Roger has invited Caleb to his party. Roger must choose whether or not to hire a...

Roger has invited Caleb to his party. Roger must choose whether or not to hire a clown. Simultaneously, Caleb must decide whether or not to go to the party. Caleb likes Roger but he hates clowns - he even hates other people seeing clowns! Caleb’s payoff from going to the party is 4 if there is no clown, but 0 if there is a clown there. Caleb’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. Roger likes clowns - he especially likes Caleb’s reaction to them but does not like paying for them. Roger’s payoff, if Caleb 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). Roger’s payoff, if Caleb does not come to the party, is 2 if there is no clown, but 3 − x if there is a clown there.

• Write down the normal form game

• Assume x = 2 Find the Nash equilibrium (Pure and Mixed if any)

Expert Solution

Rahul Sunny answered 7 months ago

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