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

2/2

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 (1903-57).

• 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. 1954

Southern Route

BISMARCK SEA

Northern Route

Rain

ClearWeather

NewGuinea

New Britain

NorthernRoute

SouthernRoute

Northern SouthernRoute Route

2 days 2 days

1 day 3 days

Japan

US

Battle of the Bismarck Sea, 1943

Military Decision & Game Theory

Source: O. G. Hayward, Jr. 1954

Southern Route

BISMARCK SEA

Northern Route

Rain

ClearWeather

NewGuinea

New Britain

NorthernRoute

SouthernRoute

Northern SouthernRoute Route

2 days 2 days 2

1 day 3 days 1

Japan

US

Battle of the Bismarck Sea, 1943

USmin

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 PURECONFLICT MOTIVE COORDINATION

Schelling’s Theory of Strategy

Pure Coordination Pure Conflict

1, 1 0, 0 0, 0

0, 0 1, 1 0, 0

0, 0 0,0 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).

·

Realism

• The actor (nation-state) is rational: goal-directed, concerned with maximizing power or security.

• The environment is anarchic: there is no supervening authority that can enforce agreements.

• The solution is an equilibrium or balance of power, enforced by the interests of those involved w/o the need for external enforcement mechanisms.

Schelling’s Reorientation

• In the 1940s and ’50s, game theory lent itself to the analysis of military strategy, casting Realist principles and assumptions at an abstract level of analysis.

• Von Neumann’s minimax theorem and the doctrine of military decision both recommend prudence: maximize the minimum payoff available.

• Given Realist assumption, conflict is inevitable. The Security Dilemma arises because one nation’s attempt to increase it’s security decreases the security of others.

• Arm Races (e.g., WWI). Is security zero-sum?

Schelling’s Reorientation

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 Reorientation

• In the 1940s and ’50s, game theory lent itself to the analysis of military strategy, casting Realist principles and assumptions at an abstract level of analysis.

• Von Neumann’s minimax theorem and the doctrine of military decision both recommend prudence: maximize the minimum payoff available.

• Given Realist assumption, conflict is inevitable. The Security Dilemma arises because one nation’s attempt to increase it’s security decreases the security of others.

• Arm Races (e.g., WWI). Is security zero-sum?

Schelling’s Reorientation

The Reciprocal Fear of Surprise Attack

The technology of nuclear warfare created a fundamentally new kind of arms race – the speed and devastation of the new generation of weapons meant that “[f]or 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 Reorientation

The Prisoner’s DilemmaThe 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 AlConfess Don’t

Confess

Bob

Don’t

10, 10 0, 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 whatAl does.

We call Confess adominant strategy.

The Prisoner’s Dilemma

In years in jail AlConfess Don’t

Confess

Bob

Don’t

10, 10 0, 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 AlConfess Don’t

Confess

Bob

Don’t

1, 1 5, 0

0, 5 3, 3Again, the outcome isinefficient.

If we assign P(ayoffs),so that the players try to maximize P . . .

The Prisoner’s DilemmaCommunication? 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

2/9 The Logic of Indeterminate Situations.

Schelling, Strategy and Conflict: 53-80.