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Game theory is used to model conflict and cooperation. A non-cooperative game consists of two or more players, each with a set of strategies and a utility function that assigns an individual payoff to each combination of strategies. In zero-sum games, a gain for one player is always a loss for the other, which precludes the possibility of cooperation for mutual gain. In variable-sum games, some players can be better off without making others worse off. In cooperative games, the problem is to negotiate the distribution of resources among a coalition of players. Sociologists use cooperative game theory to study the effects of network structure on power inequality in social exchange. Variable-sum non-cooperative games can be used to model social dilemmas in which individual rationality leads to collective irrational outcomes. This can include games in which there is a Pareto Deficient Nash Equilibrium (NE). A NE obtains when every strategy is a best reply” to the other strategies played, hence, no player has an incentive to unilaterally change strategy. The equilibrium is Pareto Deficient when the outcome is preferred by no one while one or more players prefer some other outcome.
Knowing that an outcome is a NE means that if this state should obtain, the system will remain there forever, even in the absence of an enforceable contract. However, even when there is a unique NE, this does not tell us whether this state will ever be reached or what will happen if the equilibrium should be disturbed. Moreover, in most games, NE cannot identify a unique solution. In games that model ongoing interactions among players who care about future payoffs, the number of NE becomes indefinitely large, even in games that have a unique equilibrium in one-shot play. When games have multiple equlibria, NE cannot tell us which will obtain or how a population of players can move from one equilibrium to another.
Another limitation is the forward-looking analytical simplification that players have unlimited cognitive capacity with which to calculate the best response to any potential combination of strategies by other players. However, laboratory research on human behavior in experimental games reveals widespread and consistent deviations from best-response assumptions.
These limitations have led game theorists to explore backward-looking alternatives based on evolution and learning. Evolution alters the frequency distribution of strategies at the population level, while learning alters the probability distribution of strategies at the level of the individual player. In both, the outcomes that matter are those that have already occurred, not those that an analytical actor might expect to obtain in the future. This avoids the need to assume players have the ability to calculate future payoffs in advance, thereby extending applications to games played by highly routinized players, such as bureaucratic organizations or boundedly rational individuals whose behavior is based on heuristics, habits, or norms.
Sociology has lagged behind other social sciences in embracing game theory, in part because of skepticism about the heroic behavioral assumptions in the analytical approach. However, these backward-looking alternatives show that the key assumption in game theory is not rationality, it is instead what ought to be most compelling to sociology, the interdependence of the actors. The game paradigm obtains its theoretical leverage by modeling the social fabric as a matrix of interconnected agents guided by outcomes of their interaction with others, where the actions of each depend on, as well as shape, the behavior of those with whom they are linked. Viewed with that lens, game theory appears most relevant to the social science that has been most reluctant to embrace it.
- Maynard-Smith, J. (1982). Evolution and the Theory of Games. Cambridge University Press, Cambridge.
- Nash, J. F. (1950) Non-Cooperative Games. Princeton University Press, Princeton, NJ.