Program equilibria and discounted computation time

Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite twoplayer game where each player can base their strategy on the other player’s strategies. Tennenholtz’s model allowed each player to produce a “loop-free” computer program that had access to the code for both players. He showed a folk theorem where the result of any mixed-strategy individually rational play could be an equilibrium payoff in this model even in a one-shot game. Kalai et al. gave a general folk theorem for correlated play in a more generic commitment model. We develop a new model of program equilibrium using general computational models and discounting the payoffs based on the computation time used. We give an even more general folk theorem giving correlatedstrategy payoffs down to the pure minimax of each player. We also show the existence of equilibrium in other games not covered by the earlier work.

• Type: Conference
• Year: 2009
• Where: TARK
• Authors: Lance Fortnow
• Keywords: Artificial Intelligence, Folk Theorem, General Folk Theorem, Program Equilibrium, TARK 2009