Static game

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? Why or why not?
3 Does Odd have a dominant strategy? Why or why not?
4 What is the Nash Equilibrium of this game?
5 If there are multiple Nash Equilibria, which one will be selected in the end? If there is no Nash Equilibrium, how will
the game end?

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