Methods for Solving the Game against Nature with Vector Payoffs

벡터이득 대자연게임의 해법

The traditional theories of games are based on an assumption that the payoffs have a single dimension. In reality, any alternative is likely to imply more than one payoff. This paper deals with the game against nature with vector payoffs. The purpose of this paper is to develop methods for finding the practical optimal strategy in the game against nature with vector payoffs. Under the assumption that a prior probability over the stats of nature is given, this paper shows that a practical optimal strategy in this game can be obtained by applying a entropy method in order to assess the payoff weight and by employing the concept of compromise solutions in order to reduce the non-dominated solutions. When subjective payoff weights are unknown as well as known, these methods can be used. A numerical example is given.