You are reorganizing your firm. There are many legacy employees the old CEO was too weak to fire. They are inefficient and incompetent but their connection to the old CEO – an insider – kept their jobs safe. You were hired from the outside and feel no particular affection for the old guard. There is one employee Mr X who is high up. He is terrible at his job but has survived by using his charm and by buttering up the customers. Sometimes he went too far. You hear rumors of “liasons” between your staff and the customers. Also, there were inappropriate exchanges of gifts. While nothing was strictly illegal, if news gets out, your firm will look bad and business will suffer.
You want to sack Mr X. Your problem is that he knows too much: if you fire him, he threatens to go to the press and tell them everything he knows. This would be a catastrophe. One thing can save you: what is bad for you is also bad for him. Mr X played no small part in the sleazy business he threatens to reveal. He’ll have a hard time getting a new job if he spills the beans. Even if he gets a new job, stabbing is old boss in the back will make his new boss worry if he can trust Mr X. It seems you are safe.
What can Mr X do to make his threat credible? This is an classic problem in game theory and perhaps I have something new to say. But it cannot be better than what Schelling and Ellsberg said many years ago. For example, see the Theory and Practice of Blackmail by Daniel Ellsberg. Ellsberg identifies four strategies for the blackmailer: (1) commitment, (2) contracts with third parties, (3) uncertainty about payoffs and (4) cultivating a reputation for irrationality.
Mr X might give his evidence over to a lawyer and instruct him to release it should Mr X ever be fired. He might write a contract with a third party stipulating that he will pay a large fine to the third party if Mr X is fired and does not release the evidence. These solutions seem far fetched to Mr X. He has no wealth to hand over as a fine and anyway contracts can be renegotiated (e.g. The third party knows that he will not get paid in equilibrium. So Mr X and the third party could agree to write a new contract after Mr X is fired. The agree to small payment to the third party even if Mr X does not reveal the evidence.)
So, Mr X is left with the last two options which are quite related. He has to look either as if he enjoys a fight for its own sake or that he does not but is crazy enough to take actions against his own self-interest. The topic of many subsequent papers in game theory.
Ellsberg’s paper is the text of a lecture he gave to a general interest audience. It is an easy and fun read. Ellsberg offers a very clear definition of rationality as used in economics. The paper is notable for an aesthetic in game theory that it espouses: Game theory offers qualitative intuition and is not inherently quantitative. And it is an art not a science.
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February 7, 2011 at 11:35 am
k
what with all this stuff about game theory being a piece of logic, not being inherently quantitative…it would seem that an experiment approach simply cannot work, because the equivalence of the utility function (in the minds of the subjects) to the monetary payoffs decided by the experimenter is unclear.
Is there a way then to generate an experiment in the lab that does not require monetary payoffs? Instead, one literally makes people play a game without any monetary gain or loss whatsoever, and then infers from the actions taken the “payoffs” they receive. These can then form the data to which game theoretic predictions can be applied.
February 7, 2011 at 10:32 pm
Lones Smith
I got into blackmail from overdosing on Columbo episodes. The plot goes — the blackmailer extracts money, then when he tries to do it again, the murderer rubs him out. But this sort of blackmail violates your property what is bad for you is also bad for him”.
Anyhow, for this more rational form of blackmail, I thought the subgame perfect solution was an annuity. In fact, it is more subtle than that, as I found out reading a nice paper that beat me to the punch: Steven Shavell and Kathryn Spier (2002), “Threats Without Binding Commitment”
http://www.law.harvard.edu/faculty/spier/pdf/threatswithoutbindingbepress.pdf
February 8, 2011 at 10:18 am
Sandeep Baliga
Thanks, Lones. Paper looks interesting. I will take a look at maybe write another post, probably next week since I am teaching four days this week!