Symmetry in 2x2 Games
| E | F | |
|---|---|---|
| E | a, a | b, c |
| F | c, b | d, d |
Only 12 out the 144 ordinally distinct 2x2 games are symmetric. However, many of the commonly studied 2x2 games are at least ordinally symmetric. The standard representations of chicken, the Prisoner's Dilemma, and the Stag hunt are all symmetric games. Formally, in order for a 2x2 game to be symmetric, its payoff matrix must conform to the schema pictured to the right.
The requirements for a game to be ordinally symmetric are weaker, there it need only be the case that the ordinal ranking of the payoffs conform to the schema on the right.
Read more about this topic: Symmetric Game
Famous quotes containing the words symmetry and/or games:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)
“The rules of drinking games are taken more serious than the rules of war.”
—Chinese proverb.