Question

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 6,1 10,7 8,4 10,3 Grace Vampire Pirate b. (3 pts.) It's the end of the soccer game, and it's time for a penalty shot. Goalie Left Right 0,2 2,0 2,0 0,2 -3,1 -3,1 Left Right Oops Kicker c. (3 pts.) Two doctors are deciding whether to order pizza for lunch. Dr. Blah Whatevs \_( _/ Sure 2,1 Dr. Meh Okay 2,1 2,1 2,1

Answer 1

a) For Grace, Pirate is always as good as Vampire. Hence he will remove Vampire from his selection set.

For Matt, Parrot gives a higher payoff.

Grace: Pirate, Mqtt: Parrot.

b) Oops is always the worst strategy. Dominated by Right. Hence Lichee removes oops from his strategy set.

The others remain same. There is no PSNE.

c) All the payoffs are the same. hHence all are equally good. All are PSNEs.