So Long From So Long From ECONOMICSECONOMICS 10401040::

SSTRATEGY, TRATEGY, CCONFLICT & ONFLICT & CCOOPERATIONOOPERATION

Spring 2007W 7:35-9:35

Sever 102Instructor: Robert Neugeboren

neugebor@fas.harvard.edu

Teaching Fellow: Rajiv Shankar rshankar@fas.harvard.edu

Website: http://www.courses.fas.harvard.edu/~ext21946/

Office Hours: W 3-4 51 Brattle St.

Unit IV: Thinking about Thinking

•Choice and Consequence•Fair Play•Learning to Cooperate•Summary and Conclusions5/7

Unit IV: Thinking about Thinking

•Summary and Conclusions

– Problem Set 4: Due Wed May, 14, by 5pm.

– Tournament deadline: Friday, May 16, 5pm.

– Grad Paper deadline: Friday, May 16, 5pm.

– Final Exam: Wednesday, May 21, 7:30pm.

Exam Format

• 100 points in 120 minutes.

– Problems (60 points)– Short Answers (20 points)– Essays (20 points)

Game theory was developed to “solve” simple parlor games. In the 1940s and ‘50s, it was applied to international conflict A THEORY OF WAR

Schelling “reoriented” game theory to seek ways of resolving conflict as an alternative to war.

In the Post-war period, attention turned to expanding trade among Western economies EXCHANGE

The Prisoner’s Dilemma exposed a deep problem at the heart of game theory, calling forth a new approach.

Finally, analysis of repeated games offered a way to understand today’s global problems COOPERATION

The Evolution of Game Theory

1928 1944 1950 1960 1984 19941949 1989

ZEROSUM GAMES NONZEROSUM GAMES REPEATED GAMES

MINIMAX THEOREM NASH EQUILIBRIUM FOLK THEOREM

PRISONER’S DILEMMA

WAR EXCHANGE COOPERATION

PARLOR GAMES NUCLEAR TRADE SUSTAINABLE ARMS RACE DEVELOPENT

Theory of Games Strategy & Conflict The Evolution & Economic Behavior of Cooperation

Soviet A-Test The End of the Cold War

Nobel: Harsanyi, Selten & Nash

The Evolution of Game Theory

“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 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; in the minimax strategy of a zero-sum game … -- one’s whole objective is to avoid any meetings of the mind, even an inadvertent one”

Schelling, 1960, p. 96.

The Evolution of Game Theory

The Evolution of Game Theory

Once we move to nonzero-sum games, however, the status of game theory grows ambiguous:

• Coordination Games• Bargaining Games• Repeated Games• Public Goods Games

PLAY BEST RESPONSE STRATEGY? There may be more than one, and the “right” one will depend on what the other/s choose\s.

PLAY DOMINANT STRATEGY (when it exists)? PD!

Multiple and/or inefficient equilibria

1928 1944 1950 1960 1984 19941949 1989

ZEROSUM GAMES NONZEROSUM GAMES REPEATED GAMES

MINIMAX THEOREM NASH EQUILIBRIUM FOLK THEOREM

PRISONER’S DILEMMA

WAR EXCHANGE COOPERATION

PARLOR GAMES NUCLEAR TRADE SUSTAINABLE ARMS RACE DEVELOPENT

Theory of Games Strategy & Conflict The Evolution & Economic Behavior of Cooperation

Soviet A-Test The End of the Cold War

Nobel: Harsanyi, Selten & Nash

The Evolution of Game Theory

A fourth paradigm?

EVOLUTIONARY GAMES ??ESS

Summary & Conclusion

[W]here trust and good faith do not exist and cannot be made to by our acting as though they did, we may wish to solicit advice from the underworld, or from ancient despotism, on how to make agreements when trust and good faith are lacking and there is no legal recourse for breach on contract. The ancient exchanged hostages, drank from the same glass to demonstrate the absence of poison, met in public places (…) and even deliberately exchanged spies to facilitate transmittal of authentic information. It seems likely that a well-developed theory of strategy could (…) discover modern equivalents that, though offensive to our taste, may be desperately needed in the regulation of conflict.

– Schelling,1960, p. 20

For Further Interest

Binmore, K. Game Theory & the Social Contract, II (1998).

Gintis, H. Game Theory Evolving (2000).

Kreps, D. Game Theory and Economic Modelling (1994).

Raiffa, H. The Art and Science of Negotiation (1982).