"Game theory is the study of mathematical models of strategic interactions among rational agents."
A study of mathematical models of conflict and cooperation between intelligent rational decision-makers.
Probability theory: The theoretical framework for calculating the likelihood of events occurring in a game.
Decision theory: The study of decision-making processes, including strategies for maximizing expected outcomes.
Nash equilibrium: A fundamental concept in game theory where each player's strategy is optimal given the strategies of the other players.
Prisoner's dilemma: A classic game demonstrating how rational individuals may choose not to cooperate, despite it being in their best interests.
Iterated prisoner's dilemma: A game scenario where the prisoner's dilemma is played repeatedly among the same group of players, allowing for cooperation to emerge.
Game trees: Graphical representations of decision trees, showing all the possible paths and outcomes in a game.
Zero-sum games: Games where the total gains and losses among players sum to zero, implying that gains for one player correspond with losses for another.
Non-zero-sum games: Games where the total gains and losses among players do not sum to zero, allowing for mutual gains or losses.
Mixed strategies: A strategy that involves randomizing among various pure strategies.
Dominant strategy: A strategy that is optimal regardless of the strategies chosen by other players.
Bayesian games: Games where players have private information that affects their strategies, requiring them to reason about what others might believe about the game.
Stochastic games: Games where the outcome of each move is uncertain, often due to random events.
Correlated equilibria: A solution concept where players coordinate their decisions based on some external signal.
Evolutionary game theory: A framework for modeling and analyzing how game dynamics can lead to the evolution of certain behaviors or strategies.
Cooperative games: Games where players can form coalitions and work together to achieve a common goal.
Normal-Form Games: A type of game where players make decisions simultaneously.
Extensive-Form Games: A type of game where players make decisions sequentially, with each decision depending on the outcome of previous decisions.
Cooperative Games: A type of game where players can form coalitions and work together to achieve a common goal.
Non-Cooperative Games: A type of game where players act independently and do not form coalitions.
Bayesian Games: A type of game where players have incomplete information about the other players' strategies.
Symmetric Games: A type of game where players have the same set of choices and payoffs.
Asymmetric Games: A type of game where players have different sets of choices and payoffs.
Zero-Sum Games: A type of game where one player's gain is another player's loss.
Non-Zero-Sum Games: A type of game where both players can gain or lose.
Simultaneous Games: A type of game where players move simultaneously.
Sequential Games: A type of game where players move sequentially with each decision depending on the outcome of previous decisions.
Repeated Games: A type of game where the same game is played multiple times.
"It has applications in all fields of social science, as well as in logic, systems science, and computer science."
"The concepts of game theory are used extensively in economics as well."
"The traditional methods of game theory addressed two-person zero-sum games."
"Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann."
"Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets."
"Co-written by John von Neumann and Oskar Morgenstern, the book considered cooperative games of several players."
"The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty."
"Therefore, it is evident that game theory has evolved over time with consistent efforts of mathematicians, economists, and other academicians."
"Game theory was developed extensively in the 1950s by many scholars."
"Game theory was explicitly applied to evolution in the 1970s."
"Game theory has been widely recognized as an important tool in many fields."
"With the Nobel Memorial Prize in Economic Sciences going to game theorists Paul Milgrom and Robert B. Wilson, fifteen game theorists have won the economics Nobel Prize."
"John Maynard Smith was awarded the Crafoord Prize for his application of evolutionary game theory."
"Fifteen game theorists have won the economics Nobel Prize."
"Game theory is used in all fields of social sciences."
"Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets."
"Oskar Morgenstern co-wrote the book with John von Neumann."
"The second edition provided an axiomatic theory of expected utility."
"Game theory has evolved over time with consistent efforts of mathematicians, economists, and other academicians."