"Game theory is the study of mathematical models of strategic interactions among rational agents."
It studies the behavior of individuals and groups in strategic situations, where each person's decision-making affects others' outcomes.
Game theory basics: This covers the fundamental concepts of game theory, including the definition of a game, players, strategies, and payoffs.
Nash equilibrium: This refers to the state in which no player can improve their payoff by unilaterally changing their strategy.
Dominant strategy: This refers to the strategy that is best for a player regardless of what the other players do.
Pareto optimal: This refers to a state in which no player can be made better off without making another player worse off.
Prisoner's dilemma: This is a classic example of a non-zero-sum game where two players can either cooperate or defect, often used in game theory to illustrate the tension between individual and group interests.
Mixed strategies: This refers to a strategy that involves randomizing between multiple pure strategies.
Game theory applications: This includes how game theory is used in economics, political science, sociology, psychology, and military strategy.
Evolutionary game theory: This is an extension of game theory that considers how strategies evolve over time in a population of interacting individuals.
Social network analysis: This is an approach that considers how individuals' social connections affect their strategies and outcomes in a game.
Mechanism design: This refers to the process of designing the rules and incentives of a game to achieve a desired outcome.
Bargaining and negotiation: This covers how game theory can be used to analyze bargaining situations and negotiations between individuals or groups.
Game design: This includes the use of game theory principles in designing multiplayer games and online platforms.
Experimental game theory: This is an approach that involves testing game theory predictions in laboratory settings.
Behavioral game theory: This is a subfield of game theory that considers how human behavior often deviates from the assumptions of rationality and self-interest.
Game theory applications in real-world contexts: This includes how game theory has been applied in fields such as auctions, voting, and environmental policy.
Cooperative Game Theory: This type of game theory focuses on situations where players can collaborate to achieve mutual benefit.
Non-Cooperative Game Theory: This type of game theory assumes that players act in their own self-interest and do not collaborate with each other.
Zero-Sum Game Theory: This type of game theory assumes that the gains of one player come at the expense of other players, and that the total gains and losses in the game balance out to zero.
Non-Zero Sum Game Theory: This type of game theory assumes that the gains and losses of the players are not constrained to balance out to zero.
Sequential Game Theory: This type of game theory studies situations where players make decisions in a sequence, with each player taking into account the previous player's choices.
Simultaneous Game Theory: This type of game theory studies situations where players make decisions simultaneously, without knowledge of each other's choices.
Bayesian Game Theory: This type of game theory incorporates uncertainty about the other player's strategies into the model.
Evolutionary Game Theory: This type of game theory studies how game theory applies in situations where the players are evolving or adapting over time.
Mechanism Design Theory: This type of game theory studies how to design mechanisms (e.g., voting systems, auctions) that will achieve desired outcomes in the face of strategic behavior by the players.
"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."