In a symmetric game, every player is identical with respect to the game rules. We show that a symmetric 2strategy game must have a pure-strategy Nash equilibrium. We also discuss Nash’s original paper and its generalized notion of symmetry in games. As a special case of Nash’s theorem, any finite symmetric game has a symmetric Nash equilibrium. Furthermore, symmetric infinite games with compact...

The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. ...

This paper explores the link between status-seeking and the exploitation of a common-property exhaustible resource. The extracted resource is an input in the production of a final good. The other input is man-made capital, which is a second state variable. Extraction requires efforts. Economic agents derive utility not only from absolute consumption, but also from relative consumption, because ...

pricing and advertising are two important marketing strategies in the supply chain management which lead to customer demand’s increase and therefore higher profit for members of supply chains. this paper considers advertising, and pricing decisions simultaneously for a three-level supply chain with one supplier, one manufacturer and one retailer. the amount of market demand is influenced by pri...

In his dissertation of 1950, Nash based his concept of solution to a game on the principles that “a rational prediction should be unique, that the players should be able to deduce and make use of it.” In this paper, we address the issue of when such definitive solutions are possible. We assume player rationality at least as strong as Aumann’s rationality. By formalizing Nash’s reasoning, we sho...

warranty as a kind of service contract today plays a role key in business and legal transactions. in this paper, we present a manufacturer, an agent and a customer's model under different service contracts suggestions. the manufacturer's profit is maximized by determining sale price, warranty period and warranty price. in addition we obtain optimal maintenance cost or repair cost for ...

Sequential game and Nash equilibrium are basic key concepts in game theory. In 1953, Kuhn showed that every sequential game has a Nash equilibrium. The two main steps of the proof are as follows: First, a procedure expecting a sequential game as an input is defined as “backward induction” in game theory. Second, it is proved that the procedure yields a Nash equilibrium. “Backward induction” act...

In this paper, we propose a method of designing energy tax rate based on game theory. Through this method, the effect of energy tax on encouraging manufacturers’ improvement in energy efficiency is enhanced. Consequently policy makers can reduce the average burden of manufacturers brought by energy tax. Through utilizing game theory in a numerical example, we explain the effect of energy tax on...

Here we present a ground-breaking new postulate for game theory. The first part of this postulate contains the axiomatic observation that all games are created by a designer, whether they are: e.g., (dynamic/static) or (stationary/non-stationary) or (sequential/one-shot) non-cooperative games, and importantly, whether or not they are intended to represent a non-cooperative Stackelberg game, the...

We study the supercore of a system derived from a normal form game. For the case of a finite game, we define a sequence of games and show that the supercore coincides with the set of Nash equilibrium strategy profiles of the last game in that sequence. This result is illustrated with the characterization of the supercore for the n-person prisoner’s dilemma. With regard to the mixed extension of...