"Game theory is the study of mathematical models of strategic interactions among rational agents."
A general introduction to the idea of strategic interactions between players in a game.
Prisoner's Dilemma: In this scenario, two players are faced with a decision and have to decide whether to cooperate or defect, knowing that their outcome is dependent on the action of the other player.
Nash equilibrium: This refers to a stable state in a game where each player's strategy is optimal given the other player's actions.
Dominant strategy: This occurs when a player's strategy always results in the best outcome, regardless of the other player's actions.
Mixed strategy: This refers to a player's decision to randomize their actions to avoid predictability.
Zero-sum games: This is a scenario where the gain of one player is equal to the loss of the other player.
Sequential games: These are games where each player takes turns making decisions.
Simultaneous games: This is a scenario where both players make their decisions at the same time.
Repeated games: This is a scenario where a game is played multiple times, and each player's strategy may change based on the outcome of the previous game.
Game tree: This is a way of representing the various paths and outcomes of a game.
Social dilemmas: These are situations where individual rationality conflicts with collective rationality.
Evolutionary game theory: This is used to study the evolution of strategies in a population over time.
Mechanism design: This refers to the process of designing a game to achieve a specific outcome.
Stable matching: This is a mechanism design technique that involves matching individuals or groups based on preferences.
Information asymmetry: This is a scenario where one player has more information than the other player, leading to an uneven playing field.
Signaling: This refers to the strategy of sending signals to the other player to influence their decision-making process.
Auctions: This is an example of a mechanism design where a group of individuals bids on an item or service.
Behavioral game theory: This is a field that studies the psychological and emotional factors that affect decision-making in strategic interactions.
Bargaining: This is a scenario where two or more parties negotiate over a specific outcome.
Voting: This is an example of a mechanism where individuals make collective decisions based on their preferences.
Public goods games: These are games where players can choose to contribute to a common resource, but also have the option to free ride.
Prisoner's Dilemma: A common game theory example where two rational individuals make decisions that lead to suboptimal outcomes due to mistrust and lack of cooperation.
Coordination Game: A situation where multiple players have to coordinate their actions to reach a better overall outcome.
Battle of the Sexes: A game where players have different preferences for outcomes, and they align differently when forced to choose.
Chicken: A game where two players are in a head-to-head conflict, and there are two non-colliding options. The last car to swerve loses.
Stag Hunt: A situation where two players can hunt for higher or lower value prey. It's difficult to win if players are not both willing to work together.
Ultimatum Game: A game consisting of two players, one of which must propose a distribution of a resource between them, and the other must either accept or reject the offer.
Dictator Game: A game similar to the Ultimatum Game, but the proposing player faces the choice of keeping everything, dividing it or sharing it entirely.
Trust Game: Imagines two people who do not know each other and have to decide how much they want to trust the other player in a one-off game. What they get back, if anything, depends on how much they invest non-cooperatively.
Auctions: A competitive selling process that awards the product to the highest bidder. Different types of auctions have different bidding methods, prices, and rules.
Market Competition: A game in which multiple players compete for a common opportunity or resource by setting prices. It can also involve a range of new strategic actions, like marketing and public relations, that are not exhibited in some other game models.
"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."