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Can game theory help in negotiations and resolution of interstate conflicts? How has regulation based on the Prisoner's Dilemma contributed to the fight against cartels in Europe? Why is it important to take into consideration future interactions for the game’s outcome? These and other questions were discussed in a recent episode of the "Economics Out Loud" podcast with NES Professor Sergei Izmalkov. GURU shares a summary of the episode.
The interaction of people, companies, and states can be represented as a type of game with participants simultaneously trying to achieve their goals by choosing the optimal strategy. Therefore, we can say that game theory deals with fundamental life issues.
People have been thinking for centuries about ways to formalize a person's choice in various situations. In the 1920s, mathematician Emile Borel was one of the first to describe the concept of strategy as a plan of action for arbitrary situations. Any situation can be viewed as a model, i.e. a game where each player has a set of strategies and each pair of strategies can bring players certain rewards.
In 1944, mathematician John von Neumann and economist Oskar Morgenstern published the book Theory of Games and Economic Behavior, which became the cornerstone of formal analysis in game theory. Neumann and Morgenstern showed that for any zero-sum game, it is mathematically possible to find a solution – an equilibrium in which both players can adhere to an optimal strategy for themselves.
In zero-sum games, one player's gain is equivalent to another’s loss. Zero-sum games were actively used to analyze military conflicts, and there appeared a large number of papers on this topic.
However, military conflicts are in fact games with a non-zero sum. Losses are most often borne by both sides, while in zero-sum games, the loss of one side must be equal to the gain of the other. A nuclear confrontation between the United States and the USSR would also be a non-zero-sum game, because when using nuclear weapons, both sides were threatened with mutual destruction.
In games with a non-zero sum, it is also always possible to come to an equilibrium. This was proved by the famous mathematician and a Nobel Prize winner in Economics John Nash, whose biography became the basis of the Beautiful Mind film. The Nash equilibrium is a situation where it is disadvantageous for each of the players to deviate from their strategy while the behavior of the other remains unchanged.
Game theory remains the only way to analyze strategic interactions and is actively applied in practice. For example, European and American antitrust authorities used to fight against cartels employing a method based on the famous Prisoner's Dilemma, in which prisoners choose between a cooperative strategy and an egoistic one. Firms involved in a cartel were offered exemption from fines if they were the first to tell the authorities about the cartel. The rest of the participants in the collusion were to be punished. When there was no guarantee of exemption from fines, it was easier for firms to maintain a collusion, but the introduction of exemptions for the first company to disclose the cartel changed the whole nature of the interaction of cartel participants.
Many interactions in the real world can be described with the Prisoner's Dilemma, where the optimal strategy is non-cooperative, i.e. betrayal. But that is true only for a static game, one in which a single decision is made by each player. If the game is dynamic, one in which players move sequentially or repeatedly, then the nature of interaction may change: cooperation becomes the optimal strategy if players value future interaction.
In economies with inefficient institutions, people and firms often do not value future interactions due to high uncertainty. And vice versa: the lower the uncertainty, the more valuable the future interaction is and the easier it is to maintain cooperative rather than selfish, individual strategies. This is very important for investments – both corporate and personal, for example, in human capital. Reducing uncertainty is a task for the state, which must guarantee the protection of property rights and an effective judicial system.
