Answer Happy

4. Tom has invited Jeff to his party. Tom must choose whether or not to hire a clown. Simultaneously, Jeff must decide whether or not to go the party. Jeff likes Tom but he hates clowns - he even hates other people seeing clowns! Jeff's payoff from going to the party is 4 if there is no clown, but O if there is a clown there. Jeff's payoff from not going to the party is 3 if there is no clown at the party, but 1 if there is a clown at the party. Tom likes clowns - he especially likes Jeff's reaction to them - but does not like paying for them. Tom's payoff if Jeff comes to the party is 4 if there is no clown, but 8 - x if there is a clown (x is the cost of a clown). Tom's payoff if Jeff does not come to the party is 2 if there is no clown, but 3 - x if there is a clown there. (a) (5 points) Write down the normal form game. (b) (5 points) Suppose x = 0. Identify any dominated strategies. Explain. Find the Nash equilibrium. What are the equilibrium payoffs? (c) (5 points) Suppose x = 2. Identify any dominated strategies. Explain. Find the Nash equilibrium. What are the equilibrium payoffs? (d) (5 points) Suppose x = 3. Identify any dominated strategies. Explain. Find the Nash equilibrium. What are the equilibrium payoffs? (e) (5 points) Suppose x = 5. Identify any dominated strategies. Explain. Find the Nash equilibrium. What are the equilibrium payoffs?