War and Peace
Prize Lecture, December 8, 2005
By Robert J. Aumann
Center for the Study of Rationality, and Department of Mathematics, The
Hebrew University, Jerusalem, Israel
Summarized by Sandro Zolezzi
The lecture suggests that instead of focusing on resolving specific conflicts, efforts should be made to study war as a general phenomenon in order to understand it defining characteristics and common denominators. The concept of rationality is defined as a person's behavior being in their best interests given their information. It is argued that war can be rational because it may serve the best interests of certain parties involved.
An economic analysis of war is proposed, focusing on the incentives that lead to war and building incentives that prevent war. It is suggested that disarmament may not always be the best approach to preventing war, as demonstrated by the example of the cold war.
The theory of repeated games is discussed as a way to model long-term interactions and explain phenomena such as altruism, cooperation, trust, revenge, and threats. It is argued that repetition enables cooperation and can lead to the emergence of cooperative outcomes in equilibrium.
The concept of the Folk Theorem is introduced, which states that cooperative outcomes of a game coincide with the equilibrium outcomes of its supergame. The Perfect Folk Theorem is also mentioned, which extends this idea to perfect equilibrium outcomes. The core outcomes of a game are shown to coincide with the strong equilibrium outcomes of its supergame.
The relationship between repeated games and cooperation is that repetition enables cooperation. In a one-time game, where players interact only once, it may not be in their best interest to cooperate because there are no future consequences for their actions. However, in a repeated game, where players interact multiple times, cooperation becomes more feasible.
Repetition provides an enforcement mechanism for cooperation. Players are more likely to cooperate in a long-term relationship because they know that their actions in the present will have consequences in the future. They understand that inappropriate behavior will be punished in subsequent stages of the game.
In repeated games, players can use strategies that involve punishments or rewards based on the other player's behavior. For example, if one player deviates from a cooperative outcome, the other player can punish them by deviating as well, leading to a worse outcome for both. This threat of punishment acts as a deterrent and encourages players to cooperate.
The concept of strategic equilibrium is crucial in repeated games. Players are said to be in strategic equilibrium when their actions and plans are rational given the actions and plans of the other players. In this equilibrium, cooperation can be achieved and maintained over time.
Overall, repetition in games provides the opportunity for players to establish trust, build a reputation, and develop a long-term relationship that encourages cooperation. It allows for the emergence of cooperative outcomes that may not be achievable in a one-time game.
The core concept in cooperative game theory is the notion of the "core." The core represents a set of outcomes in a cooperative game where no subset of players can improve their individual outcomes by forming a coalition and deviating from the agreed-upon outcome.
In other words, the core is a solution concept that captures the idea of stability and fairness in cooperative games. It ensures that no group of players has an incentive to break away from the agreed-upon outcome and form a new coalition to achieve a better outcome for themselves.
The core is defined by a set of outcomes that satisfy two conditions:
Feasibility: The outcome must be feasible, meaning that it is possible to achieve through cooperation among the players. It represents a distribution of the total payoff or resources among the players.
Non-emptiness: The core must not be empty, meaning that there exists at least one outcome that is acceptable to all players and no coalition can improve upon it.
The core concept is particularly relevant in situations where players can form coalitions and negotiate agreements to distribute the benefits or costs of cooperation. It provides a benchmark for evaluating the fairness and stability of outcomes in cooperative games.
It is important to note that the core is not always guaranteed to exist in every cooperative game. In some cases, the core may be empty, indicating that no stable and fair outcome can be achieved through cooperation. In such situations, alternative solution concepts, such as the Shapley value or the nucleolus, may be used to determine a reasonable distribution of payoffs among the players.
The author suggests a shift in efforts to bring about world peace by focusing on studying war as a general phenomenon, rather than solely focusing on resolving specific conflicts. The author argues that while resolving specific conflicts is important and laudable, studying war as a general phenomenon can provide insights into its defining characteristics, common denominators, and differences. This includes studying war from historical, sociological, psychological, and rational perspectives.
The author draws a comparison to the field of cancer research, where there are two approaches: clinical and basic science. The clinical approach focuses on treating individual cases of cancer based on clinical tests and information, while the basic science approach aims to understand the underlying processes and mechanisms of cancer. The author suggests applying a similar approach to war, where efforts should be made to understand the reasons behind why wars occur and the rationality behind human decision-making in conflicts.
By studying war as a general phenomenon, the author believes that a deeper understanding of its causes and dynamics can be gained. This understanding may eventually lead to more effective strategies and policies for preventing and resolving conflicts, contributing to the achievement of world peace. The author emphasizes the importance of approaching war as a subject of scientific inquiry, similar to how infectious diseases were studied by scientists like Louis Pasteur and Robert Koch, which eventually led to significant advancements in disease treatment and prevention.
The relationship between repeated games and war lies in the insights that repeated game theory can provide into the dynamics of long-term interactions and the potential for cooperation or conflict.
Repeated games model situations where players engage in a series of interactions over time, allowing for the possibility of learning, reputation building, and the establishment of norms of behavior. These games can capture the essence of ongoing conflicts, such as wars, strikes, or other interactive situations.
One key insight from repeated game theory is that repetition enables cooperation. In the context of war, this means that when conflicts are viewed as a series of repeated interactions, there is a greater potential for cooperation and the emergence of peaceful outcomes. Players are more likely to adopt cooperative strategies when they recognize that there is a future and that their actions will have consequences.
The theory of repeated games suggests that cooperation can be achieved through the threat of punishment. Players who deviate from cooperative behavior can be punished in subsequent stages of the game, creating incentives for them to maintain cooperation. This idea is similar to the concept of mutually assured destruction (MAD) during the Cold War, where the threat of nuclear retaliation acted as a deterrent to prevent hot war.
However, the success of cooperation in repeated games depends on the discount rate, which represents how much players value immediate gains compared to future gains. If the discount rate is too high, players may prioritize short-term benefits over long-term cooperation, making it difficult to sustain peaceful outcomes.
It is important to note that the relationship between repeated games and war is not a direct one-to-one correspondence. Repeated game theory provides insights into the potential for cooperation and the dynamics of long-term interactions, which can be applied to understand the possibilities for peaceful resolutions in conflicts, including wars. By studying repeated games, researchers can gain a deeper understanding of the factors that influence cooperation and conflict in war-like situations, and potentially develop strategies to promote peace and prevent future conflicts.
