The theory of socially embedded games: Applications and extensions to openand closed games

An earlier article, drawing on the mathematical theory of rules and rule co mplexes, extends and generalizes game theory (GGT). The theory has been use d to conceptualize and analyze diverse social relationships, roles, and gam es as particular types of rule complexes. For instance, a social role, as a major basis of a parent's action in a game, consists of at least four key components - which are mathematical objects - in the determination of actio n: value complex, model of reality (including beliefs and knowledge bases), a repertoire of acts, routines, programs, and strategies, and modality, a role-specific algorithm for determining or generating action in game settin gs. This article applies and extends GGT in analyses of a market bargaining game (a type of open game) and of the classical game of prisoners' dilemma (a type of closed game). The applications show the concrete effects of soc ial embeddedness on game structuring, game interaction patterns and outcome s, and social equilibria.