Learn your opponent's strategy (in polynomial time)!
Agents that interact in a distributed environment might increase their utility by behaving optimally given the strategies of the other agents. To do so, agents need to learn about those with whom they share the same world.
This paper examines interactions among agents from a game theoretic perspective. In this context, learning has been assumed as a means to reach equilibrium. We analyze the complexity of this learning process. We start with a restricted two-agent model, in which agents are represented by finite automata, and one of the agents plays a fixed strategy. We show that even with this restrictions, the learning process may be exponential in time.
We then suggest a criterion of simplicity, that induces a class of automata that are learnable in polynomial time.
KeywordsDistributed Artificial Intelligence Learning repeated games automata
Unable to display preview. Download preview PDF.
- 1.R. Aumann and A. Brandenburger. Epistemic conditions for Nash equilibrium. Working Paper 91-042, Harvard Business School, 1991.Google Scholar
- 2.L. Fortnow and D. Whang. Optimality and domination in repeated games with bounded players. Technical report, Department of Computer Science University of Chicago, Chicago, 1994.Google Scholar
- 3.I. Gilboa and D. Samet. Bounded vs. unbounded rationality: The tyranny of the weak. Games and Economic Behavior, 1:213–221, 1989.Google Scholar
- 4.Ehud Kalai. Bounded rationality and strategic complexity in repeated games. In T. Ichiishi, A. Neyman, and Y. Tauman, editors, Game Theory and Aplications, pages 131–157. Academic Press, San Diego, 1990.Google Scholar
- 5.Michael J. Kearns and Umesh V. Vazirani. An Introduction to Computational Learning Theory. MIT press, Cambridge, Massachusetts, 1994.Google Scholar
- 6.Yishay Mor. Computational approaches to rational choice. Master's thesis, Hebrew University, 1995. In preparation.Google Scholar
- 7.Yishay Mor and Jeffrey S. Rosenschein. Time and the prisoner's dilemma, 1995. International Conference on Multiagent Systems.(to appear).Google Scholar
- 8.A. Neyman. Bounded complexity justifies cooperation in finitely repeated prisoner's dilemma. Economic Letters, pages 227–229, 1985.Google Scholar
- 9.Christos H. Papadimitriou. On players with a bounded, number of states. Games and Economic Behavior, 4:122–131, 1992.Google Scholar
- 10.R. Rivest and R. Schapire. Inference of finite automata using homing sequences. Information and Computation, 103:299–347, 1993.Google Scholar
- 11.Alvin E. Roth, Vesna Prasnikar, Mashiro Okuno-Fujiwara, and Shmuel Zamir. Bargining and market behavior in jerusalem, ljubljana, pittsburg, and tokyo: an experimantal study. American Economic Review, 81(5):1068–1095, 1991.Google Scholar
- 12.A. Rubinstein. Finite automata play the repeated prisoner's dilemma. ST/ICERD Discussion Paper 85/109, London School of Economics, 1985.Google Scholar