Dridi, Slimane (2019) Plasticity in evolutionary games. Biorxiv, Toulouse

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Abstract

The ability to respond appropriately to environmental cues is fundamental to the success of all forms of life, but previous theoretical studies of the evolution of plasticity make so diverse assumptions that the conditions under which plasticity can emerge in evolving populations are unclear when fitness is frequency-dependent. We study the effect of adding plastic types to symmetric evolutionary games. Since frequency-dependence induces an evolutionary change in the environment of players, one might expect that plastic individuals who can adapt their phenotypes to the environment could have a fitness advantage over simpler purely genetically determined phenotypes. In our model, plastic individuals can detect the type of their opponent before an interaction and condition their action on it. Even though it might appear as an outstanding advantage, such an ability cannot guarantee global stability in all games for even the smallest positive plasticity costs. We identify classes of games where plasticity can or cannot be globally or locally stable. In games where the standard replicator dynamics converge to a pure state, costly plasticity cannot invade an equilibrium population. Costly plasticity can however be locally stable, but the way to achieve this is not to play the best-response to any possible encountered type. Rather, part of the stability success of plastic types is based on establishing Pareto-efficiency as residents; in certain social dilemma games such as the Prisoner’s Dilemma and the Snowdrift game, this implies that plastic types need to cooperate with a strictly positive probability in order to ensure their stability against invasion by pure types. Zero-sum games always allow for the global stability of plastic types. This study offers a more principled way of thinking about the evolutionary emergence of plasticity in social scenarios, and helps demonstrate that such an emergence is strongly dependent on the type of game individuals are faced with.