The Games
People Play
Oh the games people play now
Every night and every day now
Never meaning what they say now
Never saying what they mean
People might not know they are playing games, but how they play can
reveal a lot about them.
Game Theory is concerned about how people make
decisions to win games. The Ultimatum Game
in behavioral economics is a very simple
game. Player One is given an amount, say
$100. Player One must make an offer to a
Player Two. If Player Two accepts
the offer, then they both get to keep their respective amounts. If Player Two rejects that amount, then neither
player gets to keep anything.
The User Optimal solution for a single non-repeating
game is for Player One to offer as small an amount as possible. Let’s assume that offer is $1. Player Two, should accept that offer, because
even $1 is better than nothing.
The System Optimal solution is for Player One
to offer to split the money equally with Player Two, and for Player Two to
accept that offer. Then they both have
$50.
It might sound like the User Optimal solution
would be the one chosen. However in
practice those who were Player Two often rejected any offer that was less than
$30. Why?
Player One in the User Optimal solution assumed
that the game would never be repeated, and by offering less than $30, both
players walked away with nothing. An offer of greater than $30 to Player Two would normally be accepted.
Player Two recognized that an offer of less than $30 indicated that Player
One assumed that the game would never to be repeated, and the roles would
never be reversed.
The difference between the User Optimal offers
and the minimum acceptable offer is what economists call the shadow price. This
includes not only an acknowledgement that the game might be repeated and the roles
reversed, but also an indication of how Player
One values the future. I.e. what discount rate that Player One applies to future values.
That $29 dollar difference is the future value of the $50 that would have been
the System Optimal cost. The fact that
we value the future less than the present, i.e. apply a discount rate to future
values, is reflected in the adage "A bird in the hand is worth two in the bush".
So what discount rate does a shadow price of $29 price imply?. It implies a discount rate of 42%, if the
game is repeated one time. A $1 offer
implies a 98% discount rate if the game is repeated once and the roles are reversed.
Player Two won’t play with player One if those are the rules.