For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value ind...

An impartial game is called (strongly) miserable if its normal and misère versions differ just slightly; more precisely, if some (all) zeros and ones of the Sprague-Grundy (SG) functions swap, while all larger values remain the same. We obtain necessary and sufficient conditions for (strong) miserability and show that NIM, Wythoff’s NIM, and game Euclid are miserable but not strongly miserable,...

In this article we consider zero and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, under suitable assumptions show that game has value. We also establish existence of stationary saddle point equilibrium. Nash

We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player’s priority value satisfies a weak dynamic programming principle and thus solves the associated fully non-linear partial differential equation in the viscosity sense.

A coupling game is a new model for partly cooperative and partly non-cooperative games. This paper describes benefits that result when coupling rational cooperation, under some situations, is increased. We prove that if a coupling game is strictly rational and partly cooperative, the higher the coupling factors, the larger the social payoff, which is the sum of the payoffs of all players. Other...

We analyze a Colonel Blotto game in which opposing parties have di¤ering relative intensities (i.e. the game is non-zero sum). We characterize the colonels’ payo¤s that sustain a pure strategy equilibrium and present an algorithm that reaches the equilibrium actions (when they exist). Finally we show that the set of games with a pure strategy equilibria is non-empty. JEL Classi…cation: C72, D7,...

We examine experimentally how humans behave when they, unbeknownst to them, play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects’ play was consistent with their Nash equilibrium strategy. But a larger percentage of subjects’ play was more consisten...