Albin Elmfeldt: Militär tillämpning av matematisk spelteori

Abstract.

This paper presents and formulates key concepts and theorems in game theory. Thereafter, these concepts and theorems are applied to three different strategic games with military themes, this is to show how strategic games can help us understand military conflicts at a strategic level. The focus of the paper is mainly on utility functions, strategic games, and Nash equilibrium. The paper examines both pure and mixed strategies and the differences between these. Within the framework, the Nash Theorem is formulated and proven, the theorem declares under what conditions it is possible to find a Nash equilibrium. A Nash equilibrium is a situation in a strategic game where a player has nothing to win by changing his strategy in case no other player changes their strategy.

In the paper, two strategic games are formulated to exemplify the game theoretic concepts. These games are Prisoners Dilemma and Matching Pennies. The military application is made with three games: The Arms Race, The War of Attrition, and a version of Contribution to a public good. Nash equilibria are investigated in these games. One conclusion is that game theory can help us illustrate military dilemmas. However, military situations are often complex and therefore, it is difficult to embrace all different preferences and quantify different results to a utility function that should represent different results in a military conflict. Instead, the games presented are overly simplified and do not provide much assistance in military decision-making.