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...

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are “strategically equivalent” if, for every player, the payoff differences between two strategies (holding other players’ strategies fixed) are identical. A zero-sum equivalent game is a game that is st...

Abstract We discuss a game theoretic variant of the subset sum problem, in which two players compete for common resource represented by knapsack. Each player owns private set items, pack items alternately, and each either wants to maximize total weight his own packed into knapsack or minimize other player. show that finding best packing strategy against hostile selfish adversary is PSPACE-compl...

Modern game theory was born in 1928, when John von Neumann published his Minimax Theorem. Inter alia, this theorem ascribes to all two-person zero-sum games a value—what rational players should expect to get. Almost 80 years later, strategic game theory has not gotten beyond that initial point, insofar as the basic question of value is concerned. To be sure, we do have equilibrium theories: the...