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Compliance with Social Norms as an Evolutionary Stable Equilibrium
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Springer International Publishing
Pierre-Olivier Pineau, Simon Sigué & Sihem Taboubi. Games in Management Science - 2020. Essays in Honor of Georges Zaccour. 2020, p. 283-313.
This paper studies a two-population evolutionary game in a new setting in between a symmetric and an asymmetric evolutionary model. It distinguishes two types of agents: Sanchos, whose payoffs are defined by a prisoner’s dilemma game, and Quixotes, whose payoffs are defined by a snowdrift game. Considering an imita- tive revision protocol, a revising agent is paired with someone from his own popula- tion or the other population. When matched, they observe payoffs, but not identities. Thus, agents in one population interact and imitate agents from their own population and from the other population. In this setting we prove that a unique mixed-strategy asymptotically stable fixed point of the evolutionary dynamics exists. Taking as an example the compliance with social norms, and depending on the parameters, two type of equilibrium are possible, one with full compliance among Quixotes and par- tial compliance among Sanchos, or another with partial compliance among Quixotes and defection among Sanchos. In the former type, Sanchos comply above their Nash equilibrium (as they imitate compliant Quixotes). In the latter type, Quixotes comply below their Nash equilibrium (as they imitate defecting Sanchos).
Two-population evolutionary game Heterogeneous preferences Prisoner’s dilemma game Snowdrift game Social norms
This study was funded by the Spanish Government (projects ECO2014- 52343-P and ECO2017-82227-P), as well as financial aid from Junta de Castilla y León (projects VA024P17 and VA105G18), co-financed by FEDER funds.
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