Convexity on Nash Equilibria without Linear Structure

Francesco Ciardiello ()

Quaderni DSEMS from Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia

Abstract: To give sucient conditions for Nash Equilibrium existence in a continuous game is a central problem in Game Theory. In this paper, we present two games in which we show how the continuity and quasi-concavity hypotheses are unconnected one to each other. Then, we relax the quasiconcavity assumption by exploiting the multiconnected convexity's concept (Mechaiekh & Others, 1998) in spaces without any linear structure. These results will be applied to two non-zero-sum games lacking the classical assumptions and more recent improvements (Ziad, 1997), (Abalo & Kostreva, 2004). As a minor result, some counterexamples about relationship between some continuity conditions due to Lignola (1997), Reny (1999) and Simon (1995) for Nash equilibria existence are obtained.

Keywords: Nash Equilibria Existence; Fixed Point Theorem; Generalized Convexity; 2 Person Game; 3 Person Game; Symmetric Game; Generalized Continuity. (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Date: 2007-07
New Economics Papers: this item is included in nep-gth and nep-mic
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