Question

Suppose India and Pakistan sign a treaty requiring both countries to stop building nuclear weapons. If both countries abide by the treaty, India receives a payoff of 8 and Pakistan receives a payoff of 13. If India cheats on the treaty while Pakistan abides by it, India receives a payoff of 14 and Pakistan receives a payoff of zero. If Pakistan cheats on the treaty while India abides by it, Pakistan receives a payoff of 14 while India receives a payoff of zero. If both countries cheat on the treaty, India receives a payoff of 5 while Pakistan receives a payoff of 3.

1. Draw the strategic (normal) form of the game.
2. What is the Nash equilibrium/equilibria of the game? Will India and Pakistan abide by the agreement?

Answer 1

Answer 1

    Pakistan

Abide Cheat

India Abide    8,13 0,14

Cheat 14,0 5,3  

Answer 2

The Nash Equilibrium is : (Cheat, Cheat) = (5,3). No, Inida and Pakistan will not abide by the agreement.

Reason:

Case 1: When India cheats, while Pakistan either abides by the decision or cheats respectively

India's payoffs would be either 14 or 5 depending on whether Pakistan abides by the decision or cheats respectively. However, the payoffs of India would be lower if he had chosen the other strategy to abide by the decision (8 or 0 depending on Pakistan's strategy)

Thus, India's dominant startegy is to cheat.

Case 2: When Pakistan cheats, while India either abides by the decision or cheats respectively

Pakistan's payoffs would be either 14 or 3 depending on whether India abides by the decision or cheats respectively. However, the payoffs of Pakistan would be lower if he had chosen the other strategy to abide by the decision (13 or 0 depending on India's strategy)

Thus, Pakistan's dominant startegy is to cheat.