The Theory of Socially Embedded Games: Applications and Extensions to Open and Closed Games

An earlier article, drawing on the mathematical theory of rules and rule complexes, extends and generalizes game theory (GGT). The theory has been used to conceptualize and analyze diverse social relationships, roles, and games 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 action: 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 settings. 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 social embeddedness on game structuring, game interaction patterns and outcomes, and social equilibria.