In a game, each of two players can volunteer some of their spare time planting and cleaning up the community garden. They both like a nicer garden and the garden is nicer if they volunteer more time to work on it. However, each would rather that the other person do the volunteering. Suppose that each player can volunteer 0, 1, 2, 3, or 4 hours. If player 1 volunteers x hours and 2 volunteers y hours, then the resultant garden gives each of them a utility payoff equal to x + y . Each player also gets disutility from the work involved in gardening. Suppose that player 1 gets a disutility equal to x (and player 2 likewise gets a disutility equal to y). Hence, the total utility of player 1 is x + y - x, and that of player 2 is x + y - y.

 

a. Write down the normal form of this game.

b. Show that the strategy of volunteering for 1 hour weakly dominates the strategy of volunteering for 2 hours. Does it strongly dominate as well?

c. Are there any other weakly dominated strategies for player 1? Explain.

d. Is there a dominant strategy for player 1? Explain.

e. Write down the best response of a player to every strategy of the other player.

f. Determine the Nash equilibria of the game

2) Consider the following normal form game:

	L	C	R
U	5,1	0,4	1,0
M	3,1	0,0	3,5
D	3,3	4,4	2,5

a) Find all possible equilibria using dominance and Nash equilibrium concepts.