Here is the current syllabus for this course.

I am teaching my course on game theoretic approaches to Conflict and Cooperation in Winter 2012 for the second time.

Here is a webpage with links to papers (many require JSTOR subscription).  I have adopted Hobbes’s theories of conflict to give structure to the lectures.  Hobbes says the three sources of conflict are greed, fear and honour. The solution is to have a government or Leviathan which enforces property rights. I begin with greed.

Greed: Guns vs Butter

I started with the classic guns vs butter dilemma: why produce butter when you can produce guns and steal someone else’s butter?  This incentive leads to two kinds of inefficiency: (1) guns are not directly productive and (2) surplus is destroyed in war waged with guns.  The second inefficiency might be eliminated via transfers (the Coase Theorem in this setting). This still leaves the first inefficiency which is similar to the underinvestment result in hold-up models in the style of Grossman-Hart-Moore.

These models have bilateral conflict. If there are many players, there is room for coalitions to form, pool guns, and beat up weaker players and steal their wealth. What are stable distributions of wealth? Do they involve a dictator and/or a few superpowers? Are more equitable distributions feasible in this environment? It turns out the answer is “yes” if players are “far-sighted”. If I help a coalition beat up some other players, maybe  my former coalition-mates will turn on me next. Knowing this, I should just refuse to join them in their initial foray. This can make equitable distributions of wealth stable.

I am writing up notes and slides as I am writing a book on this topic with Tomas Sjöström.  Here are some slides.

Fear: Spiral model/reciprocal fear of surprise attack.

This week I switched to models of conflict where each player puts positive probability on his opponent being a dominant strategy type who is hawkish/aggressive in all circumstances.  This possibility increases the incentive of a player to be aggressive if actions are strategic complements and decreases it if actions are strategic substitutes.  The idea that fear of an opponent’s motives might drive an otherwise dovish player into aggression comes up in Thucydides (“The growth of Athenian power and the fear this caused in Sparta, made war inevitable.”) and also Hobbes.  But both sides might be afraid and this simply escalates the fear logic further.  This was most crisply stated by Schelling in his work on the reciprocal fear of surprise attack (“[I]f I go downstairs to investigate a noise at night, with a gun in my hand, and find myself face to face with a burglar who has a gun in his hand, there is a danger of an outcome that neither of us desires. Even if he prefers to leave quietly, and I wish him to, there is a danger that he may think I want to shoot, and shoot first. Worse, there is danger that he may think that I think he wants to shoot. Or he may think that I think he thinks I want to shoot. And so on.”).  Similar ideas also crop up in the work of political scientist Robert Jervis.

Two sided incomplete information can generate this kind of effect. It arises in global games and can imply there is a unique equilibrium while there are multiple equilibria in the underlying complete information game.  But the theory of global games relies on players’ information being highly correlated.  Schelling’s logic does not seem to rely on correlation and we can imagine conflict scenarios where types/information are independent and yet this phenomenon still arises.  In this lecture, I use joint work with Tomas Sjöström to identify a common logic for uniqueness that is at work for information structures with positively correlated types or independent types.  Our sufficient conditions for uniqueness can be related to conditions that imply uniqueness in models of Bertrand and Cournot competition.

With these models in hand, we have some way of operationalizing Hobbes’ second motive for war, fear. I will use these results and models in future classes when I use them as building blocks to study other issues.  Here are the slides.

Conflict and Cooperation: Communication and Deception

I began with the guns vs butter model of arms acquisition out of greed. Suppose the cost a player suffers if there is war is private information. The lower the cost the more likely he is to acquire guns and go to war or try to extract payment to voluntarily abstain from war. But a high cost type has an incentive to pretend to be a low cost type and get lots of guns to extract payments too. But then an opponent who observes arms acquisition does not know if he faces a low cost or high cost type. He may call the other;s bluff and refuse to make a transfer. Then war will occur with positive probability

A player who seeks to be aggressive against an opponent prefers to catch him by surprise and passive and not well-prepared.  The chance that an opponent may attack by surprise makes a player cautious and well prepared and not passive.  Hence, uncertainty about each player’s intentions can create a vicious cycle where everyone turns aggressive.

Next we study communication and fear. The same incentives that generate conflict generate incentives for deception: whether a player intends to be aggressive or passive, he wants his opponent to be passive.  Hence, he might always send the message that maximizes the probability that his opponent is passive but then cheap-talk is not effective and does not affect the equilibrium. An argument along these lines was made by Aumann in a Stag Hunt game.

We show that while deception occurs in equilibrium, it is still possible to transmit enough information to create less conflict.  While players may always seek to minimize the probability their opponent is aggressive, they may also value information about his action so they can coordinate against it.   If the trade-off between these two benefits is type-dependent in a conflict game with incomplete information, separating equilibria are possible and so is coordination on peace.

The ideas above relate to conflict and escalation, where it is known that aggression begets aggression.  What if aggression may beget deterrence not escalation?  For example, revealing weapons may create deterrence but trigger escalation.  Revealing you have no weapons may reduce escalation but eliminate deterrence.  In this situation it can be optimal to employ strategic ambiguity: neither reveal weapons if you have them, nor reveal you do not have them if you do not.  Strategic ambiguity allows a player to employ “deterrence by ambiguity” as he may be armed behind the veil of ambiguity.  He has less incentive to acquire arms as he can pretend to have arms even when he does not behind the veil of ambiguity.  This reduction in arms proliferation can help all players not just the player employing ambiguity strategically.

Here are the slides.

Communication: Greed and Mechanism Design

Suppose there are players and each has private information about how tough they are.  The two toughness parameters together determine the probability of winning should there be a war.  If the parameters are common knowledge, it is possible to avoid war by making a transfer that makes war pointless.  By making a transfer, the target has less resources to capture and the challenger has more to lose and an appropriate transfer can create the right balance to avoid war.  But if there is incomplete information, a player might start  a war.

Is it possible to set up transfers to completely prevent inefficient war?  Myerson and Satterthwaite asked this question in a classical model of trade with incomplete information.  We can use similar techniques to answer a similar question in a conflict scenario.  In other words, we can use the revelation principle and ask whether it is possible to design transfers as a function of reports to guarantee peace in all circumstances.  Players’ types – their toughness parameters – directly affect their payoffs only if there is war.  Since there is no war in equilibrium, it is impossible to separate out different types and transfers must be constant as a function of reports.  The constant payoff each player then receives must be enough to dissuade his toughest type from starting a war.  If this is impossible to guarantee for both players’ toughest types simultaneously, there must be war.  Here are the slides.

Leviathan: Democratic Peace

Why might democracies be less warlike than other regime types?

Two early and related ideas:

Thomas Paine ([3] p. 169): “What inducement has the farmer, while following the plough, to lay aside his peaceful pursuit, and go to war with the farmer of another country?”

Immanuel Kant ([1], p. 122): “if the consent of the subjects is required to determine whether there shall be war or not, nothing is more natural than that they should weigh the matter well, before undertaking such a bad business.”

This idea has influenced policymakers of different political persuasions.  Is there a rational choice/strategic theory for the democratic peace?  This lecture discusses various alternatives.

First, we study the fear motive for war. The median voter might be a coordination type who wants his country’s leader to be dovish against a dovish opponent but aggressive against an aggressive opponent.  This captures the Kant/Paine idea but also Schelling’s idea that aggression might arise out of fear.  These incentives imply that democracies are more responsive to aggression that other regime types.  A second possibility is that a leader can survive with the support of the “mob” (which has the same preferences as the median voter) or with the support of an elite that favors war. The leader loses power if he is weak in the face of aggression (no one supports him) but survives if he is aggressive even when an opponent is not (the hawkish elite support him).  This kind of regime is more aggressive than a dictatorship.  Data support these these comparative statics.

Second, we study the greed motive.  The leader of country may get a disproportionate share of the spoils of war should his country win but not suffer a large cost if it should lose.  He has a bias. If both leaders are biased, it may be impossible to avoid inefficient war even if transfers are possible.  But if both leaders are unbiased then transfers can resolve conflict and may even be unnecessary.

Third, bargaining may devolve into a war of attrition.  A democratically elected leader suffers greater “audience costs” if he backs down.  This makes him a tough bargainer and his opponent correspondingly weak.  A player may even deliberately “talk up” his audience costs to become a tough bargainer.

Here are the slides.

Terrorism and Counterterrorism

Non-state actors with extreme agendas try to influence state actors.  This class overviews a potpourri of models that explore why a player might join a non state organization, the logic of non state actor strategy and the costs and benefits of torture.

Iannaccone has a classic paper on religious sects and their purpose and strategy.  It has been applied to terrorism by Eli Berman.  Such organizations provide public goods (healthcare, childcare etc) which are non-rival and excludable.  They are club goods.  And individual who joins such an organization is tempted to free-ride and and use his labor on privately productive secular activities.    A religious sect might then prohibit secular activities and will require sect members to wear some kind of uniform to make monitoring easier. Also, a sect would like to admit members who have bad outside options to minimize the free-rider problem.  Requiring a sacrifice, a costly signal, can help to identify the ideal member.

There are many theories for the logic of non state actor strategy.  The simplest is that terrorists seek to impose large costs on some “occupier” and drive them out.  Another is the opposite: terrorists seek to inflame a perceived enemy (a secondary audience). This in turn influences a primary audience whose support is necessary to achieve the non state actor’s ends.  This is in effect a three player game where the extremist inflames a primary audience by changing the behavior of a secondary audience.  This is only worth doing if the primary audience is suggestible.  It might for example signal that the chances for peace are good if only extremism could be ignored.

Finally, what if a potential terrorist is in custody and may have valuable information that can save lives?  He might break under torture.  A cost-benefit analysis, a favorite of moral philosophers, recommends torture if the value of lives saved is large even though torture is morally reprehensible.  But the same cost-benefit calculation subverts the process of torture. If the suspect starts talking, the value of his remaining information outweighs the costs of torture.  If he is silent and probably innocent, it recommends stopping.  But this undercuts the rationale for torture: the terrorist should stay silent as this is his best hope of escape.  But then the value of torture is minimal as information is unlikely to be conceded.

Here are the slides.

In the final part of the course, we had some student presentations. Here are the slides:

Chen Cheng on Myerson’s Federalism and Incentives for Success in Democracy

Jorege Catepillan of Acemoglu, Golosiv, Tyivinski and Yared’s A Dynamic Theory of Resource Wars

Amir Khorsohahi on Esteban and Ray’s A Model of Ethnic Conflict.

Yang on Acemoglu and Robinson’s Why Did The West Extend The Franchise?

Chris Romeo on Grossman and Kim’s Swords or Ploughshares.

Chris Li on Fearon’s Bargaining Over Objects That Influence Future Bargaining Power

Ricardo Pique on Ethan BdM’s Politics And The Suboptimal Provision Of Counterterror

Omar on Jackson and Morelli’s Strategic Militarization, Deterrence and War