When the Other Matters. The Battle of the Sexes Revisited
In this paper we address bimatrix games when the players take into account not only their own payoff, but they also show some concerns about the payoff of the other player. We propose a weighted Rawlsian representation of players’ preferences which can accommodate the behaviours of different types of players, which are identified with different values of the parameters. The Battle of the Sexes game is analyzed in this extended setting where certain social interactions between the players determine their strategic behaviours. The best response correspondences are described depending on the relative importance that each player assigns to her own payoff and to the payoff of the other. This permits the identification of the corresponding sets of equilibria and the study of the changes produced with the variation of the parameters.
KeywordsBattle of the sexes Equilibria Bi-matrix games Rawlsian function
The research of the authors is partially supported by the Spanish Ministry of Science and Innovation, Project ECO2015-68856-P (MINECO/FEDER).
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