Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact

Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact

Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact

Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our results show that this question strongly depends on the expected number of actions observed by new agents. Specifically, we show that if the expected number of observed actions is: (1) less than one, then the population converges to the same behavior independently of the initial state; (2) between one and two, then in some (but not all) environments there are learning rules for which the initial state has a lasting impact on future behavior; and (3) more than two, then in all environments there is a learning rule for which the initial state has a lasting impact

Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner’s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature

Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications

Producción CientíficaWe consider a family of population game dynamics known as Best Experienced Payoff Dynamics. Under these dynamics, when agents are given the opportunity to revise their strategy, they test some of their possible strategies a fixed number of times. Crucially, each strategy is tested against a new randomly drawn set of opponents. The revising agent then chooses the strategy whose total payoff was highest in the test, breaking ties according to a given tie-breaking rule. Strict Nash equilibria are rest points of these dynamics, but need not be stable. We provide some simple formulas and algorithms to determine the stability or instability of strict Nash equilibria.Agencia Estatal de Investigación (project PID2020-118906GB-I00/AEI/10.13039/501100011033)Ministerio de Ciencia, Innovación y Universidades (projects PRX19/00113 and PRX21/00295)Fulbright Program (projects PRX19/00113 and PRX21/00295

Instability of defection in the prisoner’s dilemma under best experienced payoff dynamics

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner’s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature

Instability of defection in the prisoner’s dilemma under best experienced payoff dynamics

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner’s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature