Question

Suppose two players are playing a game, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then Even keeps both pennies, so wins one from Odd ( 1 for Even, -1 for Odd). If the pennies do not match (one heads and one tails) Odd keeps both pennies, so receives one from Even (-1 for Even, 1 for Odd).
1. Please draw the payoff matrix for this game.
2. Does Even have a dominant strategy?

Answer 1

Answer:

1.  

E(down) / Odd(Across)     H                  T

H                                  (1,-1)        (-1,1)

T                                   (-1,1)        (1,-1)

2. Even doesn't have a dominant strategy as both the strategies are providing equal payoffs for pure strategy.