tailieunhanh - RATIONAL AND SOCIAL CHOICE Part 6

Pollock và Schlag (1999) xem xét cá nhân biết trò chơi mà họ chơi, do đó, không chắc chắn là chỉ về sự phân bố của các hành động. Họ điều tra các điều kiện về một quy tắc lấy mẫu duy nhất mà mang lại một động lực giọng đều đều chi trả trong một trò chơi mà có một cấu trúc đáp ứng tốt nhất theo chu kỳ như trong Pennies phù hợp. | 290 CARLOS ALÓS - FERRER AND KARL H . SCHLAG M 2 then the dynamics will circle close to and around the Nash equilibrium if sufficiently few individuals observe the play of others between Pollock and Schlag 1999 consider individuals who know the game they play so uncertainty is only about the distribution of actions. They investigate conditions on a single sampling rule that yield a payoff monotone dynamics in a game that has a cyclic best response structure as in Matching Pennies. They find that the rule has to be imitating and that the continuous version of the population dynamics will have like the standard replicator dynamics closed orbits around the Nash equilibrium. They contrast this with the finding that there is no rule based only on a finite sample of opponent play that will lead to a payoff monotone dynamics. This is due to the fact that information on success of play has to be stored and recalled in order to generate a payoff monotone dynamics. Dawid 1999 considers two populations playing a battle-of-the-sexes game where each agent observes a randomly selected other member of the same population and imitates the observed action if the payoff is larger than their own and the gap is large enough. For certain parameter values this model includes PIR. The induced dynamics is payoff monotone. In games with no risk-dominant equilibrium there is convergence towards one of the pure-strategy coordination equilibria unless the initial population distribution is symmetric. In the latter case depending on the model s parameters play might converge either to the mixed-strategy equilibrium or to periodic or complex attractors. If one equilibrium is risk-dominant it has a larger basin of attraction than the other one. Imitating your Opponents In the following we consider the situation where player roles are not separated. There is a symmetric game and agents play against and learn from agents within the same population. Environments where row players .