Question

Its Simple spock smashes scissors scissors cuts paper scissors decapitates lizard paper disproves spock spock vaporiz0S rock rock crushes scissors lizard poisons spock paper covers rock lizard eats paper rock crushes lizard

Answer 1

A.

No this is not a zero sum game, as there is a chance of tie for both selecting same.

In case that is not allowed then it becomes a zero sum game.

B.

	Player 2
		Spock	Scissors	Paper	Rock	Lizard	P(1) Win
Player 1	Spock	(0,0)	(1,-1)	(-1,1)	(1,-1)	(-1,1)	0.4
	Scissors	(-1,1)	(0,0)	(1,-1)	(-1,1)	(1,-1)	0.4
	Paper	(1,-1)	(-1,1)	(0,0)	(1,-1)	(-1,1)	0.4
	Rock	(-1,1)	(1,-1)	(-1,1)	(0,0)	(1,-1)	0.4
	Lizard	(1,-1)	(-1,1)	(1,-1)	(-1,1)	(0,0)	0.4
	P(2) win	0.4	0.4	0.4	0.4	0.4

C.

As in the above play off matrix winning for any strategy is exactly the same and opposing it the other player has the exact same options there is no strategy that will act as a maxima. Local or global. Hence there is no saddle point in this game.

D.

For any given strategy

P(win for 1) = 0.4

P(loss for 1) = 0.4

P(tie for 1) = 0.2

same holds good for Player 2.

Hence there is no strategy that is better than the rest.

The game is in same condition for each of the strategy and there does not any maxima and hence no optimal solution exists.