2011/02/14 by Walter Briec, Briec, Walter, QiBin Liang +3
Economics, Econometrics and Finance · Decision Sciences · #Economic theories and models #Game Theory and Applications #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.1102.2716
We prove that, under appropriate conditions, an abstract game with\nquasi-Leontief payoff functions ui : \∏j=1nXj\→\ℝ has a\nNash equilibria. When all the payoff functions are globally quasi-Leontief, the\nexistence and the characterization of efficient Nash equilibria mainly follows\nfrom the analysis carried out in part I. When the payoff functions are\nindividually quasi-Leontief functions the matter is somewhat more complicated.\nWe assume that all the strategy spaces are compact topological semilattices,\nand under appropriate continuity conditions on the payoff functions, we show\nthat there exists an efficient Nash equilibria using the Eilenberg-Montgomery\nFixed Point Theorem for acyclic valued upper semicontinuous maps defined on an\nabsolute retract and some non trivial properties of topological semilattices.\nThe map in question is defined on the set of Nash equilibria and its fixed\npoints are exactly the efficient Nash equilibria.\n