Paula Abdul has left American Idol.  Apparently,

“Paula didn’t place as much importance on remaining on the show as some other people did,” said a person close to Ms. Abdul who, like several people interviewed for this article who were involved in the negotiations, spoke on the condition of anonymity to preserve relationships on both sides. “She thinks there are a lot of opportunities out there for her, and she will be fine without that show.”  NYT

That is, Paula’s assessment of her value, i.e. her outside option, was greater than American Idol’s assessment of her value for their show.  This is a reasonable possibility.  After all American Idol (AI) has Simon Cowell and then the marginal contribution of Abdul might be lower in AI than her value to a show like “Dancing with the Stars” where there are no recognizable personalities.  In this scenario, there are no gains to trade for Abdul and American Idol and so they have to part.

But there is another possibility.  Abdul and American Idol have private information, Abdul about her outside option and AI producers about her value for their show.  The producers have an incentive to shade their value to minimize the salary they have to pay Abdul.  Abdul has an incentive to exaggerate her value to AI. Even if she might be an American Idle she should pretend she is very busy and has lots of options.  Joint bluffing can lead to no-trade even when there might be real gains to trade if everyone’s information is public not private.  In a famous theorem, Myerson and Satterthwaite proved that for this to happen there has to be chance that there really are no gains to trade.  I made the argument in the previous paragraph that this scenario is a possibility.  But this scenario then affects bluffing behavior even when there are true underlying gains to trade. So, Paula may be leaving AI even though her value is higher there than at Dancing with the Stars.  Tragedy.

Where’s the silver lining?  Well, I think there’s one for me.  I have an English accent.  I can pout like Posh Spice, Paula’s replacement on AI.  And I’m pretty sure people think I’m a bit of a  overcritical d**khead.  In other words, I am an ideal combination of Simon Cowell and Posh Spice.  I have huge potential.  In fact, the phone is ringing.  Maybe it’s Hollywood on the line……