Question

1 Static games (9 pts.) For each of the following games: Circle all payoffs corresponding to a player's best response. Identify any/all strictly dominant strategies (or indicate that there are none). Identify any/all strictly dominated strategies (or indicate that there are none). Identify any/all pure strategy Nash equilibria by writing the equilibrium strategies as an ordered pair. (If there is no PSNE, write "no PSNE".) a. (3 pts.) Two friends are deciding what costumes to wear for Halloween. Matt Parrot Zombie Vampire 10,7 10,3 6, 1 Grace Pirate 8, 4 b. (3 pts.) It's the end of the soccer game, and it's time for a penalty shot. Goalie Left Right Left 2,0 0, 2 Kicker Right 2,0 0,2 -3, 1 Oops 3,1

microecon

Answer 1

a) We take Matt to be player 1 and Grace to be player 2.

When Matt chooses to be Parrot, Grace's best response (BR) is playing Pirate as 4>1

When Matt chooses to be Zombie, Grace's best response (BR) is playing Vampire as 7>3

There is no dominant or dominated strategy here.

When Grace chooses to be Vampire, Matt's best response (BR) is playing Zombie as 10>6.

When Grace chooses to be Pirate, Matt's best response (BR) is playing Zombie as 10>8

Therefore, for Matt Zombie is a strictly dominant strategy and Vampire and Pirate are dominated.

Here the PSNE strategy is (Vampire,Zombie)

b) When Goalie chooses left (L), Kicker chooses L over RIght(R) and Oops (O) as 2>1>0.

When Goalie chooses R, Kicker chooses R over L and O as 2>1>0.

When Kicker chooses L, Goalie chooses R over L as 2>0.

When Kicker chooses R, Goalie chooses L over R as 2>0.

When Kicker chooses O, Goalie is indifferent between the two.

Here there is dominant, dominated strategies and no PSNE.

c) Here all the strategies give the same payoff and thus there can be no strategic interaction here. All the strategies are PSNE and none are dominant/dominated.