Jean-Pierre P. Langlois

When Fully Informed States Make Good the Threat of War: Rational Escalation and the Failure of Bargaining

Why would fully informed, rational actors fight over possession of a valued asset when they could negotiate a settlement in peace? Our explanation of the decision to fight highlights the incentives that are present when the defender holds a valued asset coveted by the challenger. The defender receives utility from possession of the contested asset and sees any compromise as a loss that is lower if postponed. The challenger, instead, sees any compromise as a gain that is more valuable if reached earlier. Faced with the defender’s vested interest in the status quo, the challenger needs to threaten war and may have no choice but to implement the threat to force a settlement. For the defender, the threat of war is a deterrent that might incite the challenger to back down. In the perfect equilibria that we describe, the players’ ability to threaten each other credibly allows them to maintain incompatible bargaining positions instead of helping them narrow their differences. But the very credibility of these threats leads our rivals to engage in what can become lengthy protracted wars.

Rationality in International Relations: A Game Theoretic and Empirical Study of the U.S.-China Case

This paper develops a model of rational behavior that is found to be compatible with the evolution of China-U.S. relations from the early 1970s to the late 1980s. The authors introduce countervailing strategies that broaden our understanding of what is rational in a game-theoretic context. Countervailing behavior accommodates inertia and delay, as well as reactivity, and is shown to be involved in every equilibrium strategy. The terms of the interaction between the United States and China are identified in light of a countervailing model, and the payoff structure that supports the observed dynamic interaction is inferred. Prior to 1979, which marks the inception of Chinas open-door policy, the payoff structure found conforms to a little-known mixed-motive game, whereas the 1980s are characterized by a Prisoners Dilemma. In the 1980s rational play involves positive reactivity on the part of each country, while prior to 1979 rational behavior on the part of the U.S. takes the form of an inverse response to Chinese initiatives, a behavior that draws its rationality from its ability to move China to a more cooperative stance despite a Deadlock-type payoff structure.

Engineering Cooperation: A Game Theoretic Analysis of Phased International Agreements

odern international treaties are often phased agreements that specify a goal to be reached together with a time frame within which to achieve it. This is a characteristic of arms-reduction agreements, but it is also pervasive in free-trade agreements as well as treaties designed to protect the environment. Our goal in this article is to understand the rational underpinnings of such phasing. To this end, we will exhibit a class of strategies in the repeated Prisoners Dilemma game that prescribe a gradual approach to cooperation. We will show that, in the presence of noise, these strategies promise better dynamic stability of the coop

Modeling Deterrence and International Crises

The continuous Prisoners Dilemma is a reasonable model for nuclear crises (usually represented by “Chicken”), and for the arms race. This article addresses the existence of credible deterrence strategies that promote cooperation as a dynamically stable steady state. Decisions made repeatedly in time are the selection by each side of a level of hostility. Assessment of the resulting situation is represented by a utility function for each player. As the game proceeds, players are concerned with the current situation as well as with the future consequences of their present decisions. Thus each side must formulate intentions and expectations of each others future behavior and use them to infer their own present optimal decisions. A formal concept of deterrence strategy is introduced: It promises the other side retaliation in kind to prevent any gain from aggressive play, and it inflicts increasing losses as a result of escalation. If one side adopts such a deterrence strategy, the other side cannot do better than acting similarly, and when both sides adopt it, they both enjoy optimal decision rules that confirm intentions and expectations. The resulting dynamical system endows cooperation with asymptotic stability provided the threats of retaliation contain a fair mix of firmness and restraint.

Existence and local stability of Pareto superior reaction function equilibria in discounted supergames

Abstract The existence of locally asymptotically stable subgame perfect reaction function equilibria (RFE) is demonstrated for a general class of n-player discounted supergames. Benefit denial, a fundamental identity of all subgame perfect equilibria defined on a convex range, is introduced and is the key to the equilibrium existence proof.

Tacit Bargaining in International Relations A Game Model and a Case Study

The authors develop a characterization of subgame perfect equilibrium strategies in discounted repeated games that highlights a class of strategies called countervailing. When using countervailing strategies, the players focus on manipulating the other sides payoff to induce his cooperation. These strategies do not require one player to entertain specific expectations about the strategic choice of the other. For this reason, countervailing strategies are promising vehicles for tacit bargaining. The authors test their relevance using a case of international trade—Japans penetration of the U.S. automobile market in the early 1980s. The empirical section provides evidence of the tacit bargaining behavior that the model predicts.

Does the Principle of Convergence Really Hold? War, Uncertainty and the Failure of Bargaining

Convergence occurs in war and bargaining models as uninformed rivals discover their opponents type by fighting and making calibrated offers that only the weaker party would accept. Fighting ends with the compromise that reveals the other sides type. This article shows that, if the protagonists are free to fight and bargain in the time continuum, they no longer make increasing concessions in an attempt to end the war promptly and on fair terms. Instead, the rivals stand firm on extreme bargaining positions, fighting it out in the hope that the other side will give in, until much of the war has been fought. Despite ongoing resolution of uncertainty by virtue of time passing, the rivals choose not to try to narrow their differences by negotiating.

Costly Interference: A Game Theoretic Analysis of Sanctions

Sanctions are often described as having two strikes against them: they are costly to the sanctioner, and they take time to achieve their goal, if they succeed at all. We argue in this paper that these are instead characteristics of rational sanctioning strategies. We view the sanctioning game as a subtle mix of bargaining and war of attrition. Our formal analysis shows that equilibrium behavior involves making ones opponent indifferent between accepting an ungenerous offer and continuing the struggle, a condition we call countervailing. Countervailing behavior implies that the costs incurred by the sanctioner correlate positively with the probability that the target will acquiesce to the senders demands, and conversely. This insight runs counter to the conventional wisdom on the impact of costs in sanctioning episodes and suggests that policy makers think differently about the success or failure of sanctions.

Holding Out for Concession: The Quest for Gain in the Negotiation of International Agreements

If the terms of a potential international agreement are interpreted as sharing surpluses generated by cooperation, they can be viewed, on an item by item basis, as giving an advantage to one or the other party. By interpreting bargaining outcomes in terms of gains or losses relative to the status quo, we modify Rubinsteins full information bilateral alternative offers bargaining model, and find that this opens up new bargaining tactics in equilibrium. The Rubinstein solution no longer provides unique resolution to the bargaining problem. Instead, negotiators can choose from a continuum of strategies that involve holding tough positions and waiting for the other to concede. The tactic is visible in negotiations as diverse as Strategic Arms Limitation Talks (SALT) or North American Foreign Trade Agreement (NAFTA). This occurs although our negotiators are assumed to be fully informed about each others priorities. Given the others offer, a negotiator can choose optimally from a whole range of counteroffers in our model. But all of these leave her with the same ex ante expected utility. By focusing on the possible outcomes of a given strategy choice, we define an expected ex post evaluation of strategy that discriminates between strategies that were equivalent ex ante. Negotiators who seek to maximize this ex post valuation choose a tough bargaining position, offering less than the Rubinstein share, and wait, hoping that the other side will concede before they do.

The Escalation of Terror: Hate and the Demise of Terrorist Organizations

Our goal in this article is to examine the strategic interaction between terror groups, hosts, and the United States in order to better understand the parameters of the interaction and the elements of a winning strategy. We adopt a game theoretic approach assuming that each player has a well defined goal and accounts for the anticipated behavior of the others to develop strategy. The game that we develop is a repeated game in which the host and the US must decide whether to fight a terrorist organization whose membership and resources will grow indefinitely if left unchecked. Our model predicts circumstances in which a host will begin to push back against the terrorists in anticipation of a future involvement of the US. It also predicts circumstances in which the terrorist organization’s hatred of the US prompts attacks that seal its fate and early demise.