WOLFRAM|DEMONSTRATIONS PROJECT

2x2 Ordinal Games

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game
prisoner's dilemma
player 1's ranking
{3,1,4,2}
player 2's ranking
{3,4,1,2}
player 1'schoice
player 2'schoice
outcomeof game
player 1'sranking
player 2'sranking
C
C
CC
3
3
C
N
CN
1
4
N
C
NC
4
1
N
N
NN
2
2
player 2
player 1
C
N
C
{3,3}
{1,4}
N
{4,1}
{2,2}
The dominant strategy for player 1 is {N}.
The dominant strategy for player 2 is {N}.
The Nash equilibria correspond to outcome(s) {NN}.
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.