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