Rock-paper-scissors is a simultaneous two-player zero-sum game in which rock defeats scissors, scissors defeats paper, and paper defeats
rock. Assigning payoff 1 to a win, 
to a loss, and 0 to a tie gives the row player's payoff
matrix
 |
(1)
|
with the rows and columns ordered as rock, paper, and scissors.
The game has no Nash equilibrium in pure strategies. Its unique mixed-strategy Nash equilibrium assigns probability 
to each action, and its game
value is 0.
