2. johnf nash entered Princeton University as a young doctoral student in mathematics from 65438 to 0948. His research results can be found in his doctoral thesis Non-cooperative Game (1950). This doctoral thesis contributed to the publication of two papers: equilibrium point (1950) and non-cooperative game (195 1) in n-person game. Nash introduced the difference between cooperative game and non-cooperative game in the above paper. His most important contribution to non-cooperative games is to define a general solution concept that includes any number of people and any preference, that is, it is not limited to two-person zero-sum games. The concept of this solution was later called Nash equilibrium.
3. Nash's main academic contributions are embodied in his two papers 1950 and 195 1. It was only in 1950 that he published his research results in the Monthly Bulletin of the American Academy of Sciences, which immediately caused a sensation. Speaking of it, it all depends on the work of Brother David Gale. Just a few days after being belittled and ridiculed by von Neumann, he met Gail and told him that he had found the promotion method and balance point of von Neumann's "minimum-maximum principle", just like talking in a dream. The fledgling Nash has no idea about the dangers of competition and has never thought about the consequences of academic cheating. So, David Gale acted as his "agent" and drafted a short message to the Academy of Sciences, while Lev Shetz, the head of the department, used the convenient relationship to personally submit the manuscript to the Academy of Sciences. Nash didn't write many articles. He advocated that less is the best. A professor in China asked how many articles to be published in "core journals". According to this standard, Nash may not be qualified.
4. Morris, winner of the Nobel Prize in Economics from 65438 to 0996, did not publish any articles when he was a professor of economics in edgeworth at Oxford University. Special talents should have special selection methods.
5. Nash equilibrium refers to the situation in the game. For each participant, as long as others don't change their strategies, they can't improve their situation. Nash proved that Nash equilibrium must exist on the premise that each player has limited strategy choices and allows mixed strategies. Taking the price war between the two companies as an example, Nash equilibrium means that both parties may lose: under the condition that the other party does not change the price, it can neither raise the price, otherwise it will further lose the market; You can't reduce the price because you will lose money. So the two companies can change the original interest pattern and seek a new interest evaluation and distribution scheme through consultation, that is, Nash equilibrium. Similar reasoning can of course be applied to elections, conflicts of interest between groups, deadlock before the outbreak of potential wars, debates on bills in parliament and so on.
6. Suppose there are n players in the game, and given the strategies of others, everyone chooses their own Nash equilibrium.
7. Optimal strategy (individual optimal strategy may or may not depend on other people's strategies), so as to maximize their own interests. All players' strategies form a strategic outline. Nash equilibrium refers to such a strategic combination, which consists of the optimal strategies of all participants. That is, given other people's strategies, no one has enough reason to break this equilibrium. Nash equilibrium is essentially a non-cooperative game state.
8. Achieving Nash equilibrium does not mean that both sides of the game are in a state of immobility. In sequential games, this equilibrium is achieved in the continuous actions and reactions of players. Nash equilibrium does not mean that both sides of the game have reached the overall optimal state. The following prisoner's dilemma is an example.