Consider the following game between two players. Each player i has an initial endowment of 5 cans of beer. This beer can hidden in their private account (xi) or put in a public account, the fridge (yi). The happiness/payoff (πi) of each player depends on the beer in her private account and the beer in the public account and takes the following form:

(assume only whole cans of beer can be allocated to each account.)

a) What is the happiness function for player i = 1?

b) What are the Nash equilibrium contributions for each player? And what is each player's happiness?

c) Is there a set of contributions that gives each player a higher level of happiness than under the Nash Equilibrium? If not explain why not.

d) What is the socially optimal allocation that maximizes total happiness?

1 T: = 2 ; + (y1 + y2)