In class on Monday evening, I showed a couple of video segments taken from a UK game show called “Golden Balls”.  The payoff matrix for the “Split or Steal” game that they played is as follows (the numbers refer to the % of the jackpot that gets shared or not shared).

 

Player 2


Player 1

 

Steal

Split

Steal

0,0

100,0

Split

0,100

50,50

 

If you check this matrix for dominant strategies, there is no strong dominance; however, there is weak dominance. To see this, let’s think through the strategy choices of the two players. Suppose Player 2 plays Steal. In this case, the payoffs for Player 1 are 0 if she Steals and 0 if she Splits. Now suppose Player 2 plays Split. In this case, payoffs for Player 1 are 100 if she Steals and 50 if she Splits. Thus Steal weakly dominates Split for Player 1, since it ties with Split when Player 2 plays Steal, and it is better than Split when Player 1 plays Split (see page 10 of last Monday’s lecture note for a formal definition of Weak Dominance). By symmetry, Steal weakly dominates Split for Player 2 as well.

The “coordination” problem here is that since neither player is able to credibly commit to playing Split, the “best” response for both players is to play Steal.  Therefore, this is a Prisoners Dilemma, in the sense that if hypothetically given the choice between the Split, Split (50,50) and the Steal, Steal (0,0) payoffs, both players would obviously prefer Split, Split.  Unfortunately, there is no way for them to arrive at this state because of the incompatibility of incentives that is part and parcel of the game’s structure.

From a business perspective, I think that it is quite clever to produce a game show based upon a prisoner’s dilemma game.  The production costs for a show like this are nominal, and most of the time the production company won’t have to pay out a jackpot.  It doesn’t take a game theory expert to figure out that the incentive structure of the game is incompatible with a Split, Split outcome.  Of course this (Steal, Steal) is what occurs in the first video that I showed:

 

 

In the second video, apparently one of the contestants failed to realize that Split is weakly dominated by Steal.  This also works to the production company’s benefit; the “drama” of the game creates a buzz and possibly more viewership (thus bringing in more revenue from commercials).  In all likelihood, the production company also manages the risk of a player playing Split by purchasing an insurance policy covering the cost of the jackpot from Lloyds of London:

 

 

Let me make one final point about Prisoners Dilemmas and television shows.  The next time you watch Law and Order, keep in mind that virtually every episode is organized around some variation of a Prisoners Dilemma game.  The downside of realizing this is that this makes Law and Order much less interesting to watch, since you can often deduce what will likely happen just a few minutes into each episode!

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