Research On Game Payoff And Nash Equilibrium Selection Based On Information Entropy

Game theory is also called countermeasure theory, and it focuses on the best decision-making at the condition of confliction of the real world with religious mathematics model. Game theory has a wide application, and it has penetrated into economics, politics, sociology, military and artificial intelligence. It is applied into nearly every study field.Game payoff is one of the basic conceptions of game theory. It's the foundation of accounting the players' reward and forming the payoff matrix so as to find the equilibriums. Its precision has a direct effect on the game result. But because of the imperfection of information and the wide use of game theory, it's difficult for us to get a payoff function, and it has caused some handicaps to the application of game theory. As to this issue, this thesis gives a general model to construct game payoff based on information entropy. In this model, we use information entropy to token the risk caused by the general uncertainty of the objective risk, and use the standard deviation to token the risk caused by deviation of risk anticipation. We introduce the conception of player's risk characteristics to combine these two so that we can measure the objective risk effectively. At the foundation of proper risk measurement, we get the game payoff with the yield distribute of risk. And we also give two methods to find the yield distribute of risk.Nash equilibrium is the core conception of game theory. It's the general equilibrium of game result and it's the consistency prediction of the players' best decision. But the multi-equilibriums cause the multi-consistency prediction, and lead the players into an uncertainty of Nash equilibrium selection. As to this issue, this thesis gives a Nash equilibrium selection method based on payoff and risk weighed with information entropy. We first token the uncertainty caused by multi-equilibriums with information entropy. We combine it with standard deviation of the game payoff anticipation so as to weigh the risk caused by multi-equilibriums completely. We then introduce the player's risk characteristics and risk-preferred degree. We combine the risk and payoff properly and adjust the weights of risk and payoff with entropy weight method. Finally, we get the fitness values of each strategy available, so that we can select a proper Nash equilibrium according to the strategy's fitness value. We validate the given method by two game samples, and the result proves it an effective method and way of thought.