You are in a group of five people. Each member of the group has an initial holding of $15. 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 $25 and your action has no effect on any other group member;
(B) If you choose RIGHT, you earn $50 but your action also imposes a cost of $10 on each member of the group (yourself included, so you net $40).So, holding constant the choices of all others, you earn $15 more by choosing RIGHT rather than LEFT.
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 five members in the group, this game has six 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.
5
0
$25
--
$125
2.
4
1
$15
$40
$100
3.
3
2
$5
$30
$75
4.
2
3
-$5
$20
$50
5.
1
4
-$15
$10
$25
6.
0
5
--
$0
$0