental features related to the
history of the dispute, as well as recent threats and promises.11The scenario con-
cludes by stating that the crisis is serious and that many observers consider major
military action in the near future likely. Respondents are then asked the primary
outcome question for both countries:
What is your best estimate, given the information available, about whether Country A/
B will back down in this dispute?
Respondents have five options, ranging from “very unlikely” (0 percent to 20
percent chance) to “very likely” (80 percent to 100 percent chance). Note that this
question exactly matches our definition of resolve in Section “Resolve, Reputation,
and Higher-Order Beliefs.”12
Before detailing our sampling strategy, we briefly address the benefits and draw-
backs of our abstract survey design. Our survey vignette describes a crisis between8 Journal of Conflict Resolution XX(X)
two abstract states, AandB, and the scenarios respondents read were typically no
more than 150 words. The benefit of this approach is its flexible simplicity; short
vignettes are less taxing for respondents, and abstracting away from real-world states
may permit cleaner manipulation of the concepts of interest (though not necessarily;
see Dafoe, Zhang, and Caughey 2018). The attendant drawback is a decreased level
of realism in abstract survey scenarios, relative to vignettes that feature actual
countries (Tingley 2017). Reassuringly, however, recent research employing both
abstract and real-world crises scenarios recovers reputational effects of a very sim-
ilar magnitude to those presented below (Renshon, Dafoe, and Huth 2018).
Regardless of the design, it is of course not possible to create environments akin
to those faced by real-life decision-makers through surveys alone, and it is therefore
best to complement survey experiments with other kinds of evidence. Though more
systematic observational work will have to await future research, we offer some
preliminary supportive evidence for our claims in Section “Discussion: Interdepen-
dent Resolve in Real Life,” and discuss the conditions under which evidence of
interdependent resolve is most and least likely to be found.
Sample
We administered the survey to a conveni ence sample of respondents recruited
through Stephen Walt’s Foreign Policy blog. On August 1st, 2011 Walt posted a
blog entry inviting readers to “Become a data point!” (see Online Appendix B.1).
From this advertisement, over 1,000 respondents took the survey.
This sampling strategy was intended to mitigate potential biases that may arise
from using regular citizens to proxy for elite policymakers. The general concern is
that elites are better informed about and more experienced with foreign policy
decision-making than the average citize n—as a result, they are more likely to
employ higher-order strategic reasoning and consider their opponents’ perspective
(Hafner-Burton, Hughes, and Victor 2013; Hafner-Burton et al. 2014). Ideally, then,
one would run our experiment on key decision-makers, such as military leaders,
foreign policy advisors, and politicians. Unfortunately, such subjects are rarely
accessible, and even if they are it is usually as part of a small convenience sample.
To approximate our elite population of interest, we instead sought to recruit a
sample of quasi-elite respondents who are abnormally well-informed about and
interested in foreign policy, whose backgrounds and world views more closely
parallel those of high-level elites. We expected a sample drawn from Walt’s Foreign
Policy readership to be highly educated and knowledgeable of foreign policy, and
that is indeed the case. Of those 87 perccent who answered the demographic ques-
tions, 83 percent reported having a college degree or higher, and 50 percent a
postgraduate degree. Moreover, 60 percent claimed to have “particular expertise
with foreign affairs, military affairs, or international relations.” Politically, the group
leans Democratic, as 89 percent claimed to agree more with the policies of Demo-
crats (11 percent more with those of Republicans). The respondents were 88 percentDafoe et al. 9
male, which is far from representative of the general population but not obviously
unrepresentative of foreign policy elites. More details about the sample are provided
in Online Appendix A.
To be sure, then, our sample remains an imperfect approximation of foreign
policy elites. Still, we argue that these imperfections will likely lead us to under-
estimate the effect of reputation and higher-order beliefs on perceived resolve. To
start, the Democratic bias should cut against our proposed hypothesis, as liberals are
generally less likely than conservatives to invoke concerns over credibility, reputa-
tion, and honor in international affairs (Trager and Vavreck 2011). And while
respondents may also hew closer to Stephen Walt’s particular foreign policy views,
Walt has repeatedly argued against the importance of reputation.13Lastly, our
sample likely remains less experience d with actual foreign policy decision-
making than true elites. But as mentioned above, experience is linked to higher-
order strategic reasoning, and Tingley and Walter (2011) show that experienced
players care more about reputation than inexperienced ones. If anything, then, our
results likely underestimate the reputational effects that would be found among
actual elites.
In short, given the cost and difficulty in obtaining elite samples, our sampling
design is a reasonable first step toward the empirical study of higher-order beliefs in
international crises.14Importantly, we think it highly unlikely that our sample would
produce an opposite effect of reputation on perceived resolve relative to true elites—
our respondents may be less attentive to reputation, but this should only depress the
magnitude of reputational effects, not reverse their direction.
Results
To preview our results, we reach two main findings. First, reputations for resolve
matter; when respondents learn that a stat e has stood firm in past crises, they
consider it much more likely to stand firm today. Second, resolve is interdependent;
we find that increases in A’s perceived resolve are associated with decreases in B’s
perceived resolve, and estimate that higher-order belief updating is responsible for a
large proportion of the total observed effect of past behavior on the balance of
resolve.15
Can States Build Reputations for Resolve?
We begin with HREP, which considers whether a country’s past behavior affects
perceptions of its current resolve. We find strong evidence that it does. Respondents
who learned that “Country Adid not back down and Country Aachieved its aims” in
past crises thought that Awas more likely to stand firm than those that received no
information about past behavior (a 10 percentage point increase, from 60 percent to
70 percent). Similarly, when A“backed down in each crisis and failed to achieve its10 Journal of Conflict Resolution XX(X)
aims,” respondents thought Awas roughly 10 percentage points more likely to back
down. These effects are both highly significant (Figure 1).
Moreover, this reputational treatment has the largest effect of all manipulations in
the survey. The effect of going from a history of backing down to a history of
standing firm is about 20 percentage points, which represents a quarter of the resolve
variable’s total range.16This reputational effect is roughly twice the size of the
second-largest effect, informa tion about power: shifting from Bhaving
“substantially stronger military forces” to Ahaving “substantially stronger military
forces” increases perceptions of A’s resolve by roughly 10 percentage points.17
Readers may wonder whether this potent reputational effect is driven only by a
subset of respondents. Reputation skeptics contend that even if past behavior mat-
ters, it does so only to the extent that “a decision maker uses an adversary’s history of
keeping commitments to assess the adversary’s interests or military power” (Press
2005, 21). An observable implication of this view is that we should only see effects
of past behavior on respondents that lack information about the balance of power.
We find, however, that the reputational effect persists among respondents who were
told about military capabilities (Figure 12, Online Appendix C.1).18And while the
reputational effect decreased slightly as scenario complexity increased,19it
remained above 10 percentage points even among respondents who received the
maximum amount of information about the scenario (Figure 11, Online Appendix
C.1). Reputational effects also persist across state leaders and across demographic
subgroups, including gender, education, political affi liation, and cultural back-
ground. In sum, we find strong support for HREP.
In contrast, we find no evidence for HDTP. According to HDTP, a state that backs
down once after a history of standing firm will be perceived to be more resolved to
stand firm in the present, as observers expect it to try to re-establish its lost repu-
tation for resolve. Yet as Figure 1 shows, backing down once after a history of
always standing firm reduces perceived resolve by a bout 8 percentage pointsA Did Not Back
 Down Three TimesA Backed Down in Most
 Recent Crisis, History
 of Not Backing DownA Backed Down
 Three Times
0.2 0.1 0.0 0.1 0.2
Change in Perceptions of A's ResolveTreatment
Figure 1. Effect of A’s past behavior on perceptions of A’s resolve, relative to respondents
that received no information about past behavior (baseline probability of standing firm /C2560
percent). X-axis displays percentage point change; horizontal lines represent 90 percent and
95 percent CIs.Dafoe et al. 11
compared to a history of standing firm ( p<0:0001), nearly returning perceived
resolve to its baseline probability in the no-information condition. In other words,
backing down once almost entirely eliminates the reputational gains that Aachieves
by standing firm in the initial three crises.
Do Higher-Order Beliefs Contribute to Reputational Effects?
Typically, reputational effects like the ones reported above are interpreted in terms
of first-order updating: Atakes an action, and observers update their beliefs about A.
Yet as discussed in Section “Reputational Effects and Higher-Order Beliefs,” the
total reputational effect of A’s past behavior on AandB’s resolve may also consist of
higher-order effects. To test this idea, we need a treatment that affects beliefs about
A’s resolve, but cannot affect B’s resolve through any channel except (beliefs about)
A’s resolve. If such a treatment affects B’s resolve, then we can conclude that
perceptions of B’s resolve are influenced by perceptions of A’s resolve—in other
words, that respondents form higher-order beliefs and that resolve is interdependent
(HINT).
It is useful to define the relevant estimand and identifying assumptions more
formally. Let Ridenote the resolve of agent i,kdenote a level of belief updating,
and ^Rk
idenote an observer’s beliefs about actor i’s resolve after the kth level of
updating. Next, define D^Rk
ias the change in beliefs about actor i’s resolve after the
kth level of updating, i.e. ^Rk
i/C0^Rk/C01
i. In these terms, the “direct” or “immediate”
effect of our reputation treatment T(information about A’s past behavior) is given by
D^R1
i¼^R1
i/C0^R0
i, where ^R0
irefers to perceptions of i’s resolve before observing T
(i.e. among respondents in the “no information” condition).
Now, suppose that observers go through two levels of belief updating following
reputation treatment T(this updating process is shown graphically in Figure 2). Our
argument suggests that we should see D^R1
A>0, and, by interdependence, D^R2
B<0.
In this situation, our estimand, which we will call the interdependence coefficient
and label y, is given byD^R2
B
D^R1
A. This ratio tells us by how much an immediate one-unit
change in A’s perceived resolve subsequently changes B’s perceived resolve. For
example, if a 10 percentage point increase in A’s resolve decreases B’s resolve by 5
percentage points, y¼/C05
10¼/C00:5. More generally, if we assume that the interde-
pendence of resolve is symmetric across actors and constant across levels of updat-
ing, we have y¼D^Rk
A
D^Rk/C01
B¼D^Rk
B
D^Rk/C01
Afor all k2N. We can then empirically estimate yby
taking the ratio of the observed total effect of treatment on B’s and A’s resolve,D^RB
D^RA,
and state our interdependent resolve hypothesis more precisely as HINT:y<0.20
As mentioned above, our treatment must fulfill two conditions for this estimation
strategy to succeed, analogous to the ident ifying assumptions in instrumental12 Journal of Conflict Resolution XX(X)
variable analysis: ( C1)D^R1
A>0 (instrument strength) and ( C2)D^R1
B¼0 (exclusion
restriction). Notably, most treatments do not satisfy C2. For example, the fact that A
stood firm against Bin the past could lead to inferences not just about A’s resolve,
but also about Band the A-Bdyad, such as B’s dispositional determination or
domestic audiences, violating our identifying assumption. Thus, we cannot use
information about A’s past behavior against Bto estimate the interdependence of
AandB’s resolve.
However, information about A’s past actions against another country is a treat-
ment that likely satisfies C2.21When told about A’s extra-dyadic behavior, observers
can make inferences about how much Avalues its reputation, whether A’s domestic
public is liable to punish leaders for backing down, or any other factor that shapes
A’s resolve. But the treatment is uninformative about the A-Brelationship, the
territory under dispute, or other factors that could reasonably shape perceptions of
B’s resolve—except, that is, perceptions of A’s resolve. This treatment, then, allows
for a clean test of our interdependence hypothesis.
The results of this test are displayed in Figure 3. We find that A’s behavior against
other countries significantly affects perceptions of B’s resolve as expected—
respondents who were told that Astood firm against other countries in the past
assess B’s resolve to be roughly 7 percentage points lower relative to baseline, and
Abacking down against other countries leads to a similar increase in perceptions
ofB’s resolve. For Astanding firm in extra-dyadic crises, ^y¼/C0:065
:091¼/C0:71, and for
Abacking down in extra-dyadic crises, ^y¼:074
/C0:098¼/C0:75. Both of these effects are
statistically significant, lending strong support to HINT.22Figure 2. A model of belief updating, where kdenotes the level of belief updating, Rk
idenotes
beliefs about actor i’s resolve after the kth level of updating, and DRk
idenotes the change in
beliefs about i’s resolve due to the kth level of updating. If conditions C1 and C2 are met, then
the thick black lines have DRk
i¼DRk/C01
j/C2y, and we can estimate yasD^RB
D^RA.Dafoe et al. 13
The Interdependence Multiplier
These results offer compelling evidence that reputational effects exist, and that they
are compounded by higher-order beliefs. Still, we have yet to specify precisely how
important are higher-order beliefs. Can we estimate the proportion of the total
reputational effect—the effect of past behavior on the overall difference in resolve
between AandB—that is attributable to higher-order belief updating?
To help us answer this question, define the interdependence multiplier (IM)a st h e
factor by which a first-order reputational effect should be multiplied in order to
obtain the total reputational effect. In our simple formalization, the magnitude of the
interdependence multiplier depends on two parameters: the interdependence coeffi-
cient, y, and the number of levels of belief updating, which we label n.23Given our
model (and assuming jyj<1), Online Appendix D.2 derives the IMto be, for any n,
IM¼1/C0jyjn
1/C0jyj/C18/C19
which converges to 1 =ð1/C0jyjÞasn!1 , a situation with “common knowledge” in
which everybody knows about a fact or event, knows that everybody knows it, and
so on.
Figure 4 plots the magnitude of the IMacross hypothetical values of yandn.A t
one extreme, if we assume that actors engage only in first-order reasoning (the light
blue line), the IMis always 1, and the total reputational effect is equal to the first-
order reputation effect. This, implicitly, has been the assumption in most past dis-
cussions of reputation. At the other extreme, if it is plausible to assume common
knowledge (the red line), the total reputational effect is more than twice as large as
the first-order effect for any jyj>0:5, and nearly four times as large at j^yj¼0:73
(the average of our jyjestimates calculated from Figure 3 above).24Between these
extremes, the IM‘s magnitude is substantial across a range of parameter values,A Backed Down Against Other
 Country (Not B) Three TimesA Stood Firm Against Other
 Country (Not B) Three Times
0.2 0.1 0.0 0.1 0.2
Change in Perceptions of ResolveTreatmentActor's
Resolve
A
B
Figure 3. Effect of A’s past behavior against “other countries” (not B) on perceived resolve,
relative to respondents that received no information about past behavior ( A’s baseline
probability of standing firm /C2560 percent). X-axis displays percentage point change; horizontal
lines represent 90 percent and 95 percent CIs.14 Journal of Conflict Resolution XX(X)
underscoring that higher-order beliefs can be responsible for a large proportion of
any given total reputational effect.
We can now use the IMto estimate the effects of higher-order beliefs on per-
ceived resolve in our survey experiment. As stated above, our average estimated
y¼/C00:73, and the average total effect of the reputation treatments presented in
Figure 3 is roughly 16 percent. To estimate how much of that 16 percent change is
attributable to higher-ord er beliefs, let us assume that n¼3. This implies
IM¼1/C00:733
1/C0:73¼2:26. The estimated first-order effect is then simply the total effect
divided by the IM,16
2:26¼7:08. This leaves roughly 9 percentage points attributable
to higher-order reasoning—a sizable 55 percent of the total effect.
We can also more intuitively verify this result by beginning with the first-order
effect, and then building out via n¼3 reasoning to the total effect. Suppose that, as
we just estimated, respondents on average perceive Ato initially be 7.08 percentage
points more likely to stand firm when Ahas stood firm repeatedly in past cases
(D^R1
A¼7:08). The respondent reasons, however, that Bwill become less resolved
after inferring this change. Specifically, B’s resolve decreases by 7 :08/C2ypercent-
age points ( D^R2
B¼/C05:17). This, in turn, will increase A’s perceived resolve by
/C05:17/C2y(D^R3
A¼3:77). The total reputational effect is therefore jD^R1
Ajþ
jD^R2
BjþjD^R3
Aj¼16:02/C2516 percentage points, which is indeed the total reputa-
tional effect that we observe in the data (and is also 7 :08/C2IM).
This estimation strategy is limited by our inability to directly observe n, respon-
dents’ level of higher-order reasoning—we assumed n¼3 above, but the true value
could be higher or lower. While we therefore cannot definitively identify the pro-
portion of the total reputational effect attributable to higher-order beliefs, we remain1.02.03.04.0
0.00 0.25 0.50 0.75 1.00
Absolute Value of Magnitude of Interdependence Multiplier (IM)Nth Order
Beliefs (n)
1st
2nd
3rd
4th
Common
Knowledge
Figure 4. jyj,n, and the Interdependence Multiplier. Vertical line indicates j^yj¼0:73.Dafoe et al. 15
confident that these beliefs drive a substantial portion of the effect in this case, for
several reasons. First, we can quantify our uncertainty by deriving bounds. As our
survey recovers reputational effects that are inconsistent with mere first-order rea-
soning, we use n¼2 as a lower bound. In this case, the IM¼1:73, and higher-order
effects are responsible for about 42 percent of the total reputational effect. The upper
bound is represented by common knowledge ( n¼1 ). In this case, the IM¼3:7,
and the higher-order effects constitute about 73 percent of the total reputational
effect (see Online Appendix D.2).25Note that our reputation treatment had a rela-
tively large effect on B’s perceived resolve ( j^yj¼0:73 is large), which results in
correspondingly large higher-order effect estimates even assuming low levels of
higher-order reasoning (Figure 4 is instructive). Of course, the interdependence
coefficient ymight vary in size in different settings or contexts—we discuss this
possibility extensively in Section “The Degree of Interdependence.”
Second, numerous other studies and examples discussed in Section “Higher-
Order Beliefs” suggest that at least some degree of higher-order reasoning, be it
conscious or intuitive, is a regular feature of human cognition in political, economic,
and social settings—though higher-order belief chains can become prohibitively
complex, n¼2 reasoning is relatively common. This reassures us that n¼2i sa
reasonable lower bound to estimate higher-order effects.
In sum, we find clear evidence that higher-order beliefs are responsible for a large
portion of our observed reputational effects—even restricting the calculations to a
minimal level of higher-order reasoning, the proportion approaches 50 percent. In
the next section, we move beyond our survey data to discuss real-world applications
and implications of our argument.
Discussion: Interdependent Resolve in Real Life
Above, we provided evidence of higher-order reputational dynamics, and argued
that the magnitude of these effects depends on the order to which people form beliefs
(n) and the degree of interdependence ( y). Our abstract survey vignette allows us to
observe the effect of higher-order belief updating in a way that is difficult to do in the
real world. Still, some uncertainty remains as to whether and how the interdepen-
dence of resolve manifests in the messier context of real-world bargaining situations.
This section discusses the circumstances under which we expect higher-order beliefs
and interdependent resolve to matter most, and the attendant implications of our
argument for real-world crisis bargaining.
Higher-Order Beliefs
As discussed in Section “Reputational Effects and Higher-Order Beliefs,” one broad
issue is whether decision-makers engage in higher-order reasoning (Kertzer 2016;
Mercer 2012). If they do not, our arguments have little relevance to the real world.
Fortunately, evidence from a variety of contexts suggests that explicit and implicit16 Journal of Conflict Resolution XX(X)
higher-order reasoning is common, and does not require especially sophisticated
agents.
First, experimental evidence from behavioral economics suggests that most peo-
ple often form at least second-order beliefs, and many reach higher orders as well
(e.g. Nagel 1995; Camerer, Ho, and Chong 2004). In psychology, researchers have
found that the magnitude of the famous “bystander effect” depends on whether the
context allows bystanders to form beliefs about other bystanders’ beliefs (Thomas
et al. 2014, 2016). A third example comes from a recent field experiment in Benin,
where voters who learned information about politicians’ behavior punished and
rewarded performance only when they thought that others knew this information
as well, suggesting a higher-order understanding of coordination dynamics (Adida
et al. 2020). Many other studies also find significant effects from interventions
targeted at higher-order beliefs (Bicchieri 2016; Mildenberger and Tingley 2019).
Moreover, scholars have produced abundant evidence of higher-order reasoning
among policymaking elites in high-stakes situations. At the domestic level, autocrats
faced with potentially unsatisfied publics go to great lengths to create impressions of
widespread support for their rule, or, if that fails, at least keep everyone guessing
about each other’s beliefs (Kuran 1995; Chwe 2001, 20-21). Internationally, as
McManus (2014, 726) illustrates with the case of Israel-US bargaining over Iran’s
nuclear program, states often attempt to stake their allies’ reputation on supporting
them, believing that their allies will then believe themselves bound to act (see, e.g.
Jervis 1978, 180; Trager 2017, Ch. 1, for more examples). And conflicts are often
said to end only when “opponents succeed in coordinating their expectations”
(Slantchev 2003, 621; see also Carter 2017). In these and many other examples,
beliefs about beliefs are the driver and focus of significant strategic contention.
To be clear, our argument does not require that actors always run through every
step of the inferential process in a deliberate or conscious way. Higher-order beliefs
can be incorporated into d ecision-making heur istically, implicitly, and subcon-
sciously. As Chwe (2001, 78) argues for the case of driving, “I stop at a red traffic
light out of habit, but a fully specified argument for doing so would involve an infinite
regress: I stop because I think that other people are going, and I think that other people
are going because I think that they think that I am stopping, and so on.” Develop-
mental psychologists have found that children display a great degree of higher-order
understanding early on in life, implicitly engaging in complex theorizing about the
mental states of others long before they can explicitly articulate their reasoning
(Wellman 2014). Higher-order belief dynamics also often become embedded in
cultural and legal norms (O’Neill 1999; Ridgeway 2011; Morrow 2014).
The Degree of Interdependence
While it is therefore clear that real-world actors do engage in higher-order reasoning,
the extent to which first-order reputational effect are amplified also depends on the
degree to which resolve is interdependent, i.e. the extent to which an initial change inDafoe et al. 17
A’s resolve affects B’s resolve. Here, contextual factors are likely to play a large
role. We identify and discuss four such factors.
First, the degree of interdependence depends on the extent to which the context
resembles a prototypical contest of resolve . The central features of such contests are
(1) the costs of conflict are so great that losing is preferred to both sides standing
firm, but (2) the issue under dispute is sufficiently valuable for a coercive victory to
be preferred to a peaceful compromise (Morrow 1989, 941). We expect resolve to be
most interdependent in conflicts that most closely approximate these conditions.
Nuclear crises are often cited as the quintessential examples of such contests (Schel-
ling 1966; Powell 1990), but they are by no means the only ones. In the 1898
Fashoda Crisis, for example, France dispatched a mission to Egypt in an attempt
to force Britain to make concessions, but withdrew when it became convinced that
Britain was more resolved than it initially believed (Trachtenberg 2012, 13-16).26
More contemporary examples can be found in proxy conflicts like the ongoing
Syrian civil war. Direct conflict between the U.S. and Russia over Syria seems
prohibitively costly, yet Damascus remains a valuable prize. In these circumstances,
resolve can be highly interdependent. Indeed, this interdependence featured regu-
larly in debates about U.S. intervention in Syria. Critics argue that Obama’s failure
to enforce the infamous chemical weapons red-line in 2013 undermined U.S. deter-
rence, paving the way for Russian intervention in 2015—Putin might have been
compelled to stay out, were it not clear (to both parties) that the U.S. was irresolute.
At the same time, Obama’s reluctance to engage in Syria resulted in part from his
belief that Russia would counter-escalate in response to limited U.S. intervention,
especially after Russia stepped up its involvement in 2015.27In other words, U.S.
lack of resolve fueled Russian resolve, further depressing U.S. resolve.
Second, interdependence is also affected by the extent to which actors are able to
act strategically , conditioning their behavior on what they think others are likely to
do. Actors may fail or be unable to do so for various reasons. A prominent example is
found in the expansive literature on credible commitments, which discusses com-
mitment devices that may leave actors unconditionally resolved in a crisis. The
moment actors truly commit to a strategy—when they throw their only steering
wheel out of the window—they have effectively set their interdependence coeffi-
cient to 0: even if they subsequently change their beliefs about their opponent’s
resolve, their own course of action is already set. That said, absolute commitments
are exceedingly difficult and risky to make.28In the real world, then, resolve is
almost always interdependent at least to some extent.
A third and related factor is the concentration of decision-making authority : when
leaders have the ability to change course quickly, their resolve is likely to depend
more on the other side’s resolve. If, on the other hand, authority is diffuse, it will be
difficult for a country to change course in the face of new information. One example
is the delegation of military decision-making to local commanders, who can then
choose to stand firm or back down in their theater of operations. Such delegation
may be necessary from a practical perspective, but it also means central decision-18 Journal of Conflict Resolution XX(X)
makers have less flexibility. Another obstacle to short-term policy change in
response to belief updating is the number of veto players in a political system
(Tsebelis 2002). To the extent that this number is correlated with regime type, there
is reason to think that the resolve of democracies is less interdependent than that of
their autocratic counterparts.
Lastly, a fourth factor affecting the degree of interdependence is the observability
of resolve . An actor’s resolve is more likely to influence its opponents calculations
when it is readily observable. Resolve is likely to be more observable the more an
actor’s deliberative processes are public, or when opponents share a cultural under-
standing of the meaning of certain behaviors or events (O’Neill 1999, 153-54).
Strategic intelligence can also play an important role. The interdependence of
resolve was on clear display, for example, during the Washington Disarmament
Conference in 1921, when the United States was able to break Japan’s ciphers and
read Tokyo’s private diplomatic communication. One such message stated the abso-
lute minimum naval tonnage ratio that the Japanese government would be willing to
accept. “Knowing how far Japan could be pushed ...allowed the United States to do
so with full confidence, merely waiting for the Japanese to give in” (Bauer 2013,
211). When Japan’s (lack of) resolve became perfectly observable to the US, Amer-
ican resolve dramatically increased in response.
In sum, we expect actors’ resolve to be most interdependent in real-world con-
texts that resemble prototypical contests of resolve, where actors are strategic and
have centralized decision-making structures, and where resolve can be inferred with
confidence. When interdependence is high, higher-order amplification of first-order
reputational effects can produce especially large swings in the balance of resolve. It
is in these circumstances, then, that beliefs about beliefs should be most consequen-
tial for crisis outcomes. These intuitive sources of variation in the interdependence
of resolve could themselves be the object of empirical study, but for now, we leave
this task for future work.
The Power of Beliefs
Each party is the prisoner or the beneficiary of their mutual expectations.
—Thomas Schelling (Schelling 1960, 60)
Reputations for resolve have long been the subject of debate: some see them as
indispensable assets, while others dismiss past actions as irrelevant to current crises.
Using an experimental approach, this article strongly reinforces the former view—
states and leaders can form reputations for resolve and leverage them to their
advantage during crises. Moreover, we emphasize that higher-order beliefs play
an under-appreciated yet crucial role in this process, as first-order reputational
effects are amplified by actors’ beliefs about their opponents’ beliefs. In this sense,
international contests of resolve hinge not merely on past actions, but on actors’
combined expectations about the implications of past actions for present behavior.Dafoe et al. 19
In conclusion, we make several suggestions for further empirical research on
higher-order beliefs and interdependent resolve in international politics. As men-
tioned earlier, one limitation of our study is that we lack direct knowledge of the
level of higher-order reasoning at which respondents analyzed the crisis scenario. A
number of studies in behavioral economics measures “k-level reasoning” directly in
laboratory game settings (see Hafner-Burton, Hughes, and Victor 2013, for a
review), but these measures are rarely found in survey research on international
politics. Future studies could adapt such techniques to shorter survey formats, where
they could serve as useful individual-level measures of strategic competence.
We also highlight several interesting avenues for future research. One promising
idea is that opponents’ perceptions of a leader’s competence could influence their
higher-order inferences about that leader’s likely beliefs, consequently shaping their
own bargaining behavior. Some leaders are understood to be especially experienced,
calculating, or wise, whereas others may be seen as inexperienced, impulsive, or
even wholly incompetent. Not only could variation in leader competence directly
affect a state’s behavior, but the perception of competence or ineptitude might also
shape others’ higher-order expectations about that leader’s beliefs and world view,
with implications for their own behavior during crises.
Moreover, there are also strong reasons to expect that beliefs about beliefs matter
in contexts far beyond crisis bargaining, including collective action and coordination
on many important international issues, such as climate change and international law
(Mildenberger and Tingley 2019; Morrow 2014). Schelling’s argument that sets of
beliefs can act as prisons (or paradises) matters as much to problems like gender
inequality as it does to international conflict (Ridgeway 2011). Along these lines, the
study of higher-order belief dynamics also presents an exciting opportunity for
collaboration across research fields. Such dynamics can only be understood by
combining the insights and methods of psychological, cultural, and strategic
approaches—whether and how one actor forms and acts on beliefs about another
actor’s beliefs depends on cognitive processes, systems of social meaning, and the
anticipated consequences of different courses of action (O’Neill 1999). And once
they are understood, insights on higher-order beliefs are likely to travel across many
domains and issue areas.
In short, higher-order beliefs are an incredibly rich area for future studies of broad
applicability and substantive importance. This article offered some theory and a
novel methodological framework for diagnosing the effects of higher-order beliefs,
which we hope will contribute to a vibrant sub-literature on this topic in international
relations scholarship.
Acknowledgments
We would like to thank Stephen Walt for generously agreeing to advertise the survey, Tyler
Bowen and Mojmir Stehlik for research assistance, and for help on this and related work,
Sophia Hatz, Maria Hjelm, Susan Hyde, Jos h Kertzer, James Morr ow, Barry O’Neill,
Jonathan Renshon, Todd Sechser, Steve Web er, Alex Weisiger, Keren Yarhi-Milo, the20 Journal of Conflict Resolution XX(X)
participants of the Department of Peace and Conflict Research workshop at Uppsala Univer-
sity and the Division of Social Science seminar at Hong Kong University of Science &
Technology, and especially Robert Trager.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, author-
ship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of
this article.
ORCID iD
Remco Zwetsloot https://orcid.org/0000-0002-2788-6257
Supplemental Material
Supplemental material for this article is available online.
Notes
1. For clarity, we use gendered pronouns to refer to A (female) and B (male) throughout the
article.
2. McManus (2014, 728) briefly alludes to higher-order belief dynamics, but does not
explore them empirically.
3. In real-world crises, the “game” is obviously more complicated. We collapse the policy
space to “back down” or “stand firm” simply for ease of exposition.
4. For more on the meaning of resolve in international relations, see Fearon (1992, 66);
O’Neill (1999, 107); Kertzer (2016, Ch. 1).
5. Our behavioral definition is not optimal for all research objectives. For instance, it is often
productive to focus on the “value for war” because bargaining models can be solved with
respect to this exogenous parameter. Such models tend to assume common knowledge (or
common beliefs) about many aspects of the world (for exceptions, see Acharya and Grillo
2015; Chadefaux 2020; Smith and Stam 2004). Our broader definition, in contrast, is
helpful for those seeking to understand “pre-equilibrium” dynamics in a world where
common beliefs have not yet been established, as is often true when crises and wars
happen.
6. A state’s reputation for resolve encompasses a number of more specific reputations—
such as those for military competence and cost tolerance—concerning characteristics that
affect its probability for standing firm. The extent to which behavior in one dispute affects
how a state is expected to act in another dispute depends on a number of factors; for an in-
depth discussion see Dafoe, Renshon, and Huth (2014).
7. Within conflict studies, past behavior has been found to affect dispute initiation (e.g.
Weisiger and Yarhi-Milo 2015), coercive success (Cebul, Dafoe, and Monteiro Forth-
coming), war onset (e.g. Crescenzi, Kathman, and Long 2007), and military alliances (e.Dafoe et al. 21
g. Mattes 2012; LeVeck and Narang 2017). Others examine the importance of reputation
for cooperation; see Crescenzi (2017).
8. For other recent experimental work, which focuses on first-order beliefs, see Kertzer,
Renshon, and Yarhi-Milo (2021), Kertzer (2016), and Renshon, Dafoe, and Huth (2018).
9. The relevant “perceiver” of a state’s resolve could be any other international observer, be
it another state involved in a dispute with the state in question, or an uninvolved third
party—in either case, agents should make similar reputational inferences. For the pur-
poses of empirical testing, however, the “perceivers” are our survey respondents, who
assessed the resolve of two abstract states in crisis (see Section “Research Design”).
10. Some might wonder how much respondents can infer from State A’s disputes with other,
unknown states (that are not B). Additional background details would allow respondents
to form more precise beliefs, yet respondents can still make general reputational infer-
ences from A’s past behavior even without these details. It is reasonable for respondents
to infer that, if A stood firm three times in recent crises, then A is probably more likely to
stand firm in a subsequent dispute, relative to the respondents’ prior beliefs. Empirically,
we demonstrate that our respondents can and do draw reputational inferences even when
given relatively limited inf ormation. And as noted below , our results accord with
Renshon, Dafoe, and Huth (2018), who find similar reputational effects across abstract
and real-world designs. Regardless, future work on higher-order beliefs could (and ide-
ally would) employ diverse research designs in order to test the sensitivity of this or any
other particular design feature.
11. The vignette manipulates a large number of features, yielding a total of 8,640 cells. In
this, it is similar to related survey techniques such as conjoint analysis (Hainmueller,
Hopkins, and Yamamoto 2014). We discuss the advantages and possible disadvantages of
factorial vignette experiments with many manipulations in Online Appendix B.3.
12. Similar questions were used in Renshon, Dafoe, and Huth (2018) and Kertzer, Renshon,
and Yarhi-Milo (2021), though neither define resolve precisely and both discuss only
first-order effects.
13. For recent examples, see Walt (2015) and Walt (2016).
14. For other experimental work that uses non-elite samples to test theories of bargaining, see
Renshon, Lee, and Tingley (2017), Kertzer, Renshon, and Yarhi-Milo (2021), and Cebul,
Dafoe, and Monteiro (Forthcoming).
15. Main results are shown graphically below—full regression tables can be found in Online
Appendix C.3.
16. The minimum likelihood respondents could give for A standing firm is 10 percent (0 percent to
20 percent), the maximum 90 percent (80 percent to 100 percent). This effect is approximately
equal to one standard deviation of the resolve variable ( m¼62percent, s¼21percent), which
is equivalent to a Cohen’s d¼1; Cohen offered d¼0:8 as a “big” effect.
17. The capabilities results, as well as results from all other manipulations, can be found in
Online Appendix C.
18. We do not manipulate interests, but Kertzer, Renshon, and Yarhi-Milo (2021, 22) find
similar results when doing so: even when told that one side has high stakes and high relative
power, the effect of past behavior on perceptions of resolve is large and significant.22 Journal of Conflict Resolution XX(X)
19. Recall from Section “Survey Vignette” that all treatments had a “no information” option,
meaning some respondents randomly received no information about several features of
the scenario.
20. See Online Appendix D for a formal proof.
21. We say “likely” because we do not observe respondents’ belief updating processes
directly and thus cannot prove that the exclusion restriction holds (as is the case for all
instrumental variable-type identification). For more on identifying assumptions in survey
experiments, see Dafoe, Zhang, and Caughey (2018).
22.p/C250:006 and p/C250:01, respectively, with bootstrapped 95 percent CIs of ( /C01.22,/C0.22)
and (/C01.32,/C0.18).
23. Generally, when scholars say an actor has nth order beliefs, they hold beliefs about the
beliefs of others up to the ðn/C01Þth order. Actors that have only first-order beliefs, for
example, have no informative beliefs about the others’ beliefs (see Camerer, Ho, and
Chong 2004, for a more extensive discussion). In our case, n¼maxðkÞ.
24. As y!1,IM!1 , which means that even an Echange in perceptions decides the
contest of resolve. Here, the prior state of affairs will have been something of a knife-
edge equilibrium.
25. The above adopts the simplifying assumption that a linear function is a meaningful
parameterization for the interdependence of resolve (where yis the slope). Future work
could explore a more general functional form mapping a change in A’s perception of B’s
resolve, and A’s “prior” resolve, to the marginal change in A’s resolve:
fAðDð^Rk/C01
BÞ;^Rk/C01
B;Rk
AÞ. For example, it’s plausible that the impact of D^Rk/C01
Bhas a sig-
moidal shape like the logistic function, where the slope is greatest at intermediate values
of^Rk/C01
B(where A is most likely to be indifferent between escalating and backing down)
andRk
A(where Rk
Ahas the farthest to move in either direction). This conjecture can be
grounded in analysis of Chicken using Quantal Response Equilibrium, where a player’s
best response function is smooth in the other’s strategy and in fact logistically shaped; see
Goeree, Holt, and Palfrey 2016.
26. Many of the other crises Trachtenberg discusses are similarly good examples.
27. For instance, see Hof (2016) and Yacoubian (2017).
28. One example of (imperfect) real-world efforts to signal unconditional resolve comes from
the Cold War, during which many governments considered introducing an element of
automaticity in retaliation in times of crisis. Schelling (1966, 38-39) calls this “irrational
automaticity,” exemplified by Soviet Premier Khrushchev’s 1959 threat to Averell Harri-
man that Soviet rockets would fly “automatically” should the West send tanks into Berlin.
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Allan Dafoe
Remco Zwetsloot
Matthew Cebul