Analysis On Game Equilibrium's Realization And Efficiency Based On Information And Rationality

Equilibrium has been the important part of economics, and is also a core concept of game theories. The development of the equilibrium determimes the basic direction of game theory. Either Neumann max-min equilibrium in zero-sum games or Nash equilirium in general games was firstly put forward according to the assumption of complete rationality, it deviated from the fact of "bounded rationality" . As evolutional game theory develops, we always think that equilirium is achieved in the repeated games by agents with bounded rationality. In a dynamic game, when the interactional factors are in a kind of state that all factors have no tendency to leave, then we call it an equilibrium of the dynamic game. The core of equilirium analysis is to study the state vectors of the dynamic system of repeated game and find the path to reach equilirium.Some systemic research and analysis on factors influencing game equilibrium were done in the thesis. A game includes three essential elements which are game agents, context and signal. And information, rationality , and utility are the basic attributes of a game agent. These factors result in behaviors of agents in the game. The key task of the agents is to study the game context, to make subjective understanding and objective fact continuously close, to improve the rationality continuously, and to obtain the more excellent game effect finally. The description methods of information was discussed. A distributive description method which includes subjects, conditions and probabilities was put forward. And the two-dimension information measure model based on time and space was built up. On the comprehensive analysis on the essence of rationality, a concrete formal method of rationality was built up.Some typical concepts of equilirium based on dominant rationality was put forward. A dominant-strategy equilibrium is realized by dominant rationality. Dominant rationality doesn't equal full rationality. Dominant rationality is a kind of bounded rationality, while full rationality represents a state of idealism. Mutual restrictive equilibrium and mutual benefit equilibrium are the typical concepts on freedom game. Mutual restrictive equilibrium emphasizes "self-actualization" with personal rationality, and inclines to the maximal individual utility, and ignores the effects on self-behaviour from community. So, the game results often run in the opposite direction of the aim at raising agents' utility. This kind of equilibrium based on "personal dominance" usually can not obtain Pareto optimal results. Mutual benefit equilibrium emphasizes on "win-win" and cooperation based on "self-actualization". Mutual restrictive equilibrium and mutual benefit equilibrium are both the accumulation points of game evolution. By dynamic analyzing on multi-states nondegenerate game which has the above two kinds of equilibriums, the thesis studied the reaching path of harmony and equilibriums.Some research on expected equilibrium based on Pareto optimizing was done. Expected equilibrium is an identical expecting on the game equilibrium point from the players in the game or the third parties out of the game. Obviously, an expected equilibrium Pareto dominates Nash equilibrium. Expected equilibrium emphasizes mutual benefits and win-win, it demands each member of game community have an identical expectation towards the expected equilibrium point. To reach the expected equilibrium ,we can use training and learning in the game to make the expectations of all agents identical. Game trainers pass training signals to others by adopting repeated departure behaviour, then make the learners change the knowledge about the game and adopt behaviours in favor of the trainers. While using a game training,we should follow the principle of "self-beneficial, others-beneficial , believable and distinguishable". It is important to scan the whole game environment from the angle of overall situation, to choose a training method that are self-beneficial and others-beneficial,and finally to obtain more excellent training effect. Agents with different rationalities have different understandings on departure behaviours of trainers. Agents with simulating rationality will imitate departure behaviours of trainers, while agents with response-learning rationality will take the best response. Learners with following rationality think the departure behaviours of opponents as an anticipation of game result. If they recognize it and follow, it will bring agents a win-win result better than a free game.Furthermore, research on adopting the third-party filter to realize expected equilibrium was done. In expected equilibrium, the strategy-combined probability is determined by not only personal strategy choices but also restriction from the third-party. When being designed, the third-party filter must ensure to get an equilibrium and to maximize the whole utility. Most importantly, the collective interest should not conflict with personal interests. With the probability distribution of expected equilibrium, a departure of personal behavior from the equilibrium can not gain more utility. Otherwise, the third-party filter will be unfair, and restriction conditions will be unstable and of no effect.At last, the validity of equilibrium based on context, information and rationality was analyzed. Under the different context, all game agents will be subjected to a different restriction and acquire different utility. Under the same context, if the information makes our believes approaching the fact, it will definitely bring more incomes. Of course, obtaining of information may change the game environment, and then influence the effect of information in equilibrium access. The thesis got some useful conclusions by analyzing dynamic equilibrium under different rationalities. Participation of the agents with bounded rationality may lead both parties of the game throw off the game dilemma. But, the repeated game based on the simple imitating or the simple training will not be always effective. As the behaviors of agents affect each other, training strategies must be flexible and not invariable. In the model of IPD, the behaviors of agents with different rationalities also stand for training in essence, because their behaviors imply some expectations for the game.