# Game Theory in Economics

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." In other words, game theory in economics is employed to help determine the course of action taken by individuals after taking into account the decisions taken by others. Thus, an important part of game theory is the consideration of decisions taken by other individuals who are part of the same model. The use of modern game theory in economics was pioneered by John von Neumann who employed the zero-sum game model in economic scenarios. The zero-sum game stated that the magnitude of gains made by one player in the market exactly equals the magnitude of losses made by the other players in the market. Through his book, Theory of Games and Economic Behaviour (1944), with economist Oskar Morgenstern, he has explained a number of cooperative games of several players.

Decision theory is a closely related field to game theory and perhaps, better explains the sentiment behind a game theorist’s psyche. It has been defined as studying the “interactions of agents with at least partially conflicting interests whose decisions affect each other”. This theory is normative in nature in the sense that it helps people make the best decision by accounting for (or assuming) the decisions that have been taken by the other players. Thus a number of tools, methodologies and softwares have been developed to better help make economic decisions by employing game theory.

The most frequently cited example of game theory in economics is the Prisoner’s Dilemma as explained in further detail below.

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Prisoner’s Dilemma

Consider two brokers, Dave and Dean, caught on charges of fraudulent practices. Both are taken to the local police station and kept in separate interrogation rooms. They are both told that in case they both confess to their crime, they will have to face three years in jail and in case they do not confess they will be given a prison sentence of two years. In case one of them confesses while the other denies, the former’s prison sentence will be reduced to one year while the latter’s will be ten years.

Hence their pay-off matrix will appear as:

The figures in parentheses represent the number of years A and B will have to spend in prison in case the events proceed as mentioned in the table. Since the two prisoners are not allowed to communicate with each other, they cannot make an informed decision. The most beneficial outcome for both would be two years each when both deny the crime. This is known as a Nash equilibrium scenario, i.e, an outcome where no other player’s position can be improved without harming another. However, since the average number of years that either Dave or Dean will be subjected to is the least in the case where they each confess to the crime, the most common outcome of the game is a double confession resulting in a three year prison sentence for both even though this is not the most optimal outcome. This shows how one player’s decision has an impact on the others fate as well.

This situation applies to economic scenarios when rival companies have to make various marketing or production decisions that depend on the actions of the other firm. For instance, the decision to invest in R&D by one company is highly dependent on the estimation for amounts spent on the same by rival companies in the field. The pay-offs in all cases are recorded and the firm takes a decision based on its estimations of actions taken by other players in the market. Most cases result in both companies going ahead with the R&D investment since they would not like to lose their market share. Hence such situations arise quite frequently in oligopolistic market setups.

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Applications of Game Theory in Economics

The occurrence of game theoretic situations among oligopolies has already been discussed using the Nash equilibrium method. There are many other situations pertaining to oligopolies which require the use of game theory to establish the most efficient outcomes. Though in the previous example, the payoffs and matrices were simplistic, in reality they are much more complicated and require a higher degree of analysis to reach the optimal point of functioning. There may be many types of oligopolies ranging from a leader-follower to a leader-leader to a follower-follower sytem, each of which has different payoff matrices.

This could also be applied to duopolies which are a special case of oligopoly involving two players and in bilateral monopolies as expounded below. The study of cartels is another field where game theory has found its application. It is merely a special case of oligopolies with different market dynamics owing to the difference in information available to the market players (Cartels share information and set common prices).

Further, a bargaining system is of special interest in economics due to its significance in the field. In the context of a bilateral monopoly involving two firms, a labour union and a firm or two individuals engaged in barter at the market place, a game theoretic situation may arise. The payoffs will be determined based on the actions taken by the counterparty and will vary from one case to another.

However, the issue surrounding the application of game theory to such a setup stems from a non zero-sum game. Hence the gains of one party do not tally up with the losses of the counterparty. This makes it difficult to apply a Nash equilibrium or pareto optimal approach to such problems. Further, game theory in economics also makes the assumption of rationality of decisions. Since this is relied on heavily to reach an efficient outcome, it may not be completely applicable in reality.

These applications are further sub-divided into simultaneous and sequential games. As the name suggests, simultaneous games are those where the players make their decisions at the same time whereas sequential games involve one player making a decision and a subsequent decision made by the other players based on the events already in play. However, there may or may not be perfect information regarding the previous actions taken by the players. Hence all of these factors need to be taken into account before implementing game theory in economics.

Thus the practical applications of game theory have been used to gauge the behaviour of firms, markets and consumers across the world. Game theory has found its applications not only in economics but a host of other fields such as political science, psychology, logic as well as biology. It has been put to use in testing various instances of human behaviour as well. Hence, game theory in economics has been a major area of study since the early twentieth century and continues to remain one of the most fascinating areas of research till date.