Stable sampling in repeated games

Statistical inference in evolutionary dynamics

“…This is called the payoff sampling approach, and its application is studied by Spiegler (2006a,b), Miekisz and Ramsza (2012), and Mantilla et al (2020), for example. Evolutionary dynamics with such agents are considered by Sethi (2000Sethi ( , 2021, Sandholm et al (2019Sandholm et al ( , 2020, and Arigapudi et al (2021). Osborne and Rubinstein (2003) consider sampling equilibrium in static games similar to Salant and Cherry (2020) but without the consideration of statistical inference.…”

Strategy Sets Closed Under Payoff Sampling

“…This equilibrium has been named payoff-sampling equilibrium in the literature (see e.g. Selten and Chmura (2008), Chmura and Güth (2011), Cárdenas et al (2015), Sethi (2021) and Arigapudi et al (2021Arigapudi et al ( , 2022). When defining this equilibrium, most authors (e.g.…”

“…Procedurally rational agents and their associated payoff-sampling equilibria have been used in a variety of applications, including consumer choice procedures and product pricing strategies (Spiegler, 2006a), markets with asymmetric information (Spiegler, 2006b), trust and delegation of control (Rowthorn and Sethi, 2008), the Traveler's Dilemma (Berkemer, 2008), market entry (Chmura and Güth, 2011), ultimatum bargaining (Mie ¸kisz and Ramsza, 2013), use of common-pool resources (Cárdenas et al, 2015), contributions to public goods (Mantilla et al, 2020), the Centipede game (Sandholm et al, 2019;Izquierdo and Izquierdo, 2022b), the Prisoner's Dilemma (Arigapudi et al, 2021), coordination problems (Izquierdo et al, 2022), and finitely repeated games (Sethi, 2021). Sethi (2000) introduced population dynamics based on the considered procedurally rational agents.…”

“…Mie ¸kisz and Ramsza (2013); Mantilla et al (2020)) and payoff-sampling dynamics (see e.g. Sethi (2021); Arigapudi et al (2021Arigapudi et al ( , 2022), take the form ẋi = w κ i (x) − x i ,…”

“…We refer to these BEP all (κ, β uni f ) protocols as uniform payoff-sampling protocols. Sethi (2021) considers the family of regular tie-breaking rules β r , which are those that place positive probability on choosing each of the strategies that achieve the best-experienced-payoff in a battery of tests. We refer to the corresponding BEP all (κ, β r ) protocols as regular payoff-sampling protocols.…”