"Game theory is the study of mathematical models of strategic interactions among rational agents."
The study of strategic interactions between economic agents.
Strategic interactions: A general introduction to the idea of strategic interactions between players in a game.
Nash equilibrium: A concept in game theory that describes a stable state of a game in which no player can improve their payoff by unilaterally changing their strategy.
Dominant strategy: A strategy that is always the best choice for a player, regardless of the other player's strategy.
Mixed strategy: A strategy in which a player randomizes between different pure strategies. This can sometimes lead to a better outcome than playing a pure strategy.
Prisoner's dilemma: A classic example of a non-cooperative game in which two players must decide whether to cooperate or defect. The outcome depends on the strategies chosen by both players.
Coordination games: Games in which players must coordinate their actions in order to achieve a desirable outcome. Examples of coordination games include the Battle of the Sexes and the Stag Hunt.
Iterated games: Games that are played repeatedly between the same players. The outcome of each round can depend on the outcome of previous rounds, and players may be able to learn and adapt their strategies over time.
Evolutionary game theory: A branch of game theory that studies the evolution of strategies in a population of players over time. This can be used to model the spread of behavior in a society or among animals.
Auctions: Games in which players bid on an item or service. Different auction formats, such as English and sealed-bid auctions, can lead to different outcomes.
Market design: The application of game theory to the design of markets, such as auctions or marketplaces. This can involve designing rules and incentives to encourage desirable behavior among buyers and sellers.
"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."