Game Theory

Game theory is a branch of mathematics dealing with how rational and interdependent actors make decisions in situations in which their interests conflict or converge. Although the theory is normative, describing how rational actors behave, its concepts and methods have proved to be useful in all the social sciences. Recently there has been great interest in evolutionary game theory, which describes how apparently rational action can evolve through natural selection from the actions of less-than-rational actors.

Game theory is based on the assumption that interdependent actors make independent decisions based on their own interests. The scope of the approach can be widened by assuming that individuals care about the interests of others but at a cost; such a theory will be more complex and difficult to test. An important limitation of game theory is that it does not account for what individuals value; what has utility is exogenous to the theory. This means that even if game theory were completely accurate, there is much it would not account for in the determination of human action.

Game theory should be distinguished from the more inclusive category of rational choice. While game theory always involves interdependent individuals making strategic choices in reaction to others’ choices, theories of rational action can be used to prescribe rational action in games against nature—where nature is a probabilistic but nonstrategic actor. In sociology, rational choice seems often to refer simply to the assumption that actors are self-interested and that much social action can be explained without recourse to norms or culture.

Game theory is also not equivalent to microeconomics, which also assumes rational actors but which also typically uses the assumption of perfect competition within a market of many buyers and sellers. In a perfectly competitive market, all actors are faced with a set of prices that they cannot change by their own actions. Thus, members of a market do not behave strategically any more than single people interact strategically with the weather; they react to it but do not influence it. Although the two are often merged under the concept of rational choice, game theory is inherently more sociological because it deals with relationships.

The tree diagram shown in Figure 1 is meant to describe the major areas of game theory.

Figure 1

The concept game refers merely to a situation in which the outcome for a set of actors is a well-described consequence of their decisions and, possibly, of chance. In cooperative games, actors can make binding agreements, whereas in noncooperative games, they cannot. Zero-sum games are a special type of noncooperative game in which one actor can gain only at the expense of others. In N-person games, there are three or more interdependent actors, a situation usually requiring different models. A solution is an outcome satisfying specified criteria. Much of game theory is a description of solutions and their properties. The hope is that these solutions will describe the outcomes of interactions involving rational actors. The outline [Page 298]in Table 1 shows the types of solutions appropriate under the different conditions.

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