"Repeated games capture the idea that a player will have to take into account the impact of their current action on the future actions of other players; this impact is sometimes called their reputation."
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.
Dominant strategy: A strategy that is always the best choice for a player, regardless of what their opponent chooses.
Nash equilibrium: A situation where each player's strategy is optimal given the strategies of the other players.
Prisoner's dilemma: A classic game in which two players face a dilemma of whether to cooperate or defect, with payoffs that reflect the tension between individual and collective interests.
Tit-for-tat strategy: A strategy in which a player cooperates on the first move and then follows the opponent's previous move on subsequent moves.
Iterated prisoner's dilemma: A repeated version of the prisoner's dilemma, where players interact with each other over a series of rounds.
Evolutionary game theory: A branch of game theory that studies the evolution of strategies in populations of players.
Stochastic games: Games where there is an element of chance involved in determining the outcome of each move.
Fictitious play: A learning algorithm that updates a player's belief about their opponent's strategy based on observed moves.
Grim trigger strategy: A strategy in which a player defects forever after the opponent defects once.
Repeated games: Games that are played multiple times with the same group of players.
Markov decision processes: Mathematical models for decision-making in situations where future outcomes depend on existing state and stochastic transitions.
Correlated equilibrium: A situation where players coordinate based on a common signal, without necessarily communicating with each other.
Folk theorem: A theorem that states that in repeated games with an infinite number of rounds, any payoff that is Pareto-optimal and satisfies certain conditions can be achieved as a Nash equilibrium.
Coalition game: A game where players can form coalitions to gain more power than they would have individually.
Zero-sum games: Games where the total payoff is constant and one player's gain is another player's loss.
The Prisoner's Dilemma: It is the most well-known example of an iterated game, in which two individuals must decide whether to cooperate or defect from each other repeatedly, with past outcomes influencing current decisions.
The Stag Hunt: In this game, two individuals must choose between cooperating to achieve a big reward, or acting individually to fulfill a smaller payoff.
The Battle of the Sexes: Two individuals must coordinate to attend an event, with each preferring a different event, making coordination difficult.
The Chicken Game: Also known as the Hawk-Dove game, the chicken game results in disastrous outcomes if both players behave aggressively and no one backs down.
The Ultimatum Game: One player proposes a division of resources, while the other can either accept or reject the proposed distribution.
The Trust Game: One player chooses to trust the other, leaving them with a chance to betray or follow through with the trust.
The Centipede Game: Players play against each other in iterative rounds, in which each player takes turns offering a potentially better-offer to the other player.
The Dictator Game: One player has a fixed amount of a good, which they can choose to share or keep for themselves, with the other player having no bargaining power.
The Public Goods Game: Players can choose to invest resources in a communal project, with the collective benefits being shared appropriately.
The Volunteer's Dilemma: Players need to coordinate with each other to collaborate on a project, but they face the risk that others will also participate.
"The stage game is usually one of the well-studied 2-person games."
"Single stage game or single shot game are names for non-repeated games."
"For the real-life example of a repeated game, consider two gas stations that are adjacent to one another."
"They compete by publicly posting pricing and have the same and constant marginal cost c."
"When they both charge p = 10, their joint profit is maximized."
"They are motivated to deviate. By modestly lowering the price, anyone can steal all of their competitors' consumers, doubling their revenues (nearly)."
"P = c, where their profit is zero, is the only price without this profit deviation."
"In the pricing competition game, the only Nash equilibrium is inefficient (for gas stations) that both charge p = c."
"The Nash equilibrium is the only result that an agent can consistently acquire in an interaction."
"It is usually inefficient for them because the agents are just concerned with their own personal interests and are unconcerned about the benefits or costs that their actions bring to competitors."
"One of the most crucial reasons is that their interaction is not one-off."
"This condition is portrayed by repeated games, in which two gas stations compete for pricing (stage games) across an indefinite time range t = 0, 1, 2,...."
"A player will have to take into account the impact of their current action on the future actions of other players; this impact is sometimes called their reputation."
"When they both charge p = 10, their joint profit is maximized, resulting in a high profit for everyone."
"By modestly lowering the price, anyone can steal all of their competitors' consumers, doubling their revenues (nearly)."
"The only price without profit deviation is P = c, where their profit is zero."
"The Nash equilibrium is usually inefficient for the agents because they are solely concerned with their own personal interests, not the benefits or costs to competitors."
"The condition of repeated games means that their interaction is not one-off, but occurs across an indefinite time range."
"One of the most crucial reasons is that their interaction is not one-off."