This study proposes a novel way to deal with uncertainty in two-person zero-sum matrix game payoffs expressed as fuzzy rough numbers. Complete and reasonable solutions these types of games are obtained. In this research we develop two linear programming models upper lower approximation intervals numbers handle multi-objective crisp by incorporating trapezoidal payoffs. To provide each opponent ...

Recognise that people have many, possibly conflicting, aspects to their personality. We hypothesise that each separate characteristic of a personality may be treated as an independent player in a non-zero sum many player game. This idea is applied to the two person Prisoners’ Dilemma as an introductory example. We assume each prisoner has a “mercenary” characteristic as well as an “altruistic” ...

Two players engage in a repeated game with incomplete information on one side, where the underlying stage-games are zero-sum. In the case where players evaluate their stage-payoffs by using different discount factors, the payoffs of the infinitely repeated game are typically non zero-sum. However, if players grow infinitely patient, then the equilibrium payoffs will sometimes approach the zero-...

We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game—a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically equivalent to a common interest game. We present a unified framework applicable for both potential and zero-sum equivalent games by deriving a simple but useful char...

We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in [4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementi...

Abstract. A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott–Kalton, we prove the existence ...

We concentrate on discussing a class of two-person zero-sum games with rough payoffs. Based on the expected value operator and the trust measure of rough variables, the expected equilibrium strategy and r-trust maximin equilibrium strategy are defined. Five cases whether the game exists r-trust maximin equilibrium strategy are discussed, and the technique of genetic algorithm is applied to find...

We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart 2014). These are Colonel Blotto type games in which the players have capacity constraints. We consider the game with non-strict constraints, and with strict constraints. We show in most cases that when optimal strategies exist, they are necessarily unique. When they don’t exist, we characterize the ...

In 1951, Dantzig showed the equivalence of linear programming problems and two-person zerosum games. However, in the description of his reduction from linear programs to zero-sum games, he noted that there was one case in which the reduction does not work. This also led to incomplete proofs of the relationship between the Minimax Theorem of game theory and the Strong Duality Theorem of linear p...

We consider dynamic electromagnetic evasion-interrogation games where the evader can use ferroelectric material coatings to attempt to avoid detection while the interrogator can manipulate the interrogating frequencies to enhance detection. The resulting problem is formulated as a two-player zero-sum dynamic differential game in which the cost functional is based on the expected value of the in...