Here is a scenario:

Suppose that two persons (A and B) have an experiment that must be completed in either city X or city Y. If city X is chosen, A and B will pay \$2 and \$5 respectively for travel expenses. Otherwise, if city Y is chosen, both A and B will pay \$3.

Selected city the expenditure of A the expenditure of B
City X -2\$ -5\$
City Y -3\$ -3\$

Suppose that neither of them could get any benefits if the experiment is completed successfully; otherwise both of them are destined to be fired. Therefore A and B must reach an agreement on which city to be chosen.

We noticed that the expenditure paid by A and B can be adjusted privately, as long as the sum remains either \$6 or \$7.

This is what makes the given scenario different from the classic prisoners dilemma.

My questions are:

  1. How to rigorously prove that A and B must reach an agreement?
  2. How to define and measure the “relative benefit” of A and B?
  3. What is the best strategy if they reach an agreement?
  4. If the best strategy holds, the selected city must be city Y. Can we say that any information about city X is worthless?


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