More dangerous than dyads: how a third party enables rationalist explanations for war
| Published date | 01 July 2017 |
| Date | 01 July 2017 |
| DOI | 10.1177/0951629816682884 |
| Author | Max Gallop |
| Subject Matter | Notes |
Notes
More dangerous than dyads:
how a third party enables
rationalist explanations for
war
Journal of Theoretical Politics
2017, Vol. 29(3) 353–381
©The Author(s) 2016
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DOI:10.1177/0951629816682884
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Max Gallop
University of Strathclyde, UK
Abstract
For the bargaining model of war, in the absence of incomplete information and commitment
problems, war is irrational. But this finding rests on a simple and rarely discussed assumption, that
bargaining is between exactly two participants. When we relax this assumption, in a three-player
bargaining game, war is an equilibrium. Thus, a key finding of the bargaining model, that there is
always an agreement that all states prefer war, is an artifact of dyadic analysis. By removing this
limitation, we can find new factors that affect the risk of war: the number of actors, divergence in
state preferences, alliance dynamics, and the issue being bargained over.
Keywords
Bargaining; game theory; interstate war; multiplayer games
1. Introduction
1.1. Motivation
In recent years, a number of international conflicts have been particularly intractable
because they involve many parties. It has been difficult for the United States to achieve
its aims in Syria’s civil war partially because of Syria’s close ties to Russia. The struggle
over Iran’s nuclear program has been particularly fraught for the Obama administra-
tion, trying to avoid an Israeli attack on Iran on the one hand, and Iranian acquisition
of nuclear weapons on the other. Militarized interstate disputes involving more than two
actors are about seven times as likely (0.15 probability of war) to escalate to war as
purely dyadic cases (0.02 probability) (Ghosn et al., 2004).1Yet despite the proliferation
of cases in which multiple actors exert an effect on the outcome, our frame of analysis in
international relations is predominantly dyadic.2There has been some discussion of the
Corresponding author:
Max Gallop, Department of Government and Public Policy, University of Strathclyde, G11 7HY, Glasgow, UK.
Email: max.gallop@strath.ac.uk
354 Journal of Theoretical Politics 29(3)
problematic statistical property of dyads,3but there has been less discussion of the fact
that our theories of interstate conflict are dyadic.
The current dominant explanations for conflict are generated from the bargaining
model of war. This model has been used to motivate empirical work on the onset, dura-
tion and recurrence of interstate and civil war; to show how factors such as economic
interdependence and foreign support for insurgency lead to war; and even to explain non-
conflictual phenomena such as sanctions and the international criminal court Drezner,
2003; Fortna, 2003; Gartzke et al., 2001; Polachek and Xiang, 2010; Schultz, 2010; Sim-
mons and Danner, 2010; Walter, 1999, 2009; Wernerand Yuen, 2005). A major insight of
the bargaining model is that war is ex post irrational for both states; in this model, if there
is conflict, either incomplete information has obscured a mutually beneficial settlement,
or states are unable to credibly commit to abide by it.4
I find that this key finding of the bargaining model, that there is always that agreement
all states prefer war, an artifact of limiting the analysis to two players.5When there are
more than two players, the players’ preferences regarding the issue will sometimes be so
disparate that there is no way to reach an agreement that will dissuade all of them from
fighting. In the rest of this paper I briefly discuss the bargaining model of war, I model
a simple three-player bargaining game, discuss the main findings of this game, examine
the equilibria of the game to show how war is possible, and discuss comparative statics
generated by simulation.
1.2. Current bargaining models
The use of the bargaining model in the study of conflict has pointed towardtwo important
explanations for war: incomplete information and commitment problems. These results
have generally held as explanations for war whether bargaining is conceptualized as a
state making a take it or leave it offer, as in Fearon (1995), or as a set of alternating
offers, as in Powell (1999).
When there is a commitment problems, a bargain that may be beneficial to all players
presently will become unacceptable to one player in the future. The shadow of the future
renders conflict preferable to such an agreement (Powell, 2006). Informational asymme-
try occurs because states may be poorly informed about their opponent’s capabilities or
resolve (Fearon, 1995). As stronger, more resolved states receive a better outcome in a
settlement, there is incentive for misrepresentation. States face a risk/reward trade-off: if
the state is sufficiently accommodating, the dispute will be resolved peacefully, but occa-
sionally, the state can do better by making a smaller offer, which will lead to war if they
face an unexpectedly resolute foe.
There have been some models which expand bargaining beyond the dyad. Most of
this work operates under the framework of incomplete information: they examine how
additional players modify informational requirements for peace or endogenously change
the games informational content. Many of these models focus on domestic constituencies
affecting bargaining leverage, and the incorporation of a domestic actor generally has
been found to help a state reveal their resolve, get a larger slice of the pie, and avoid war
(Fearon, 1994; Putnam, 1988; Schultz, 1998). Similarly, third-party mediators are seen
as ameliorating incomplete information (Kydd, 2006).
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