Generalized game theory is an extension of game theory incorporating social theory concepts such as norm, value, belief, role, social relationship, and institution. The theory was developed by Tom R. Burns, Anna Gomolinska, and Ewa Roszkowska but has not had great influence beyond these immediate associates. The theory seeks to address certain perceived limitations of game theory by formulating a theory of rules and rule complexes and to develop a more robust approach to socio-psychological and sociological phenomena.
Overview
In generalized game theory, games are conceptualized as rule complexes, which is a set containing rules and/or other rule complexes. However, the rules may be imprecise, inconsistent, and even dynamic. Distinctions in the properties and functions of different types of rules allows the rules themselves to be analyzed in complex ways, and thus the models of the theory more closely represent relationships and institutions investigated in the social sciences.
The ways in which the rules may be changed is developed within the context of generalized game theory based on the principle of rule revision and game restructuring. These types of games are referred to as open games, that is, games which are open to transformation. Games which have specified, fixed players, fixed preference structures, fixed optimization procedures, and fixed action alternatives and outcomes are called closed games (characteristic of most classical game theory models).
Because its premises derive from social theory generalized game theory emphasizes and provides cultural and institutional tools for game conceptualization and analysis, what Granovetter (1985) refers to as the social embeddedness of interaction and social and economic processes. This is in contrast to conceptualization of games consisting of actors which are autonomous utility maximizers. Further, the modeling of the actors themselves in generalized game theory is especially open to the use of concepts such as incomplete information and bounded rationality.
Proponents of generalized game theory have advocated the application of the theory to reconceptualizing individual and collective decision-making, resolutions of the prisoners' dilemma game, agent-based modeling, fuzzy games, conflict resolution procedures, challenging and providing robust and normatively grounded alternatives to Nash equilibrium and Pareto optimality, among others.
Principles
Judgment in generalized game theory
A key aspect of actors decision making in generalized game theory is based on the concept of judgment. Several types of judgment could be relevant, for instance value judgment, factual judgment, and action judgment. In the case of action judgment, the actor seeks to take the course of action offered by the rules of the game which most closely fit the values held by the actor (where the values are a sub-rule complex of the game).
Predicting how actors will react under these sub-rules is hypothesised to be more accurate than forming traditional game theory complexes. Armstrong (2002) found that when actors hold differing beliefs and roles within a sub-game formal game theory Nash equilibriums became less reliable (it should be noted generalised game theory has received less scrutiny due to lack of notoriety).
Even the method by which the actor calculates closeness of fit can be controlled by the actors values (such as an actor might use a more speedy algorithm, or a more far-sighted one). Each actor has a judgment operator by which the actor can create a preference order of the perceived qualities of possible outcomes based on satisfying the condition that the qualities of the outcomes can be roughly said to be sufficiently similar to the qualities of the actors primary values or norms. Thus, in generalized game theory, each actor's judgment calculus includes the institutional context of the game.
General game solutions
A general or common game solution is a strategy or interaction order for the agents which satisfies or realizes the relevant norms and values of the players. This should lead to a state that is acceptable by the game players, and is not necessarily a normative equilibrium, but represents the "best result attainable under the circumstances".