The socially embedded theory of games: the mathematics of social relationships, rule complexes, and action modalities
by
Tom R. Burns
University of Uppsala, Dept. of Sociology, Uppsala Theory Circle, Box 821, 75108 Uppsala, Sweden
Coauthors: Anna Gomolińska (University of Białystok, Dept. of Mathematics), Ewa Roszkowska (University of Białystok, Dept. of Economics)

In their classic work, Von Neumann and Morgenstern defined a game as simply the totality of the rules which describe it. They did not, however, elaborate a theory of rules. Such considerations lead to conceptualizing rules and rule configurations as mathematical objects, specifying the principles for combining rules, developing the theory of revising, replacing, and, in general transforming rules and rule complexes. The mathematics is based on contemporary developments at the interface of mathematics, logic, and computer science (see Roszkowska et al, "Rule complexes for the social game theory", GAMES'2000). This article, drawing on the mathematical theory of rules and rule complexes, extends and generalizes game theory (GGT). The theory of rule complexes is used to conceptualize and analyze diverse social relationships, roles, and games as particular types of rule complexes. A social role, for instance, is the major basis of an individual's action in a game. It consists of at least four major 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, strategies, and modalities, role-specific algorithms for determininig or generating action in game settings. The paper focuses on three pure types of action modality: routine or habitual, normative, and instrumental modalities. The theory: (1) provides a cultural/institutional basis for a theory of games where games, social relationships, and roles are formalized in terms of rule complexes; (2) explains human action as a form of rule application or rule-following action, which underlies all modalities of action; (3) formulates specific models of action based on the principle that actors contruct an action or make choices among alternative actions by making comparisons and judging similarity (or dissimilarity) between an option or options considered and their norms and values, and on this basis determine whether or not, and to what degree, a value, norm, or goal will be, is, or has been realized or satisfied; (4) reconceptualizes "game" as a social form and makes a distinction between open and closed games. The paper provides 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, outcomes, and equilibria.

Date received: May 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafc-24.