## Scenario

To determine who is required to do the nightly chores, two children first select who will be represented by "same" and who will be represented by "different." Then, each child conceals in her palm a penny either with its face up or face down. Both coins are revealed simultaneously. If they match (both are heads or both are tails), the child "same" wins. If they are different (one heads and one tails), "different" wins. The game is equivalent to "odds or evens" and quite similar to a three strategy version - rock, paper, scissors.## 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

same | |||

heads | tails | ||

different | heads | -1,1 | 1,-1 |

tails | 1,-1 | -1,1 |

## General Form

Player 2 | |||

L | R | ||

Player 1 | U | a,w | b,x |

D | c,y | d,z |

c = b = -a = -d

w = z = -x = -y

updated: 12 August 2005

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Game Theory

© Mike Shor 2001-2006

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