Winning

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.