On large games with a bio-social typology - M. Ali Khan; Kali P. Rath; Yeneng Sun; Haomiao Yu (The Johns Hopkins University, Department of Economics, 2011)
We present a comprehensive theory of large non-anonymous games in which agents have a name and a determinate social-type and/or biological trait to resolve the dissonance of a (matching-pennies type) game with an exact pure-strategy Nash equilibrium with finite agents, but without one when modeled on the Lebesgue unit interval. We (i) establish saturated player spaces as both necessary and sufficient for an existence result for Nash equilibrium in pure strategies, (ii) clarify the relationship between pure, mixed and behavioral strategies via the exact law of large numbers in a framework of Fubini extension, (iii) illustrate corresponding asymptotic results.
Keywords: C62; D50; D82; G13; 330; Large non-anonymous games; social-type; traits; pure strategy; mixed strategy; behavioral strategy; saturated probability space; exact law of large numbers; ex-post Nash equilibrium; asymptotic implementation