On the Existence of Pure Strategy Nash Equilibria in Large Games

• Autor(a) principal: Carmona, Guilherme
• Data de Publicação: 2006
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10362/82986
• topic: Nash Equilibrium; Asymptotic Results; Pure Strategies; Approximate equilibria

Over the years, several formalizations of games with a continuum of players have been given. These include those of Schmeidler (1973), Mas-Colell (1984) and Khan and Sun (1999). Unlike the others, Khan and Sun (1999) also addressed the equilibrium problem of large finite games, establishing the existence of a pure strategy approximate equilibrium in sufficiently large games. This ability for their formalization to yield asymptotic results led them to argue for it as the right approach to games with a continuum of players. We challenge this view by establishing an equivalent asymptotic theorem based only on Mas-Colell’s formalization. Furthermore, we show that it is equivalent to Mas-Colell’s existence theorem. Thus, in contrast to Khan and Sun (1999), we conclude that Mas-Colell’s formalization is as good as theirs for the development of the equilibrium theory of large finite games.