Question

1. In the following payoff table, two decision makers, Gates and Dell, must make simultaneous decisions to either cooperate or not cooperate with each other. Please indicate the Nash equilibrium in the game. Does the result represent a prisoner’s dilemma situation?

Not cooperate Gates Cooperate

Not cooperae $100/$100 $600/$50

Dell Cooperate $50/600 $500/$500

2. Assume that a total $100 grant will be shared by the three researchers, X, Y, and Z. Each person is rational and selfish. There are six proposals with different shares of (X, Y, Z) for choices as the following.

Proposal I: (X, Y, Z) = (50, 40, 10)

Proposal II: (X, Y, Z) = (60, 10, 30)0

Proposal III: (X, Y, Z) = (40, 20, 40)

Proposal IV: (X, Y, Z) = (20, 30, 50)

Proposal V: (X, Y, Z) = (30, 50, 20)

Proposal VI: (X, Y, Z) = (20, 50, 30)

The rule of choosing the final proposal is simple. First, Z is the person to determine who (either X or Y) is the proposal raiser. Then the proposal raiser chooses a particular proposal. Finally, the last person has the right to pass it or reject it. If the last person’s payoff is the smallest among the three, then the proposal will be rejected and no one will get anything. The decision making process can be done by only one time. Please determine which proposal will be the final outcome and explain the decision making process briefly in one paragraph.

Answer 1

Not cooperate Gates Cooperate

Not cooperae $100/$100 $600/$50

Dell

Cooperate $50/600 $500/$500

If Gates plays Not-cooperate, then Dell will play not-cooperate (since 100>50)
If Gates plays cooperate, then Dell will play not-cooperate (since 600>500)

So Dell has a dominant strategy in playing "not-cooperate".

One can check that even Gates has a dominant strategy in "non-cooperate".

Thus the nash equilibrium will be (Not cooperate, Not cooperate) at which both firms will get $100. But, if they both cooperate then each will earn $500. But, this will never happen because the other firm might play opposite when the other firm plays cooperate. In such a case, the firm cooperating will incur a huge loss while non-cooperating will earn 600 (i.e. $100 extra).

Thus game is similar to that of Prisonner's Dilemma.

PS: In the event of multiple questions, only first 1 is attempted.