A Model of Agents Persuasion and Types Competition in a Cultural Evolution Framework
16 Pages Posted: 2 Aug 2011 Last revised: 21 May 2013
Date Written: July 22, 2011
This paper analyses the evolution of types in a society with an evolutionary game framework in which types evolve not only depending on how much they are fit but also on how much they are able to persuade others about their fitness during a cultural competition process. This creates a kind of payoffs redistribution so that it is possible to reach equilibria not feasible under standard dynamics. We first provide necessary conditions for a generic matrix and generic class of cultural competition mechanisms in order to observe polimorphic equilibria, proposing that the set of parameters such that a stable polimorphic equilibrium exists under cultural competition is a subset of the set of parameters for this to be possible under the standard case. Then, necessary and sufficient conditions for polimorphic equilibrium stability are provided in the case of specific competition rules at each competition level. We then analyse the prisoner’s dilemma framework finding that, even in this case, stable and unstable polimorphic equilibria may arise, depending on the specific parametrization and level of cultural competition among types. We then show that while a little competition among cultural types helps to maintain types heterogeneity in the long run, this effect is non monotone in the level of competition of the society.
Keywords: Cultural Evolution, Cultural Transmission, Evolutionary Selection, Replicator Dynamics
JEL Classification: C70, C73, Z13
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