具有支付冲击的模拟动力学
Imitation Dynamics with Payoff Shocks
摘要：
我们研究了回报冲击对大规模近视玩家进化的影响，这些玩家采用简单的策略修正协议，如“模仿成功”。在无噪声的情况下，这一过程是由标准的（确定性）复制动力学;然而，在噪声的存在下，诱导的随机动力学是不同于以前版本的随机复制动力学（如聚合冲击模型Fudenberg和哈里斯，1992年）。在这种情况下，我们表明，严格的平衡总是随机渐近稳定的，无论冲击的大小;另一方面，在高噪声制度，非平衡态也可能成为随机渐近稳定和主导的战略可能永远生存（他们成为灭绝，如果噪声低）。如果参与者不再那么短视，并根据累积收益修改策略，这种行为就会被消除。在这种情况下，我们得到了一个二阶随机动力系统，其吸引状态与博弈的严格均衡相一致，并且其中劣势策略灭绝（a.s.），无论噪音大小。
英文摘要：
We investigate the impact of payoff shocks on the evolution of large populations of myopic players that employ simple strategy revision protocols such as the "imitation of success". In the noiseless case, this process is governed by the standard (deterministic) replicator dynamics; in the presence of noise however, the induced stochastic dynamics are different from previous versions of the stochastic replicator dynamics (such as the aggregate-shocks model of Fudenberg and Harris, 1992). In this context, we show that strict equilibria are always stochastically asymptotically stable, irrespective of the magnitude of the shocks; on the other hand, in the high-noise regime, non-equilibrium states may also become stochastically asymptotically stable and dominated strategies may survive in perpetuity (they become extinct if the noise is low). Such behavior is eliminated if players are less myopic and revise their strategies based on their cumulative payoffs. In this case, we obtain a second order stochastic dynamical system whose attracting states coincide with the game's strict equilibria and where dominated strategies become extinct (a.s.), no matter the noise level.
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