Tuesday, April 14, 2009 by Dave Blum

Before I move on to a different subject (such as team building ideas, treasure hunt clues, scavenger hunt lists, etc.), I just wanted to wrap up my discussion of game theory with a brief description of the famous “Prisoner’s Dilemma”.   The Prisoner’s Dilemma can be described as a situation in which two (or more) people would benefit by cooperating but decide, instead, to act out of self interest, for mutual loss.

Len Fisher gives the example of two captured thieves. Unbeknownst to the two prisoners, the prosecutor has realized that his case is fairly weak and realistically, if both guys plead “not guilty”, he can only pin them with the charge of carrying a concealed weapon, which carries a jail term of two years.  All the thieves need to do is keep their mouths shut and both plead “not-guilty.”

The clever prosecutor, however, comes up with a devious plan; he approaches Thief #1 and suggests that Thief #2 is going to “cheat” on the deal and plead “guilty”.   In such a case (with Thief #2 pleading “guilty” and Thief #1 still pleading “not-guilty”), Thief #2 gets a reduced sentence of 4 years while Thief #1 now gets ten years (for burglary).  Clearly, if Thief #1 thinks that Thief #2 is going to cheat and plead “guilty”, he would do better to plead “guilty” as well, and take the four years instead of ten. Moreover, the prosecutor offers Thief #1 a deal that if he pleads “guilty” and Thief #2 doesn’t, he can go free for turning over state’s evidence.   No matter what Thief #1 does, he should logically change his plea to “guilty”.

The trouble is that the prosecutor has made the same offer to Thief #2.

To summarize, here are the four scenarios:

Thief #1:  Not Guilty
Thief #2:  Not Guilty
Result:  Thief #1 gets 2 years; Thief #2 also gets 2 years.

Thief #1:  Guilty
Thief #2:  Not Guilty
Result:  Thief #1 gets 4 years (or possibly goes free), Thief #2 gets 10 years.

Thief #1:  Not Guilty
Thief #2:  Guilty
Result:  Thief #1 gets 10 years, Thief #2 gets 4 years (or possibly goes free).

Thief #1:  Guilty
Thief #2:  Guilty
Result:  Thief #1 gets 4 years, Thief #2 also gets 4 years.

The logic seems irrefutable; out of fear that his partner will cheat, both thieves plead “guilty” and receive a sentence of four years.  Each would have received only two years if they’d simply stuck with the original plan and both pled “not guilty”.

The key to the Prisoner’s Dilemma is that cooperation, as described above, would have provided a clear benefit.  However, fear that the other would “defect” led each person to act independently, thereby choosing a path of self interest that resulted in mutual loss on both sides.

Situations like the Prisoner’s Dilemma abound in our world. Consider the arms race of the 1950’s — if the US and the Soviet Union could have cooperated to limit arms production, both sides might have saved vast amounts of money to be used for more constructive purposes.  Global warming is another example; many polluting nations see little incentive to control carbon emissions so long as other nations continue to pollute.

In my own scavenger hunts, I often see groups work in competition to each other, when cooperatively sharing clue resources would save a lot of time and effort.

Can you think of a situation in your life where distrust led to a collective loss?

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