List of games in game theory
Encyclopedia
Game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

 studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games.

Explanation of features

Games can have several features, a few of the most common are listed here.
  • Number of players: Each person who makes a choice in a game or who receives a payoff from the outcome of those choices is a player.
  • Strategies per player: In a game each player chooses from a set of possible actions, known as strategies. If the number is the same for all players, it is listed here.
  • Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best response
    Best response
    In game theory, the best response is the strategy which produces the most favorable outcome for a player, taking other players' strategies as given...

    s to the other strategies. In other words, if every player is playing their part of a Nash equilibrium, no player has an incentive to unilaterally change his or her strategy. Considering only situations where players play a single strategy without randomizing (a pure strategy) a game can have any number of Nash equilibria.
  • Sequential game
    Sequential game
    In game theory, a sequential game is a game where one player chooses his action before the others choose theirs. Importantly, the later players must have some information of the first's choice, otherwise the difference in time would have no strategic effect...

    : A game is sequential if one player performs her/his actions after another, otherwise the game is a simultaneous move game.
  • Perfect information
    Perfect information
    In game theory, perfect information describes the situation when a player has available the same information to determine all of the possible games as would be available at the end of the game....

    : A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them.
  • Constant sum: A game is constant sum if the sum of the payoffs to every player are the same for every set of strategies. In these games one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.

List of games

Game Players Strategies per player Number of pure strategy Nash equilibria Sequential
Sequential game
In game theory, a sequential game is a game where one player chooses his action before the others choose theirs. Importantly, the later players must have some information of the first's choice, otherwise the difference in time would have no strategic effect...

Perfect information
Perfect information
In game theory, perfect information describes the situation when a player has available the same information to determine all of the possible games as would be available at the end of the game....

Zero sum
Battle of the sexes
Battle of the sexes (game theory)
In game theory, battle of the sexes , also called Bach or Stravinsky, is a two-player coordination game. Imagine a couple that agreed to meet this evening, but cannot recall if they will be attending the opera or a football match. The husband would most of all like to go to the football game. The...

2 2 2 No No No
Blotto games
Blotto games
Blotto games constitute a class of two-person zero-sum games in which the players are tasked to simultaneously distribute limited resources over several objects...

2 variable variable No No Yes
Cake cutting N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

, usually 2
infinite variable Yes Yes Yes
Centipede game
Centipede game
In game theory, the centipede game, first introduced by Rosenthal , is an extensive form game in which two players take turns choosing either to take a slightly larger share of a slowly increasing pot, or to pass the pot to the other player...

2 variable 1 Yes Yes No
Chicken (aka hawk-dove) 2 2 2 No No No
Coordination game
Coordination game
In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

variable >2 No No No
Cournot game 2 infinite 1 No No No
Deadlock
Deadlock (game)
In game theory, Deadlock is a game where the action that is mutually most beneficial is also dominant. This provides a contrast to the Prisoner's Dilemma where the mutually most beneficial action is dominated...

2 2 1 No No No
Dictator game
Dictator game
The dictator game is a game in experimental economics, similar to the ultimatum game. Experimental results offer evidence against the rationally self-interested individual concept of economic behavior, though precisely what to conclude from the evidence is controversial.-Description:In the...

2 infinite 1 N/A N/A Yes
Diner's dilemma
Diner's dilemma
In game theory, the Unscrupulous diner's dilemma is an n-player prisoner's dilemma. The situation imagined is that several individuals go out to eat, and prior to ordering they agree to split the check equally between all of them. Each individual must now choose whether to order the expensive or...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

2 1 No No No
Dollar auction
Dollar auction
The dollar auction is a non-zero sum sequential game designed by economist Martin Shubik to illustrate a paradox brought about by traditional rational choice theory in which players with perfect information in the game are compelled to make an ultimately irrational decision based completely on a...

2 2 0 Yes Yes No
El Farol bar
El Farol bar problem
The El Farol bar problem is a problem in game theory. Based on a bar in Santa Fe, New Mexico, it was created in 1994 by W. Brian Arthur.The problem is as follows: There is a particular, finite population of people. Every Thursday night, all of these people want to go to the El Farol Bar. However,...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

2 variable No No No
Example of a game without a value
Example of a game without a value
In game theory, and in particular the study of zero-sum continuous games, it is commonly assumed that a game has a minimax value. This is the expected value to one of the players when both play a perfect strategy ....

2 infinite 0 No No Yes
Guess 2/3 of the average
Guess 2/3 of the average
In game theory, Guess 2/3 of the average is a game where several people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to the real numbers between 0 and 100, inclusive. The winner is the one closest to the 2/3 average.- Equilibrium analysis :In this...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

infinite 1 No No Maybe
Kuhn poker
Kuhn poker
Kuhn poker is a simplified form of poker developed by Dr. Harold W. Kuhn. It is a zero sum two player game. The deck includes only three playing cards, for example a King, Queen, and Jack. One card is dealt to each player, then the first player must bet or pass, then the second player may bet or pass...

2 27 & 64 0 Yes No Yes
Matching pennies
Matching pennies
Matching pennies is the name for a simple example game used in game theory. It is the two strategy equivalent of Rock, Paper, Scissors. Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium....

2 2 0 No No Yes
Minority Game N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

2 variable No No No
Nash bargaining game 2 infinite infinite No No No
Peace war game
Peace war game
An iterated game originally played in academic groups and by computer simulation for years to study possible strategies of cooperation and aggression. As peace makers became richer over time it became clear that making war had greater costs than initially anticipated...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

variable >2 Yes No No
Pirate game
Pirate game
The pirate game is a simple mathematical game. It illustrates how, if assumptions conforming to a homo economicus model of human behaviour hold, outcomes may be surprising. It is a multi-player version of the ultimatum game.-The game:...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

infinite infinite Yes Yes No
Prisoner's dilemma
Prisoner's dilemma
The prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...

2 2 1 No No No
Rock, Paper, Scissors
Rock, Paper, Scissors
Rock-paper-scissors is a hand game played by two people. The game is also known as roshambo, or another ordering of the three items ....

2 3 0 No No Yes
Screening game
Screening game
A screening game is a two-player principal–agent type game used in economic and game theoretical modeling. Principal–agent problems are situations where there are two players whose interests are not necessarily at ends, but where complete honesty is not optimal for one player...

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

variable variable Yes No No
Signaling game N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

variable variable Yes No No
Stag hunt
Stag hunt
In game theory, the stag hunt is a game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. ...

2 2 2 No No No
Traveler's dilemma
Traveler's dilemma
In game theory, the traveler's dilemma is a type of non-zero-sum game in which two players attempt to maximize their own payoff, without any concern for the other player's payoff....

2 N >> 1 1 No No No
Trust game 2 infinite 1 Yes Yes No
Volunteer's dilemma
Volunteer's dilemma
The volunteer's dilemma game models a situation in which each of N players faces the decision of either making a small sacrifice from which all will benefit, or freeriding....

N
N-player game
In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players...

2 2 No No No
War of attrition
War of attrition (game)
In game theory, the war of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while constantly accumulating costs over the time t that the contest lasts. The model was originally formulated by John Maynard Smith, a mixed evolutionary stable...

2 2 0 No No No
Ultimatum game
Ultimatum game
The ultimatum game is a game often played in economic experiments in which two players interact to decide how to divide a sum of money that is given to them. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. ...

2 infinite infinite Yes Yes No
Princess and monster game
Princess and monster game
In game theory, the princess and monster game is a pursuit-evasion game played by two players in a region. The game was devised by Rufus Isaacs and published in his book Differential Games as follows. "The monster searches for the princess, the time required being the payoff. They are both in a...

2 infinite 0 No No Yes

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