TY - JOUR
T1 - On the existence of pure-strategy equilibria in large games
AU - Carmona, Guilherme
AU - Podczeck, Konrad
PY - 2009/1/1
Y1 - 2009/1/1
N2 - Over the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler [D. Schmeidler, Equilibrium points of nonatomic games, J. Stat. Phys. 4 (1973) 295-300], Rashid [S. Rashid, Equilibrium points of non-atomic games: Asymptotic results, Econ. Letters 12 (1983) 7-10], Mas-Colell [A. Mas-Colell, On a theorem by Schmeidler, J. Math. Econ. 13 (1984) 201-206], Khan and Sun [M. Khan, Y. Sun, Non-cooperative games on hyperfinite Loeb spaces, J. Math. Econ. 31 (1999) 455-492] and Podczeck [K. Podczeck, On purification of measure-valued maps, Econ. Theory 38 (2009) 399-418]. The level of generality of each of these existence results is typically regarded as a criterion to evaluate how appropriate is the corresponding formalization of large games. In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games. (C) 2008 Elsevier Inc. All rights reserved.
AB - Over the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler [D. Schmeidler, Equilibrium points of nonatomic games, J. Stat. Phys. 4 (1973) 295-300], Rashid [S. Rashid, Equilibrium points of non-atomic games: Asymptotic results, Econ. Letters 12 (1983) 7-10], Mas-Colell [A. Mas-Colell, On a theorem by Schmeidler, J. Math. Econ. 13 (1984) 201-206], Khan and Sun [M. Khan, Y. Sun, Non-cooperative games on hyperfinite Loeb spaces, J. Math. Econ. 31 (1999) 455-492] and Podczeck [K. Podczeck, On purification of measure-valued maps, Econ. Theory 38 (2009) 399-418]. The level of generality of each of these existence results is typically regarded as a criterion to evaluate how appropriate is the corresponding formalization of large games. In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games. (C) 2008 Elsevier Inc. All rights reserved.
KW - Approximation
KW - strategies
KW - players
KW - equilibrium
KW - Nash
KW - Equilibrium
KW - Pure
KW - distributions
KW - Nash equilibrium
KW - Pure strategies
KW - Approximation
KW - Equilibrium distributions
U2 - 10.1016/j.jet.2008.11.009
DO - 10.1016/j.jet.2008.11.009
M3 - Article
SN - 0022-0531
VL - 144
SP - 1300
EP - 1319
JO - Journal of Economic Theory
JF - Journal of Economic Theory
IS - 3
ER -