## Scenario

To determine who is required to do the nightly chores, two children simultaneously make one of three symbols with their fists - a rock, paper, or scissors. Simple rules of "rock breaks scissors, scissors cut paper, and paper covers rock" dictate which symbol beats the other. If both symbols are the same, the game is a tie. Similar to the two-strategy Matching Pennies game.## Description

The game is zero sum. The only equilibrium is in mixed strategies. Each plays each strategy with equal probability, resulting in an expected payoff of zero for each player.## Example

Child 2 | ||||

rock | paper | scissors | ||

Child 1 | rock | 0,0 | -1,1 | 1,-1 |

paper | 1,-1 | 0,0 | -1,1 | |

scissors | -1,1 | 1,-1 | 0,0 |

## General Form

Player 2 | ||||

L | C | R | ||

Player 1 | U | a,r | b,u | c,x |

M | d,s | e,v | f,y | |

D | g,t | h,w | i,z |

c = d = h = -b = -f = -g; a = e = i = 0

t = u = y = -s = -w -x; r = v = z = 0

updated: 12 August 2005

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© Mike Shor 2001-2006

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