Mediocrity

Mediocrity is a very simple concept and can be applied to many games. I will describe it first for a simple number selection game as given in Douglas Hofstadter's brilliant book "Metamagical Themas".

The winner of a game of Mediocrity is the most "mediocre" player. In a three player game of mediocrity each player selects a number (lets say between 1-10). The player who selects the middlemost number is the winner! (Ties can be resolved by having a different fraction added to each player; this can be rotated). This is known as Level 0 mediocrity.

A Level 1 game of mediocrity involves playing N games (lets say 5) of Level 0 mediocrity. Of course the winner is the person with the middlemost number of Level 0 wins!

The progression to higher Level (2+) games of mediocrity is quite clear. It is often a good way to make boring multi-player games exciting, forcing a person to come second usually keeps the game much tighter. The strategy for higher level games of mediocrity (3+) is extremely difficult and I'd like to see an algorithm that performed well against humans.