"Game theory is the study of mathematical models of strategic interactions among rational agents."
The study of strategic interaction among individuals, with the goal of predicting and understanding their behavior.
The basic concepts of game theory: Game theory is the study of decision-making in strategic situations. It is a mathematical theory that focuses on predicting outcomes and understanding the behavior of players in strategic interactions.
The Nash equilibrium: The Nash equilibrium is a concept in game theory that describes a situation in which each player's strategy is optimal, given the strategies of the other players.
Prisoner's dilemma: Prisoner's dilemma is a game in game theory that illustrates why two completely rational individuals might not cooperate, even if it appears that it is in their best interest to do so.
Dominant strategies: A dominant strategy is a strategy that is better than any other strategy for a player, regardless of what the other players do.
Coordination games: Coordination games are games in which players must coordinate their actions, and the players' payoffs depend on whether they coordinate successfully or not.
Repeated games: Repeated games are games that are played over and over again, either with the same players or with different players each time.
Bayesian games: Bayesian games are games in which the players have incomplete information about the game, and they must make decisions based on their beliefs about the game.
Voting theory: Voting theory is the study of how voting systems work and their properties. It includes topics such as the Condorcet paradox, Arrow's impossibility theorem, and the median voter theorem.
Social choice theory: Social choice theory is the study of how individual preferences can be aggregated to form a group decision. It includes topics such as the Gibbard–Satterthwaite theorem, the Muller-Satterthwaite theorem, and the theory of judgment aggregation.
Auction theory: Auction theory is the study of how auctions work and the properties of different auction formats. It includes topics such as the winner's curse, the revenue equivalence theorem, and the Vickrey auction.
Prisoner's Dilemma: A classic game where two suspects are interrogated separately and must decide whether to cooperate with each other or betray each other to the police.
Chicken: A game where two drivers are approaching each other in their cars and must decide whether to swerve or continue driving straight ahead.
Hawk-Dove: A game where two animals are fighting over a resource and must decide whether to fight or back down.
Ultimatum: A game where one player makes an offer to another player, and the second player must decide whether to accept the offer or reject it.
Bargaining: A game where two parties are negotiating a deal and must decide on the terms of the agreement.
Matching Pennies: A game where two players simultaneously reveal a coin and must guess whether the other player will flip heads or tails.
Cournot: A game where two firms are producing a product and must decide how much to produce, knowing that their profit depends on the other firm's production level.
Bertrand: Like Cournot, but with firms setting prices instead of quantities.
Stackelberg: A game where one player, the leader, chooses their action first and the other player, the follower, chooses their action second.
Public Goods: A game where individuals must decide how much to contribute to a public good, knowing that they will benefit from it regardless of their own contribution level.
Tragedy of the Commons: A game where individuals must decide how much to use a shared resource, knowing that their use depletes the resource for everyone.
Voting: A game where individuals must decide how to cast their vote, knowing that their preferred outcome may not always win.
"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."