Mixed-Motive Games: An Overview
Abstract
Mixed-motive games are games in which multiple players interact and the outcome of the game is the result of the players’ decisions and strategies. This article provides an overview of the concept of mixed-motive games, their associated game theory, and their applications. The article also provides an overview of the literature surrounding mixed-motive games and provides examples of research that has been conducted in this area.
Introduction
Mixed-motive games, also known as games with multiple objectives, are game scenarios in which multiple players interact and the outcome of the game is the result of the players’ decisions and strategies. In a mixed-motive game, players are motivated to maximize their own gain while also taking into account the goals of other players. The concept of mixed-motive games has been studied in game theory since the 1950s (von Neumann & Morgenstern, 1953). This article provides an overview of the concept of mixed-motive games, their associated game theory, and their applications.
Game Theory and Mixed-Motive Games
Game theory is a mathematical framework used to analyze the interactions between players in a game. In game theory, a game is defined as a set of strategies and a set of payoffs or rewards that a player receives for selecting a particular strategy. In a mixed-motive game, players are motivated to maximize their own gain while taking into account the goals of other players. This type of game can be modeled as a non-cooperative game with multiple objectives.
In a non-cooperative game with multiple objectives, each player chooses a strategy based on their own preferences and the preferences of all other players. This type of game can be solved using a variety of game-theoretic techniques, such as Nash equilibria, Pareto optimality, and cooperative game theory (von Neumann & Morgenstern, 1953; Luce & Raiffa, 1957; Nash, 1950).
Applications of Mixed-Motive Games
Mixed-motive games have been used to model a variety of real-world scenarios, including negotiations, auctions, and pricing decisions (Hofbauer & Sigmund, 1998). In particular, mixed-motive games have been used to model the behavior of firms in oligopolistic markets (Fudenberg & Tirole, 1991). Mixed-motive games have also been used to model the behavior of political actors, such as countries in international relations (Fearon, 1995).
Conclusion
This article provided an overview of the concept of mixed-motive games, their associated game theory, and their applications. Mixed-motive games have applications in a variety of fields, including economics, politics, and international relations. The literature surrounding mixed-motive games is vast and varied, and the examples provided in this article are just a small sample of the research that has been conducted in this area.
References
Fearon, J. D. (1995). Rationalist explanations for war. International Organization, 49(3), 379-414.
Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge, MA: MIT Press.
Hofbauer, J., & Sigmund, K. (1998). Evolutionary game theory. Cambridge, MA: MIT Press.
Luce, R. D., & Raiffa, H. (1957). Games and decisions. New York, NY: Wiley.
Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48-49.
von Neumann, J., & Morgenstern, O. (1953). Theory of games and economic behavior. Princeton, NJ: Princeton University Press.