"A player's strategy is any of the options which they choose in a setting where the optimal outcome depends not only on their own actions but on the actions of others."
A strategy in which a player randomizes between different pure strategies. This can sometimes lead to a better outcome than playing a pure strategy.
Dominant Strategies: A concept in game theory where a player has a strategy that is always best for them, regardless of the actions of other players.
Nash Equilibrium: A solution concept in game theory where no player has an incentive to change their strategy, given the strategies of the other players.
Prisoner's Dilemma: A classic example of a game where two rational players acting in their own self-interests will not cooperate, even though cooperation would benefit both players.
Zero-Sum Games: A type of game where one player's gain is always equal to another player's loss.
Mixed Strategies: A strategy in game theory where a player randomly chooses between different pure strategies with a certain probability.
Best Response Functions: A function in game theory that describes the optimal strategy for a player, given the strategies of the other players.
Stochastic Games: A type of game where the players' payoffs depend on a sequence of random events.
Symmetric Games: A game where all players have the same set of strategies and payoff structure.
Extensive Form Games: A type of game where the players take turns making moves and the game can be represented as a tree.
Evolutionary Games: A branch of game theory that seeks to model the evolution of strategies in a population over time.
Correlated Equilibrium: A solution concept in game theory where players choose their strategies based on some external source of randomness, such as a coin toss.
Repeated Games: A type of game where the same game is played multiple times, allowing players to adjust their strategies based on previous outcomes.
Supermodular Games: A game where the payoff function is non-decreasing in each player's strategy and increasing in the other player's strategy.
Stackelberg Games: A type of game where one player moves first in a sequential game, and the other player observes that move before making their own move.
Paradox of Rationality: A paradox in game theory where rational behavior leads to a sub-optimal outcome for all players.
Pure Strategy: In Pure Strategy, each player chooses only one move, without any randomness.
Mixed Strategy: In Mixed Strategy, each player chooses a probability distribution over their set of possible moves, and selects their move based on the probability assigned to each move.
Nash Equilibrium: Nash Equilibrium is a type of Mixed Strategy where no player has an incentive to change strategies since no individual player can increase their payoff by changing their strategy while holding others' strategies fixed.
Correlated Equilibrium: In Correlated Equilibrium, players do not choose their strategies independently, but rather follow some pre-specified correlation between their moves.
Symmetric Equilibrium: Symmetric Equilibrium is a type of Nash Equilibrium where all players play the same Mixed Strategy.
Trembling Hand Equilibrium: Trembling Hand Equilibrium takes into account the possibility of mistakes made by players, and allows for some deviation from Mixed Strategy without changing the overall equilibrium.
Evolutionarily Stable Strategy: In Evolutionarily Stable Strategy, the strategy of a player is immune to invasion by new strategies that arise adaptively in a population.
Markov Perfect Equilibrium: Markov Perfect Equilibrium takes into account the dynamic evolution of strategies over time, where each player's action depends on the history of his or her own actions as well as the actions of all other players.
"The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players."
"Some examples of 'games' include chess, bridge, poker, monopoly, diplomacy, or battleship."
"A player's strategy will determine the action which the player will take at any stage of the game."
"In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines."
"A move is an action taken by a player at some point during the play of a game. A strategy, on the other hand, is a complete algorithm for playing the game, telling a player what to do for every possible situation throughout the game."
"It is helpful to think about a 'strategy' as a list of directions."
"This strategy is based on the payoff or outcome of each action."
"The goal of each agent is to consider their payoff based on a competitor's action."
"This technique can identify dominant strategies where a player can identify an action that they can take no matter what the competitor does to try to maximize the payoff."
"Nash equilibrium is a concept in game theory that identifies a situation where no player can improve their payoff by unilaterally changing their strategy."
"A strategy profile (sometimes called a strategy combination) is a set of strategies for all players which fully specifies all actions in a game."
"A strategy profile must include one and only one strategy for every player."
"In a setting where the optimal outcome depends not only on their own actions but on the actions of others, a player's strategy is influenced by the behavior or actions of other players."
"In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines."
"The strategy concept in game theory focuses on the payoff or outcome of each action in determining a player's strategy."
"A dominant strategy is an action that a player can take no matter what the competitor does, allowing them to maximize their payoff."
"Nash equilibrium aims to identify a situation where no player can improve their payoff by unilaterally changing their strategy."
"A strategy profile (or strategy combination) is a set of strategies for all players, specifying all actions in a game."
"A strategy profile must include one and only one strategy for every player."