GAME THEORY Consider the voluntary contribution to building

GAME THEORY:

Consider the voluntary contribution to building a fence game. Assume that v1 = v2 = 100, and C = 150. Select all that apply.

A. It is efficient to build the fence

B. Contributing more than her own valuation is a strictly dominated strategy for each player.

C. There are Nash equilibria in which the fence is not built.

D. Each player contributing 100 is a pure strategy Nash equilibrium in this game.

Please explain your answers! Thank you!

Solution

The correct answers are -

A. It is efficient to build the fence

B. Contributing more than her own valuation is a strictly dominated strategy for each player

C. There are Nash equilibria in which the fence is not built.

Reason

a>Since the overall cost of the fence-making is lesser than the total values, so it is efficient to make the fence.

B> One can always have at least value 0 by not paying, so paying more than his own value does not make sense.

C> When one player pays nothing, the best strategy for the other player is also to not pay anything.