A Gibbsian approach to potential game theory
| dc.creator | Campbell, Michael J. | |
| dc.date | 2005-02-03 | |
| dc.date | 2005-02-09 | |
| dc.date.accessioned | 2026-07-07T03:03:35Z | |
| dc.date.available | 2026-07-07T03:03:35Z | |
| dc.description | 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. | |
| dc.description | 27 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0502112 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0502112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/25807 | |
| dc.subject | Statistical Mechanics | |
| dc.title | A Gibbsian approach to potential game theory | |
| dc.type | text |