Friday, April 11, 2014

Golden Balls

There have been some bizarre game shows over the years.  "Find the Chair" is exactly as entertaining as it sounds, while "Oh Sit!" is a great pun title for televised musical chairs.  But for an economist there's a select few shows which rise above the rest. "The Price is Right", "Deal or no Deal", and "Golden Balls".

American audiences are familiar with the first two shows, but the third is a little known British game show that might as well be taught in game theory courses.

Golden Balls is a simple show of gradual team reduction.  A team begins with four players with one player eliminated each round until two remain.  In the first round twelve balls are drawn from a pool of one hundred. Each ball has an assigned value between ten and seventy-five thousand British pounds.  Four Killer balls are added to the twelve drawn balls and each player randomly receives four balls.

Players then place the balls they receive in two rows. The front row of two balls is visible to all players.  The back row is visible only to the owner of the balls.  Each player then attempts to convince the others that his or her hidden balls are the most valuable (thus making them important to maximizing later winnings). Players then vote to eliminate one of the team members. Round two is played in a similar fashion with each player receiving five balls total.

When the game is narrowed to two players things really get interesting.  Each player takes turns randomly picking one ball from the pool of remaining balls to add to the jackpot and one ball to eliminate from the pool.  If a Killer ball is selected to be added to the jackpot then the jackpot is divided by ten. This process is repeated five times in order to establish the size of the jackpot. I've glossed over a few minor details in the interest of brevity but the bottom line is high value balls are good, Killer balls are bad, and the game ends with two contestants going head to head.

Once the jackpot is established each contestant receives one final pair of golden balls. One ball says "split" and the other says "steal".  The contestants converse for a time (attempting to convince the other of their trustworthiness) and then choose a ball. Both players balls are revealed and one of three outcomes plays out.

If both contestants select split then everyone wins. The contestants split the jackpot evenly.  If one contestant chooses split and the other chooses steal than the stealer gets the entire jackpot.  If both contestants select steal than no one receives anything.

It's possible you may recognize this as a modification of the classic prisoner's dilemma.  Cooperation benefits everyone, but defection benefits one person more than cooperation would as long as the other doesn't defect as well.  Of course if both defect the outcome is unfortunate for everyone.

Interestingly, most shows end with at least one player choosing to steal.  It's easy to attribute this selfish play to simple greed.  However, interviews conducted with participants seem to indicate that isn't the case.  Most players claim that they choose to steal not because they wanted the money all to themselves, but rather because they feared being made a fool of by the opposing player.  The fact that fear of betrayal or public embarrassment seemingly supersedes desire for considerable monetary gain is an interesting motivational indicator.  Of course, it's also quite possible that this is a post hoc rationalization by players to justify themselves as more than simply greedy.

One player in particular stands out as having beaten the Golden Balls system.  Nick Corrigan found himself in the final two showdown with his teammate.  When the time came to convince the other that he would split Nick took another approach.  He insisted that when the time came, he would select the "steal" ball.  Nick claimed that he was going to steal and after the show he would split the money with the opposing player.

At first everyone was shocked.  The players argued at length. His opposition implored him, "Why not just both choose split and share the money?" But Nick was resolute, he would select the steal ball.

It seems like a ridiculous plan.  After all, nothing compels Nick to split the money after the show.  But look at it from his opponents perspective. If Nick is going to choose steal what choices are there?  Go along with him and choose split, hoping he'll make good on his promise.  Or choose steal and certainly get nothing.  There is no fear of betrayal, no public humiliation. Everyone knows what Nick is going to do. The choice for his opponent is simply to hope for something or guarantee nothing.

Eventually, after a long and heated debate Nick's opponent gave in and agreed to select the split ball.  True to his word when the balls were revealed it showed "Split". Nick however was not quite so honest. Not one, but two balls read "Split". Both players win and everyone walks away happy.  Interestingly, in the post game interview Nick's opponent revealed his planned strategy. He said he'd planned to steal 100%.

That's all for this week. Until next time stay safe and rationale.

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