Unbeatable imitation

Abstract

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-if-better" can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a money pump. In particular, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rock-scissors-paper variety. We also show that a sufficient condition for imitation not being subject to a money pump is that the relative payoff game is a generalized ordinal potential game or a quasiconcave game. Our results apply to many interesting examples of symmetric games including 2 × 2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

Social learning and the demise of costly cooperation in humans

“…Our results come from a study of small groups, however cooperation through social learning in larger groups is predicted to be even less likely to evolve and be maintained [70]. More generally, our conclusion is consistent with the idea that natural selection will favour social learning mechanisms that are adaptive [5,10,20,71,72]. Major tasks for the future are to determine how and why individuals use different learning mechanisms in different situations [18,[73][74][75][76], what explains individual variation in the use of social learning mechanisms [77][78][79][80] and how the behaviour of those being copied will evolve [12].…”

Ordinal Potentials in Smooth Games

“…Potentials of di¤erent types have been identi…ed for a large variety of games. Moreover, the underlying methods have been found useful for the analysis of oligopolistic markets (Slade, 1994), learning processes (Monderer and Shapley, 1996b;Fudenberg and Levine, 1998;Young, 2004), population dynamics (Sandholm, 2001(Sandholm, , 2009Cheung, 2014), the robustness of equilibria (Frankel et al, 2003;Morris and Ui, 2005;Okada and Tercieux, 2012), the decomposition of games (Candogan et al, 2011), imitation strategies (Duersch et al, 2012), dynamics in near-potential games (Candogan et al, 2013a(Candogan et al, , 2013b, the existence of Nash equilibrium (Voorneveld, 1997;Kukushkin, 1994Kukushkin, , 2011, solution concepts (Peleg et al, 1996;Tercieux and Voorneveld, 2010), games with monotone best-response selections (Huang, 2002;Dubey et al, 2006;Jensen, 2010), supermodular and zero-sum games (Brânzei et al, 2003), and even issues in mechanism design (Jehiel et al, 2008).…”

Strategic Control of Myopic Best Reply in Repeated Games

“…Their focus is on estimating such learning models with experimental data. There are only a few theoretical papers on learning in games in which players follow different learning theories (Banerjee and Weibull, 1995 Schipper, 2012Schipper, , 2014. They focus on the evolutionary selection or relative success of different boundedly rational learning rules.…”

“…They focus on the evolutionary selection or relative success of different boundedly rational learning rules. For instance, Duersch, Oechssler, and Schipper (2012) characterize the class of symmetric two-player games in which imitate-if-better cannot be beaten by any other decision rule no matter how sophisticated. Similarly, Duersch, Oechssler, and Schipper (2014) show that in symmetric two-player game tit-for-tat cannot be beaten by any other decision rule if and only if the game is an exact potential game.…”