examples of normal form games

A few example normal form games:

Prisoner’s dilemma

Probably the most famous game theory example, the prisoner’s dilemma is a two player game where $S_1=S_2=C,D$ and:

Traditionally this is interpreted as the case of two criminal partners separately being interrogated and asked to give up the other partner. $C$ stands for cooperating (with their partners) by refusing to give up information, and $D$ stands for defecting and agreeing to testify against the partner. The different payoffs reflect different jail sentences, ranging from nothing (+10) to a long jail sentence (-5), with amounts in between depending on the evidence against them.

The (much more convenient) normal form is:CDC5,5-5,10D10,-50,0

Notice that $(C,C)$ Pareto dominates $(D,D)$, however $(D,D)$ is the only Nash equilibrium.

Battle of the Sexes

Another traditional two player game. The normal form is:OFO2,10,0F0,01,2

A Degenerate Example

One more, rather pointless, example which illustrates a game where one player has no choice:

Undercut

A game which illustrates an infinite (indeed, uncountable) strategy space. There are two players and $S_1=S_2={ℝ}^{+}$.