"Game theory is the study of mathematical models of strategic interactions among rational agents."
The study of strategic decision-making in situations where the outcome depends on the behavior of others.
Nash Equilibrium: A concept in game theory that refers to the optimal outcome in a game where each player chooses their strategy based on what they think the other players will do.
Prisoner's Dilemma: A classic example of a game in which two people may each betray the other, resulting in a worse outcome for both than if they had cooperated, known as the "Nash Equilibrium".
Dominant Strategies: A strategy that is the best choice for a player, regardless of what the other player does.
Pareto Efficiency: A state of a game in which it is impossible to improve one player's payoffs without making the payoffs of another player worse off.
Zero-Sum Games: A type of game in which one player's gain is always equal to another player's loss.
Cooperative Games: A type of game in which players can form coalitions and work together to achieve a goal.
Repeated Games: A game that is played over and over again, where past actions may influence future outcomes.
Information Asymmetry: A situation in which one player has more information than another player.
Auctions: A game in which potential buyers bid on an item, with the highest bid winning the item.
Behavioral Game Theory: A branch of game theory that studies how people actually make decisions in social situations.
Social Choice Theory: A theory that studies how to aggregate individual preferences to make a collective decision.
Bayesian Games: A type of game in which some of the players have incomplete information and must make guesses about what other players know or believe.
Evolutionary Games: A type of game in which strategies change over time based on their success in the past.
Game Theory Applications: A practical implementation of game theory to decision-making in various fields including economics, politics, law and even biology.
Payoff Matrix: A table presenting the potential payoffs of outcomes for each player based on their possible strategies.
Dominant Strategy: A strategy that's always the most profitable for a player regardless of their opponent's actions.
Nash Equilibrium: A condition in which each player's strategy is optimal given the strategies of the other players.
Prisoner's Dilemma: An imbalanced situation in which the best strategy for both players contradicts their own self-interest.
Coordination Game: A scenario in which two or more players coordinate their strategies to achieve a common goal.
Zero-Sum Game: A situation in which the sum of one player's winnings is precisely equal to the other player's losses.
Mixed Strategy: A strategy that is chosen randomly with probability according to a predefined distribution.
"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."