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- Title
The Theory of Socially Embedded Games: The Mathematics of Social Relationships, Rule Complexes, and Action Modalities.
- Authors
Burns, Tom R.; Gomolińska, Anna
- Abstract
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. 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, and strategies, and modalities, role-specific algorithms for determininig or generating action in game settings. The article focuses on three 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 the theory that actors construct an action or make choices among alternative actions by making comparisons and judging similarity (or dissimilarity) between an option or...
- Subjects
SOCIAL interaction; RULE of reason; SOCIAL role; MATHEMATICAL models; HUMAN behavior; MODALITY (Theory of knowledge)
- Publication
Quality & Quantity, 2000, Vol 34, Issue 4, p379
- ISSN
0033-5177
- Publication type
Article
- DOI
10.1023/A:1004884423573