In
Big Bang Theory, Sheldon invented a variation of the standardPaper-Scissors-Rock
game. His game was called Rock-Paper-Scissors-Lizard-Spock. This isa two-player
game with the following rules (that he quickly repeats many timesin one episode):

Scissors cuts Paper
Paper covers Rock
Rock crushes Lizard
Lizard poisons Spock
Spock smashes Scissors
Scissors decapitates Lizard
Lizard eats Paper
Paper disproves Spock
Spock vaporizes Rock
(and, as always), Rock crushes Scissors

In other words, the winning item is listed first. Assuming we havetwo players (A and B),
develop the payoff matrix where 1 is a win, -1 is a loss, and 0 iseven (refer to my lecture
on the Paper-Scissors-Rock game.

Is there a dominant strategy and Nash equilibrium in this game?