A game theory brief
Game theory is a branch of economics that focuses on individuals of a competitive or confrontational nature, on the various behaviours that arise under specific rules. Game theory focuses on the expected and actual behaviour of individuals in a game, and on its best strategies
In general, game theory is about how many players play in a game choose a strategy
Basic concepts
This section will briefly describe some of the common concepts in the game theory
Cooperation/non-cooperative games
Cooperative game is a game where participants can form alliances and work together. In such games, individual non-cooperation is often punished by some external mechanismThere is no such mechanism, so participants are either unable to form alliances or rely on credible threat mechanisms to maintain cooperation
Research on uncooperative games is more systematic and mature than cooperative games. All the games discussed here are uncooperative games
Symmetric/asymmetric game
In symmetric game, the proceeds of the same conduct are the same for different participants, i. E. The proceeds depend only on the act itself and not on the identity of the actor ... The game that does not meet this condition is called asymmetric game
Zero-sum/non-zero-sum game
Main page: zero sum game
Zero-sum game means that regardless of the behaviour of each party, the total proceeds of all participants are always zero. The usual zero-sum game discussed involves two participants, at which point the proceeds of one side must necessarily be the losses of the other.... Relatively, non-zero-sum game allows multiple wins or losses, including positive-sum game and negative-sum game
Concurrent/sequencing process
In simultaneous games, all participants make decisions without knowing what others choose. Rock and paper, for example, is a classic simultaneous game. This type of game is often expressed in a revenue matrix and usually does not involve the concept of time
In contrast, the sequence game, the participants act in sequence. It needs to be noted that the latter can observe at least the behaviour of some of the first actors, otherwise the sequence will be meaningless
Perfect/imperfect information game
Perfect information means that participants are fully aware of all previous events, including the initial state of the game, when they make decisions at any given time. The perfect information is usually used to describe a sequenced game; because the players are not aware of each other's actions at the same time, it is generally assumed that the simultaneous game is not a perfect information game
Full/incomplete information game
Complete information means that all participants have a complete understanding of the game structure itself (including options for decision-making and ultimate benefits) and that this information is public knowledge. In contrast, there are incomplete information games, some of which are unknown to participants (e. G. Optional decision-making or profit function of the opponent)
It's worth noting that "full information" and "perfect information" are two separate concepts that do not cover each other. For example, mahjongg is a game of complete information but not perfect information because its rules and benefits are open, but card information is not transparent; and some games with hidden objectives but full public behaviour are games of perfect information but not complete information
Combining game theory
In algorithm competitions, the most common type of game is a combination game. The term usually refers to games that are difficult to solve because of their huge state. Because of the complexity of the usual combination game, the combination theory focuses on the following types: two-person rotation, perfect information, non-random games, chess, chess, and so on
Fair combination game
Main page: fair group game
Fair game is a combination game that meets the following conditions:
Fair play is always symmetrical
Unfair mix game
Main page: unfair combination game
The concept of a fair game is an unfair game, in which the participants depend on their identity for what they can do in a given situation. Most chess games (such as chess, chinese chess, chess, five pieces of chess, etc.) are unfair games because participants can only operate their own pieces
Normal/unusual game
In combination games, the usual winner is the last player to take action before the game ends. It's called normal game. It's corresponding to an abnormal game, where the last player to take action is a loser
Fair and unfair combinations can be normal or abnormal
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