You are in a group of six people. Each member of the group has an initial holding of $40. You have the opportunity, based on your own actions and those of the others in the group, to earn an additional amount or to lose some or all of your initial holding.
You (and each other member of the group) must choose between two actions, designated LEFT and RIGHT (no political connotations intended), which have these consequences:
(A) If you choose LEFT, you earn $10 for each other member of the group who chooses LEFT but you lose $10 for each other member of the group who chooses RIGHT.
(B) If you choose RIGHT, you earn $10 for each other member of the group who chooses RIGHT but you lose $10 for each other member of the group who chooses LEFT.In general, you earn more (or lose less) to the extent that others make the same choice you do.
Your goal is to maximize your own earnings, and you know that everyone else is similarly motivated.
Version 1. Each player must make his or her choice in isolation, without talking to other players.
Version 2. Players can talk among themselves (make deals or whatever) prior to making their choices.But, in both versions, final choices are made by "secret ballot."
Do you choose LEFT or RIGHT?
Analysis. With six members in the group, this game has seven classes of outcomes, according to how many group members choose LEFT and how many chose RIGHT, with the following "payoffs":
Then each player wins, depending
So the group as a
Number who choose
on whether he/she chooses
whole wins
LEFT RIGHT
LEFT
RIGHT
1.
6
0
$50
--
$300
2.
5
1
$30
$50
$100
3.
4
2
$10
$30
-$20
4.
3
3
$10
$10
-$60
5.
2
4
$30
$10
-$20
6.
1
5
$50
$30
$100
7.
0
6
--
$50
$300