# List of games in game theory

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Game theory 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 pure 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 responses 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 : A game is sequential if one player performs her/his actions after another player; otherwise, the game is a simultaneous move game.
• Perfect information : 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 single 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.
• Move by nature : A game includes a random move by nature.

## List of games

per player
No. of pure strategy
Nash equilibria
Sequential Perfect
information
Zero sum Move by nature
Battle of the sexes 222NoNoNoNo
Blotto games 2variablevariableNoNoYesNo
Cake cutting N, usually 2infinitevariable [1] YesYesYesNo
Centipede game 2variable1YesYesNoNo
Chicken (aka hawk-dove)222NoNoNoNo
Commune game 3Yes
Coordination game N variable>2NoNoNoNo
Cournot game 2infinite [2] 1NoNoNoNo
Dictator game 2infinite [2] 1N/A [3] N/A [3] YesNo
Diner's dilemma N 21NoNoNoNo
Dollar auction 220YesYesNoNo
El Farol bar N 2variableNoNoNoNo
Game without a value 2infinite0NoNoYesNo
Guess 2/3 of the average N infinite1NoNoMaybe [4] No
Kuhn poker 227 & 640YesNoYesYes
Matching pennies 220NoNoYesNo
Muddy Children Puzzle N 21YesNoNoYes
Nash bargaining game 2infinite [2] infinite [2] NoNoNoNo
Optional prisoner's dilemma 231NoNoNoNo
Peace war game N variable>2YesNoNoNo
Pirate game N infinite [2] infinite [2] YesYesNoNo
Platonia dilemma N 2${\displaystyle 2^{N}-1}$NoYesNoNo
Princess and monster game 2infinite0NoNoYesNo
Prisoner's dilemma 221NoNoNoNo
Public goods N infinite1NoNoNoNo
Rock, paper, scissors 230NoNoYesNo
Screening game 2variablevariableYesNoNoYes
Signaling game N variablevariableYesNoNoYes
Stag hunt 222NoNoNoNo
Traveler's dilemma 2N >> 11NoNoNoNo
Truel 31-3infiniteYesYesNoNo
Trust game 2infinite1YesYesNoNo
Ultimatum game 2infinite [2] infinite [2] YesYesNoNo
Vickrey auction N infinite1NoNoNoYes [5]
Volunteer's dilemma N 22NoNoNoNo
War of attrition 220NoNoNoNo