A Gibbsian approach to potential game theory

Abstract

In games for which there exists a potential, the deviation-from-rationality dynamical model for which each agent's strategy adjustment follows the gradient of the potential along with a normally distributed random perturbation, is shown to equilibrate to a Gibbs measure. The standard Cournot model of an oligopoly is shown not to have a phase transition, as it is equivalent to a continuum version of the Curie-Weiss model. However, when there is increased local competition among agents, a phase transition will likely occur. If the oligopolistic competition has power-law falloff and there is increased local competition among agents, then the model has a rich phase diagram with an antiferromagnetic checkerboard state, striped states and maze-like states with varying widths, and finally a paramagnetic state. Such phases have economic implications as to how agents compete given various restrictions on how goods are distributed. The standard Cournot model corresponds to a uniform distribution of goods, whereas the power-law variations correspond to goods for which the distribution is more localized.

27 pages, 1 figure

References in corpus (13)

• Statistical theory of the continuous double auction
• Quantifying Stock Price Response to Demand Fluctuations
• Irrelevance of memory in the minority game
• Phase Transition and Symmetry Breaking in the Minority Game
• A thermal model for adaptive competition in a market
• The Local Minority Game
• Minority Game With Peer Pressure
• Fluctuations around Nash Equilibria in Game Theory
• Thermal treatment of the minority game
• Large-Scale Synchrony in Weakly Interacting Automata
• Stochastic Dynamics in Game Theory
• Non-equilibrium statistical mechanics of Minority Games
• Two dimensional Ising model with long-range competing interactions