Consider a game with two players, where each player i = 1,2 has preferences

u,- = after“, where c,- is consumption and s,- is social interaction. s,- is given by Si = H +Iij *Fji: where r,- is time spent by player i alone, and ray is the time player 1' spends with

player j. Player 1' has to decide how much of his or her time T to allocate between

work, haying time alone, ti, and social interaction, raj. Assume that for each hour, player 1' works, he or she earns the wage w, and assume that the price of the

consumption good c,- is normalized to p = l. i. Carefully deﬁne the optimization problem for player 1. Write down the

Kuhn—Tucker conditions and discuss these conditions. Explain why player

1 faces a strategic situation. Find the best—response functions for player 1

and 2. Graph these functions. ii Find all Nash equilibria when assuming that players make their choices si—

multaneously.