Question

Solve the scissors, paper, rock game. This game is well known in many parts of the world. Two players simultaneously present a hand in one of three positions: an open hand (paper), a closed fist (rock), or two open fingers (scissors). The payoff is 1 unit according to the rule “Paper covers rock, rock breaks scissors, and scissors cut paper.” If both players present the same form, the payoff is 0.

Set up the payoff matrix for the game and then solve it.

Answer 1

The payoff matrix can be written as follows

	Player 2
Rock	Paper	Scissors
Player 1	Rock	0,0	-1,1	1,-1
Paper	1,-1	0,0	-1,1
Scissors	-1,1	1,-1	0,0

There is no pure strategy equilibrium for this game. We need to find a mixed strategy equilibrium

For Player 1

Let probability of rock =

Let probability of paper =

Therefore probability of scissors =

For Player 2

Let probability of rock =

Let probability of paper =

Therefore probability of scissors =

For player 1

E(Rock) =

E(Rock) =

E(Paper) =

E(Paper) =

E(Scissors) =

E(Scissors) =

For equilibrium

E(Rock) = E(Paper) = E(Scissors)

= =

Therefore he plays each of rock, paper, scissors with probability 1/3

For player 2

E(Rock) =

E(Rock) =

E(Paper) =

E(Paper) =

E(Scissors) =

E(Scissors) =

For equilibrium

E(Rock) = E(Paper) = E(Scissors)

= =

Therefore he plays each of rock, paper, scissors with probability 1/3