Penalty-regulated dynamics and robust learning procedures in games

Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space repelling. These penalty-regulated dynamics are equivalent to players keeping an exponentially discounted aggregate of their on-going payoffs and then using a smooth best response to pick an action based on these performance scores. Owing to this inherent duality, the proposed dynamics satisfy a variant of the folk theorem of evolutionary game theory and they converge to (arbitrarily precise) approximations of Nash equilibria in potential games. Motivated by applications to traffic engineering, we exploit this duality further to design a discrete-time, payoff-based learning algorithm which retains these convergence properties and only requires players to observe their in-game payoffs: moreover, the algorithm remains robust in the presence of stochastic perturbations and observation errors, and it does not require any synchronization between players.Comment: 33 pages, 3 figure

Cognition and Behavior in Two-Person Guessing Games: An Experimental Study

This paper reports experiments that elicit subjects' initial responses to 16 dominancesolvable two-person guessing games. The structure is publicly announced except for varying payoff parameters, to which subjects are given free access, game by game, through an interface that records their information searches. Varying the parameters allows strong separation of the behavior implied by leading decision rules and makes monitoring search a powerful tool for studying cognition. Many subjects' decisions and searches show clearly that they understand the games and seek to maximize their payoffs, but have boundedly rational models of others' decisions, which lead to systematic deviations from equilibrium.