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Game theory is the study of mathematical models of strategic interactions among rational agents. [1] It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science. [2] Traditional game theory addressed two-person zero-sum games, in which a participant's gains or ...
- List of Games in Game Theory
Sequential game: A game is sequential if one player performs...
- Game Theory (Disambiguation)
Game theory is the study of participants' behavior in...
- Rational Agents
A rational agent or rational being is a person or entity...
- Evolutionary Game Theory
Evolutionary game theory (EGT) is the application of game...
- Cooperative Game Theory
In game theory, a cooperative game (or coalitional game) is...
- Nash Equilibrium
In game theory, the Nash equilibrium, named after the...
- John Von Neumann
John von Neumann (/ v ɒ n ˈ n ɔɪ m ən / von NOY-mən;...
- Congestion Game
Congestion games (CG) are a class of games in game...
- Mathematical Models
A mathematical model is an abstract description of a...
- Waldegrave Problem
In probability and game theory, the Waldegrave problem...
- List of Games in Game Theory
Game theory. Game theory is the study of how and why people make decisions. [1] [2] [3] (Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".) [4] It helps people understand parts of science and politics. An alternative term suggested "as a more descriptive name for the ...
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Sep 6, 2018 · A "game" in game theory is a fully explicit structure which characterizes each player's set of actions, payoffs and possible outcomes under given rules of playing. Given this conditions, rational players act in such a way, that they maximize the expected value of their von Neumann-Morgenstern Utility. Games provide a simplified world within ...
- Strategy Set
- Pure and Mixed Strategies
- Mixed Strategy
- Behavior Strategy
- See Also
A player's strategy setdefines what strategies are available for them to play. A strategy profile is a list of strategy sets, ordered from most to least desirable. A player has a finite strategy set if they have a number of discrete strategies available to them. For instance, a game of rock paper scissorscomprises a single move by each player—and e...
A pure strategy provides a complete definition of how a player will play a game. Pure strategy can be thought about as a singular concrete plan subject to the observations they make during the course of the game of play. In particular, it determines the move a player will make for any situation they could face. A player's strategy setis the set of ...
Illustration
In a soccer penalty kick, the kicker must choose whether to kick to the right or left side of the goal, and simultaneously the goalie must decide which way to block it. Also, the kicker has a direction they are best at shooting, which is left if they are right-footed. The matrix for the soccer game illustrates this situation, a simplified form of the game studied by Chiappori, Levitt, and Groseclose (2002).It assumes that if the goalie guesses correctly, the kick is blocked, which is set to t...
Significance
In his famous paper, John Forbes Nash proved that there is an equilibrium for every finite game. One can divide Nash equilibria into two types. Pure strategy Nash equilibria are Nash equilibria where all players are playing pure strategies. Mixed strategy Nash equilibria are equilibria where at least one player is playing a mixed strategy. While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a...
Interpretations of mixed strategies
During the 1980s, the concept of mixed strategies came under heavy fire for being "intuitively problematic", since they are weak Nash equilibria, and a player is indifferent about whether to follow their equilibrium strategy probability or deviate to some other probability. Game theorist Ariel Rubinstein describes alternative ways of understanding the concept. The first, due to Harsanyi (1973), is called purification, and supposes that the mixed strategies interpretation merely reflects our l...
While a mixed strategy assigns a probability distribution over pure strategies, a behavior strategy assigns at each information set a probability distribution over the set of possible actions. While the two concepts are very closely related in the context of normal form games, they have very different implications for extensive form games. Roughly,...
Jun 2, 2003 · This is where the modern mathematical theory of games comes into play. Games such as heads-tails and stone-paper-scissors are called two-person zero-sum games. Zero-sum means that any money Player ...
Jan 25, 1997 · Game Theory. First published Sat Jan 25, 1997; substantive revision Sun Sep 3, 2023. Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents.
