examples of normal form games


A few example normal form games:

Prisoner’s dilemmaMathworldPlanetmath

Probably the most famous game theoryMathworldPlanetmath example, the prisoner’s dilemma is a two player game where S1=S2=C,D and:

u1⁢(s1,s2)={5 if s1=C and s2=C10 if s1=D and s2=C-5 if s1=C and s2=D0 if s1=D and s2=D
u2⁢(s1,s2)={5 if s1=C and s2=C10 if s1=C and s2=D-5 if s1=D and s2=C0 if s1=D and s2=D

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 sentencesMathworldPlanetmath, 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: C D C 5,5 -5,10 D 10,-5 0,0

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

Battle of the Sexes

Another traditional two player game. The normal form is: O F O 2,1 0,0 F 0,0 1,2

A Degenerate Example

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

X Y Z
A 2,100 1,7 14,-5

Undercut

A game which illustrates an infiniteMathworldPlanetmath (indeed, uncountable) strategy space. There are two players and S1=S2=ℝ+.

u1⁢(s1,s2)={1 if s1<s20 if s1≥s2
u2⁢(s1,s2)={1 if s2<s10 if s2≥s1
Title examples of normal form games
Canonical name ExamplesOfNormalFormGames
Date of creation 2013-03-22 12:51:27
Last modified on 2013-03-22 12:51:27
Owner Henry (455)
Last modified by Henry (455)
Numerical id 9
Author Henry (455)
Entry type Example
Classification msc 91A10
Classification msc 91A06
Classification msc 91A05
Defines prisoners dilemma
Defines battle of the sexes