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.