1998/01/29 by Matteo Marsili, Yicheng Zhang, Marsili, Matteo +1
Economics, Econometrics and Finance · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.cond-mat/9801309
openalex publication_date 1998/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.