In their classic work, Von Neumann and Morgensterndefined a game as simply the totality of the rules which describe it. Theydid not, however, elaborate a theory of rules. Such considerations lead toconceptualizing rules and rule configurations as mathematical objects, specifyingthe principles for combining rules, developing the theory of revising,replacing, and, in general transforming rules and rule complexes. Themathematics is based on contemporary developments at the interface ofmathematics, logic, and computer science. This article, drawing on themathematical theory of rules and rule complexes, extends and generalizes gametheory (GGT). The theory of rule complexes is used to conceptualize andanalyze diverse social relationships, roles, and games as particulartypes of rule complexes. A social role, for instance, is the major basisof an individual's action in a game. It consists of at least four majorcomponents – which are mathematical objects – in the determinationof action: value complex, model of reality (including beliefs and knowledgebases), a repertoire of acts, routines, programs, and strategies, and modalities,role-specific algorithms for determininig or generating action in gamesettings. The article focuses on three types of action modality routineor habitual, normative, andinstrumental modalities. The theory: (1) provides a cultural/institutionalbasis for a theory of gameswhere games, social relationships, and rolesare formalized in terms of rule complexes; (2) explains human action as a formof rule application or rule-following action, which underlies allmodalities of action; (3) formulates the theory that actors construct an action or make choices amongalternative actions by making comparisons and judging similarity (ordissimilarity) between an option or options considered and their norms and values,and, in general, determine whether or not, and to what degree, a value,norm, or goal will be realized or satisfied; (4)reconceptualizes ``game'' as a social form and makes a distinction between open and closed games.
Quality & Quantity – Springer Journals
Published: Oct 16, 2004
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