Stochastic Dynamics in Game Theory

Details Stochastic Dynamics in Game Theory Stochastic Dynamics in Game Theory

1998-01-29

arxiv.org/abs/cond-mat/9801309v1

Physics

Condensed Matter

Statistical Mechanics

25 pages, 4 figures requres kluwer style files (included). To appear in the proceedings of the Budapest conference ECONOPHYSIC

Scientific paper

We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from rationality in the form of a ``heat bath''. We focus on particular games of a large number of players with a global interaction which is typical of economic systems. The stable states of this dynamics coincide with the Nash equilibria of game theory. We study the gaussian fluctuations around these equilibria and establish that fluctuations around competitive equilibria increase with the number of players. In other words, competitive equilibria are characterized by very broad and uneven distributions among players. We also develop a small noise expansion which allows to compute a ``free energy'' functional. In particular we discuss the problem of equilibrium selection when more than one equilibrium state is present.

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