Since the 1970s, game theory has developed from a field for experts into a profession that is well embedded in the world of economics, and it is now part of the core theory for students of economics. In addition, game theory has expanded into other professions, including law, philosophy, and biology. The author discusses both the history of game theory and its possible future.
What’s Inside?
Because of differences in assumptions, different games exist in game theory. Some games are assumed to have a finite time horizon, while others have an infinite time horizon. In some games, the players can cooperate and form coalitions; in other games, this approach is not possible. Thus, different assumptions result in different equilibriums, and sometimes even a couple of equilibriums are present. The author discusses both the historical development of game theory and its interaction with other professions. Finally, he concludes that the rise of behavioral economics has provided game theory with a new area of application.
How Is This Research Useful to Practitioners?
The author shows that game theory faces three central challenges. First, games can have multiple equilibriums, as is the case in a coordination game: Drivers drive on either the left-hand side or the right-hand side, and coordination between the drivers leads to the best results. This idea of multiple equilibriums in economics is not new; there are also several explanations for the Great Depression. Games that are especially repetitive can imply multiple equilibriums. Using empirical results, one can avoid the existence of multiple equilibriums. Also, taking into account the personal and cultural aspects and historical development of the game’s framework can help one find the most realistic equilibrium.
Second, game theory has been more successful in auctions and matching than in other applications, including bargaining. Such details as the timing of offers, the overall process, and the possibility of withdrawals make bargaining less amenable to game theory. Moreover, outcomes in bargaining can be continuous, making it harder to apply discrete models.
Finally, cooperative game theory, in which players can form coalitions, can result in different outcomes. Cooperative game theory is more applicable in games with complete information than in those with incomplete information, where noncooperative game theory is more applicable.
The author shows that game theory has expanded beyond the fields of economics and industrial organization and is now applied in other professions, including law, psychology, biology, computer science, and electrical engineering.
Most financial professionals make decisions regarding auctions and matching, and the author provides an interesting perspective on how game theory has developed over time and what its future applications might be.
How Did the Author Conduct This Research?
The science of economics tries to explain human behavior using the principle of individual behavior. By explaining the behavior of individuals, economists can explain social outcomes. Individual behavior is explained by the principle of consistent and stable preferences as well as the principle of a competitive market, which assumes that cases of noncompetitive markets are rare. Game theory, however, challenges the principle of competitive markets and thus provides a more general framework. One example is the case of a duopoly in which firms can set either the quantity they produce (Cournot, Researches into the Mathematical Principles of the Theory of Wealth 1838) or their price (Bertrand, Journals de Savants 1883). In the latter case, all consumers buy from the firm with the lowest price. In the Cournot model, the players produce an equilibrium output quantity based on rationale. In the upgraded framework of Friedman (Review of Economic Studies 1971), with multiple time periods, the players can adjust their quantity in such a way that the monopoly quantity will be produced in the longer run. The folk theorem then states that with more players, more equilibriums are possible.
The original Nash equilibrium (Proceedings of the National Academy of Sciences 1950a, Econometrica b, Annals of Mathematics 1951, Econometrica 1953), in which players do not play weakly dominant strategies, has been refined over time—for example, by putting upper and lower bounds on the optimal output quantity. Nevertheless, the example of the matching pennies game, with no dominant strategy available to the players, shows that the application of rationalization may still be limited in practice.
Contrary to the classical application of game theory, the instrumental view focuses on the usefulness of game theory in application. If we believe that competition forces firms to sell products at marginal costs, the Bertrand model is appropriate. If we believe that the entry of new firms is the key factor, the Cournot equilibrium is more suitable. Assuming that a game has either a finite or an infinite time span affects the players’ behavior. The instrumental view also provides scope for a wider range of alternatives.
Evolutionary game theory assumes that equilibriums are reached as players acquire experience by playing the game for several rounds. By trial and error—a dynamic process—they work toward an equilibrium. Overall, evolutionary game theory results can lead to Nash equilibriums but will not always lead to refinements of Nash equilibriums.
Abstractor’s Viewpoint
Within the science of economics, game theory is usually discussed by using examples and focusing solely on the economic environment. By providing a historical overview, the author shows clearly that within the field of game theory, there are several schools of thought that have developed differently over time. In addition, by using game theory applications based on different sets of principles or assumptions, the author shows that the field is much more heterogeneous than is often perceived. This paper is an excellent way to improve one’s understanding of game theory and how this concept can be developed and applied in the near future.