A comprehensive theory of large strategic games with (socioeconomic and biological) traits (LSGT) has recently been presented in Khan et al. (2012 a and b), and in this paper, we present a reformulation pertaining to large distributional games with traits (LDGT). In addition to a generalization...

We present a comprehensive theory of large games in which players have names and determinate social-types and/or biological traits, and identify through four decisive examples, essentially based on a matching-pennies type game, pathologies arising from the use of a Lebesgue interval for player's...

This paper demonstrates the class of atomless spaces that accurately models the space of players in a large game which represents an idealized limit of a sequence of finite-player games. Through two examples, we show that arbitrary atomless probability spaces, in particular, the Lebesgue unit...

This paper characterizes both point-rationalizability and rationalizability in large games when societal responses are formulated as distributions or averages of individual actions. The sets of point-rationalizable and rationalizable societal responses are defined and shown to be convex, compact...

The existence of pure-strategy Nash equilibrium is shown for a non-cooperative game with a continuum of small players and a compact action space. The players’ payoffs depend on their own actions and the mean of the transformed strategy profiles. This covers the case when the payoffs depend on...

This paper elucidates the conceptual role that independent randomization plays in non-cooperative game theory. In the context of large (atomless) games in normal form, we present precise formalizations of the notions of a mixed strategy equilibrium (MSE), and of a randomized strategy equilibrium...