The prevalence of chaotic dynamics in games with many players
Abstract
We study adaptive learning in a typical pplayer game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space display a range of qualitatively different behaviors, with attractors that include unique fixed points, multiple fixed points, limit cycles and chaos. In the limit where the game is complicated, in the sense that the players can take many possible actions, we use a generatingfunctional approach to establish the parameter range in which learning dynamics converge to a stable fixed point. The size of this region goes to zero as the number of players goes to infinity, suggesting that complex nonequilibrium behavior, exemplified by chaos, may be the norm for complicated games with many players.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1612.08111
 Bibcode:
 2016arXiv161208111S
 Keywords:

 Quantitative Finance  Economics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Physics and Society
 EPrint:
 21 pages, 11 figures