Ambiguous Game Models Based on Nonadditive Probabilities for Decision Forecast in Real Conflict Situations

Although traditional game theory has put an important role in economics, it is often blamed for its weak descriptions and analyses in real-world conflicts mainly for its complete rationality presumptions. Thus it is difficult to forecast the players´ strategy selection and the outcomes in real conflict situations, the field which the authors named as decision forecast. We introduce nonadditive probabilities into modeling of ambiguous games, which aims to describe players´ attitude of ambiguity-aversion in strategy selections in real conflict situations. We present a payoff function which can be considered as a balance of v-N-M utility and max-min decision criterion, and introduce it into modeling of an ambiguous game in strategic form. And then, we show the existence of equilibrium under such payoffs. We also introduce nonadditive probabilities into two-phase extensive games and give diagrammatic representations of an ambiguous game tree.