Solution concepts for multiple objective n-person games

Multiple criteria decision problems with one decision-maker haven been recognised and discussed in the literature in optimisation theory, operations research and management science. Nevertheless a multiple criteria problem can naturally arise in decision situations involving conflict among n-persons and conflict among the criteria of each person. The corresponding concept with n-decision makers, namely multiple objective n-person games, has not been extensively explored. In this paper we consider several approaches for solving normal form multiple objective n-person games. One of them is to find optimal response strategies. In non-cooperative games, characterised by strategic behaviour and individual rationality, given all other player's strategies, each player may choose a best response as an efficient solution of a vector maximisation problem. Also a best response can be established as a maximin solution. Another approach to solve these games is based on security levels. We present the concept of Pareto optimal security strategies for multiple objective n-person games and explore the relations with the optimal response strategies.