Game Theory

Game Theory, branch of economics concerned with describing or predicting economic behaviour using concepts and techniques from the mathematical discipline of game theory. Many economic decisions are influenced by expectations concerning the way other economic agents will behave. Common examples are the behaviour of firms in a market where each of them has a large share of the total market, so that the pricing strategy adopted by any one firm will take account of how it expects the other firms to react. For example, it might decide whether or not to cut its price according to whether it expected its competitors to follow suit or to keep their prices at their original level. In the same way, a trade union bargaining with management will adopt a strategy that depends on what strategy it believes the management is pursuing.

This interaction between economic agents, and hence the dependence of rational decisionmaking on the assumptions each agent can make about the choices and strategies that the other agents will adopt, has given rise to the area of economic theory known as “game theory”. This originated in the classic pioneering book Theory of Games and Economic Behaviour (1944) by John von Neumann and Oskar Morgenstern. Its application goes far beyond economics, however, and constitutes a general theory of rational choice under conditions of uncertainty as to the choices that other “players” may take, as, for example, in the analysis of alternative strategies of nuclear defence.

Game theory has analogies with familiar games such as chess or bridge, where each player's strategy depends on what “moves” or choices the other players are expected to make. But this analogy does not take one very far. In order to deduce optimal strategies under different assumptions as to how the other economic agents will behave, game theory needs to allow for a variety of objectives; for the consequences of adopting different strategies; for the extent to which alliances are possible between different players, and the degree to which contracts between them and other players are binding (for example, as regards the frequent failure of members of the Organization of the Petroleum Exporting Countries (OPEC) to adhere to their agreed production quotas); for the extent to which any one “game” is a “one-off” or is likely to be repeated several times, thereby providing information to all the players about their strategies; and so on.

In spite of these difficulties, game theorists have been able to identify certain important features of certain kinds of game situation. One common tool of analysis has been the construction of a “payoff” matrix. In the simple case of only two players, for example, a payoff matrix would indicate what benefit or loss would accrue to each player for all combinations of strategies that they might adopt. It can be shown that some games will then correspond to payoff matrices in which there is a “Nash” equilibrium (after John Nash who, with two other game theorists, shared the Nobel Prize for Economics in 1994). This is a situation in which (in a game involving two people, X and Y) X's choice is optimal for him given Y's choice and Y's choice is optimal given X's choice. In such a situation, when the strategy choices are revealed neither player has any cause to regret the strategy he had adopted. However, a “Nash” equilibrium does not necessarily lead to as desirable an outcome for the players as would their cooperation. A famous example of this is the “prisoner's dilemma”, where both players have an incentive to confess to the crime for which they are accused but where they would do better if they could cooperate.