# 2x2 Ordinal Games

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A 2×2 ordinal game consists of two players, each with the strategy options of cooperation or noncooperation with the other player (these options are denoted C and N, respectively, in this Demonstration). Each player then ranks the four possible resulting outcomes from four (most desirable for that player) down to 1 (least desirable). The game is summarized in a 2×2 matrix of ordered pairs, with the entries in each ordered pair being the rankings of the corresponding outcome by player 1 and player 2, respectively. A dominant strategy for a player is a strategy (a choice of C or N) with the property that such a choice results in a more favorable outcome for that player than the other choice would, regardless of the other player's choice of strategy. A Nash equilibrium is a choice of strategy by each player with the property that a unilateral change of strategy by either player is unfavorable to that player.

Contributed by: Marc Brodie (Wheeling Jesuit University) (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The two most famous examples of 2×2 ordinal games are "The Prisoner's Dilemma", which is shown in the thumbnail, and "Chicken", which is shown in snapshot 1. Snapshot 2 illustrates a game in which one player has a dominant strategy while the other does not, and snapshot 3 illustrates a game in which there is no Nash equilibrium.

For further details, see A. D. Taylor, *Mathematics and Politics—Strategy, Voting, Power and Proof*, New York: Springer–Verlag, 1995.

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