Von Neumann

1
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).

2
UNIT I Overview History

• Introduction What is Game Theory?
• Von Neumann and the Bomb
• The Science of International Strategy
• Logic of Indeterminate Situations

2/6
3
Von Neumann the Bomb

• A Brief History of Game Theory
• Dr.Strangelove
• Military Decision Game Theory
• The Science of International Strategy
• The Prisoners Dilemma
• Securing Insecure Agreements
• Postwar Economic Regimes

4
A Brief History of Game Theory

• Minimax Theorem 1928
• Theory of Games Economic Behavior 1944
• Nash Equilibrium 1950
• Prisoners Dilemma 1950
• The Evolution of Cooperation 1984
• Nobel Prize Harsanyi, Selten Nash 1994

5
Dr. Strangelove

• John von Neumann (1907-53).
• Hilbert program
• Quantum mechanics
• Theory of Games Economic Behavior
• ENIAC
• The Doomsday Machine

6
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).

7
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)

8
Military Decision Game Theory

• Source O. G. Hayward, Jr. 1954

BISMARCK SEA
Rain
Northern Route
Japan US
Northern Route
Northern Southern Route Route
New Britain
New Guinea
2 days 2 days 1 day 3 days
Southern Route
Southern Route
Clear Weather
Battle of the Bismarck Sea, 1943
9
Military Decision Game Theory

• Source O. G. Hayward, Jr. 1954

BISMARCK SEA
Rain
Northern Route
Japan US
US min 2 1
Northern Route
Northern Southern Route Route
New Britain
New Guinea
2 days 2 days 2 1 day 3 days 1
Southern Route
Southern Route
Clear Weather
Jmax 2 3
Battle of the Bismarck Sea, 1943
10
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.

11
Schellings 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 doesnt mean beating ones 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).

12
Schellings Theory of Strategy

• In 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

13
Schellings Theory of Strategy

• Pure Coordination Pure Conflict

-1, 1 1, -1 1, -1 -1, 1
1, 1 0, 0 0, 0 0, 0 1, 1 0, 0 0,
0 0,0 1, 1
14
Schellings 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. . . .
  In the minimax strategy of a zero-sum game . .
  . ones whole objective is to avoid any meeting
  of minds, even an inadvertent one. In the
  pure-coordination game, the players objective is
  to make contact with the other player through
  some imaginative process of introspection, of
  searching for shared clues (96-98).

15
Next Time

• 2/13 The Logic of Indeterminate Situations.
• Schelling, Strategy and Conflict 53-80.