in this paper, a new approach based on game theory has been proposed to multi responses problem optimization. game theory is a useful tool for decision making in the conflict of interests between intelligent players in order to select the best joint strategy for them through selecting the best joint desirability. present research uses the game theory approach via definition of each response as ...

Mean field games are concerned with the limit of large-population stochastic differential where agents interact through their empirical distribution. In classical setting, number players is large but fixed throughout game. However, in various applications, such as population dynamics or economic growth, can vary across time and this may lead to different Nash equilibria. order account for evolu...

In this paper we consider a class of hybrid stochastic games with the piecewise openloop information structure. These games are indexed over a parameter ε which represents the time scale ratio between the stochastic (jump process) and the deterministic (differential state equation) parts of the dynamical system. We study the limit behavior of Nash equilibrium solutions to the hybrid stochastic ...

We study learning in finitely repeated 2× 2 normal form games, when players have incomplete information about their opponents’ payoffs. In a laboratory experiment we investigate whether players (a) learn the game they are playing, (b) learn to predict the behavior of their opponent, and (c) learn to play according to a Nash equilibrium of the repeated game. Our results show that the success in ...

Vehicle routing problem is one of the most important issues in transportation. Among VRP problems, the competitive VRP is more important because there is a tough competition between distributors and retailers. In this study we introduced new method for VRP in competitive environment. In these methods Two-Person Nonzero Sum games are defined to choose equilibrium solution. Therefore, revenue giv...

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a twoparameter family of max–min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point fe...

In this article, we study the convergence of Nash equilibria in an -player differential game towards optimal strategies mean field games when dynamic generic player includes a reflection process which guarantees invariance state space . The well-posedness master equation allows us to use its solution order construct finite-dimensional projections , will satisfy for almost surely, where is system.

Traditional DEA method is improper for supplier evaluation and selection, as it adopts varying weights in evaluation, and fails to consider competition among the suppliers. In order to solve these two problems, Nash bargaining game DEA model is applied to supplier evaluation in present paper. However, there is a non-uniqueness problem with Nash bargaining game efficiency of supplier in existing...

We consider finite number of users, with infinite buffer storage, sharing a single channel using the aloha medium access protocol. This is an interesting example of a non saturated collision channel. We investigate the uplink case of a cellular system where each user will select a desired throughput. The users then participate in a non cooperative game wherein they adjust their transmit rate to...

We extend the classical transportation problem from linear optimization and introduce several competing forwarders. This results in a noncooperative game which is commonly known as generalized Nash equilibrium problem. We show the existence of Nash equilibria and present numerical methods for their efficient computation. Furthermore, we discuss several equilibrium selection concepts that are ap...