In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6], we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we sha...

We consider an inventory competition game between two firms. The question we address is this: If players do not know the opponent’s action and opponent’s utility function can they learn to play the Nash policy in a repeated game by observing their own sales? In this work it is proven that by means of Maximum A Posteriori (MAP) estimation, players can learn the Nash policy. It is proven that pla...

Game theory is the study of mathematical models and cooperation between intelligent rational decision-makers. This paper provides a flexible model to calculate pay-off matrix based on several importance factors. This model is adapted by cooperative game and developed for some competitive advantages sections in pharmaceutical industry. An optimum solution is derived by considering Nash equilibri...

This is an extended write-up of a lecture introducing the concept of Nash equilibrium in the context of an auction-type game which one can observe being played by “ordinary people” in real time. In a simplified model we give an explicit formula for the Nash equilibrium. The actual game is more complicated and more interesting; players place a bid on one item (amongst several) during a time wind...

(2) NASH EQUILIBRIUM Nash Equilibrium is a solution of a game or a condition in a game involving two or more players, in which no player has anything to gain by changing only his own strategy unilaterally, i.e. no player can benefit by changing his strategy while the other players keep their strategies unchanged. The set of strategy choices and the corresponding payoffs (benefits or rewards) co...

In this paper we study boolean game with prioritized norms. Norms distinguish illegal strategies from legal strategies. Notions like legal strategy and legal Nash equilibrium are introduced. Our formal model is a combination of (weighted) boolean game and so called (prioritized) input/output logic. After formally presenting the model, we use examples to show that non-optimal Nash equilibrium ca...

We study the properties of finitely complex, symmetric, globally stable, and semi-perfect equilibria. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the ...

The generalized Nash equilibrium is a Nash game, where not only the players’ cost functions, but also the constraints of a player depend on the rival players decisions. We present a globally convergent algorithm that is suited for the computation of a normalized Nash equilibrium in the generalized Nash game with jointly convex constraints. The main tool is the regularized Nikaido-Isoda function...

In the paper we consider a class of differential games with continuous updating random information horizon. It is assumed that at each time instant, players have about game (motion equations and payoff functions) for interval length theta as evolves updates. We first considered this type in 2019. Here additionally assume variable. The subject current definition Nash equilibrium based solution c...

In another paper with the same name[1], we proposed a new representation of Game Theory, but most results are given by specific examples and argument. In this paper, we try to prove the conclusions as far as we can, including a proof of equivalence between the new representation and the traditional Game Theory, and a proof of Classical Nash Theorem in the new representation. And it also gives m...