Von Neumann & the Bomb Strategy is not concerned with the efficient application of force but with the exploitation of potential force (T. Schelling, 1960, p. 5).

UNIT I:Overview & History Introduction: What is Game Theory? Von Neumann and the Bomb The Science of International Strategy Logic of Indeterminate Situations 2/7

Von Neumann & the Bomb A Brief History of Game Theory Dr.Strangelove Military Decision & Game Theory The Science of International Strategy The Prisoner’s Dilemma Securing Insecure Agreements Postwar Economic Regimes

A Brief History of Game Theory Minimax Theorem 1928 Theory of Games & Economic Behavior 1944 Nash Equilibrium 1950 Prisoner’s Dilemma 1950 The Evolution of Cooperation 1984 Nobel Prize: Harsanyi, Selten & Nash 1994

Dr. Strangelove John von Neumann ( ). Hilbert program Quantum mechanics Theory of Games & Economic Behavior ENIAC The Doomsday Machine

The Doctrine of Military Decision Step 1: The Mission Step 2: Situation and Courses of Action Step 3: Analysis of Opposing Courses of Action Step 4: Comparison of Available Courses of Action Step 5: The Decision Source: O.G. Hayward, Jr., Military Decisions and Game Theory (1954).

Military Decision & Game Theory A military commander may approach decision with either of two philosophies. He may select his course of action on the basis of his estimate of what his enemy is able to do to oppose him. Or, he may make his selection on the basis of his estimate of what his enemy is going to do. The former is a doctrine of decision based on enemy capabilities; the latter on enemy intentions. (O. G. Hayward, Jr. 1954: 365)

Military Decision & Game Theory Source: O. G. Hayward, Jr Southern Route BISMARCK SEA Northern Route Rain Clear Weather New Guinea New Britain Northern Route Southern Route Northern Southern Route 2 days 1 day 3 days Japan US Battle of the Bismarck Sea, 1943

Military Decision & Game Theory Source: O. G. Hayward, Jr Southern Route BISMARCK SEA Northern Route Rain Clear Weather New Guinea New Britain Northern Route Southern Route Northern Southern Route 2 days 2 days 2 1 day 3 days 1 Japan US Battle of the Bismarck Sea, 1943 US min 2 1 Jmax 2 3

Military Decision & Game Theory Game theory lent itself to the analysis of military strategy, casting well accepted principles of decision making at a rigorous, abstract level of analysis. In situation of pure conflict, the “doctrine of decision based on enemy capabilities” and game theory point to the value of prudence: maximize the minimum payoff available.

Schelling’s Theory of Strategy Conflict can be seen as a pathological (irrational) state and “cured;” or it can be taken for granted and studied – as a game to be won (1960: 3). Winning doesn’t mean beating one’s opponent; it means getting the most out of the situation. Strategy is not concerned with the efficient application of force but with the exploitation of potential force (5).

Schelling’s Theory of Strategy [I]n taking conflict for granted, and working with an image of participants who try to ‘win,’ a theory of strategy does not deny that there are common as well as conflicting interests among the participants (Schelling 1960: 4). ZEROSUM NONZEROSUM PURE MIXED PURE CONFLICT MOTIVE COORDINATION

Schelling’s Theory of Strategy Pure Coordination Pure Conflict 1, 1 0, 0 0, 0 0, 01, 1 0, 0 0, 00,0 1, 1 - 1, 1 1, -1 1, -1 -1, 1

Schelling’s Theory of Strategy And here it becomes emphatically clear that the intellectual processes of choosing a strategy in pure conflict and choosing a strategy of coordination are of wholly different sorts.... [I]n the minimax strategy of a zero-sum game... one’s whole objective is to avoid any meeting of minds, even an inadvertent one. In the pure-coordination game, the player’s objective is to make contact with the other player through some imaginative process of introspection, of searching for shared clues (96-98). ·

The Security Dilemma The actor (nation-state) is rational, i.e., goal-directed, egoistic, concerned with maximizing power or security. The structure of the international system is anarchic – meaning there is no supervening authority that can enforce agreements. Given these conditions, nations often fail to cooperate even in the face of common interests. The dilemma arises because one nation’s attempt to increase it’s security decreases the security of others. Schelling’s Theory of Strategy

The Reciprocal Fear of Surprise Attack For the first time in the history of the world, it became possible to contemplate a surprise attack that would wipe the enemy off the face of the earth.... Equally important, each nation would fear being the victim of the other’s surprise attack (Poundstone, 1992, p. 4). Schelling’s Theory of Strategy

The Prisoner’s Dilemma The prisoner’s dilemma is a universal concept. Theorists now realize that prisoner’s dilemmas occur in biology, psychology, sociology, economics, and law. The prisoner’s dilemma is apt to turn up anywhere a conflict of interests exists (..). Study of the prisoner’s dilemma has great power for explaining why animal and human societies are organized as they are. It is one of the great ideas of the twentieth century, simple enough for anyone to grasp and of fundamental importance (...). The prisoner’s dilemma has become one of the premier philosophical and scientific issues of our time. It is tied to our very survival (Poundstone,1992: 9).

The Prisoner’s Dilemma In years in jail Al ConfessDon’t Confess Bob Don’t 10, 100, 20 20, 0 1, 1 Bob thinks: If Al C(onfesses), I should C, because 10 < 20 and 0 < 1, thus C is better than D(on’t), no matter what Al does. We call Confess a dominant strategy.

The Prisoner’s Dilemma In years in jail Al ConfessDon’t Confess Bob Don’t 10, 100, 20 20, 0 1, 1 Because the game is symmetric, both prisoner’s Confess, even though they are better off if both Don’t. CC is inefficient. If we assign P(ayoffs), so that the players try to maximize P...

The Prisoner’s Dilemma In Payoffs Al ConfessDon’t Confess Bob Don’t 1, 1 5, 0 0, 5 3, 3 Again, the outcome is inefficient. If we assign P(ayoffs), so that the players try to maximize P...

The Prisoner’s Dilemma Communication? We have assumed that there is no communication between the two prisoners. What would happen if they could communicate? Repetition? In the Prisoner’s Dilemma, the two prisoners interact only once. What would happen if the interaction were repeated? 2- v. n-person Games? The Prisoner’s Dilemma is a two-person game, What would happen if there were many players? Dominance Reasoning? Compelling as the reasoning is that leads to the dominant strategy equilibrium may be, it is not the only way this problem might be reasoned out. Is it really the most “rational” answer after all?

Next Time 2/14The Logic of Indeterminate Situations. Schelling, Strategy and Conflict: Hargreaves Heap & Varoufakis, Ch. 1: *