Cop and robber

From CyberOne Wiki

Cop and Robber is played between two players, Cop and Robber. Cop has two strategy options, to patrol or not to patrol. Robber has two strategy options, to rob or not to rob. If Robber decides to rob, Robber wins 1 chip if Cop is not patrolling, but loses one chip is Cop is patrolling. If Robber stays home, Robber wins 1 chip if Cop is patrolling, but loses 1 chip is Cop is not patrolling. Both players reveal their choices simultaneously. The game is repeated.

Cop and Robber Payoff Matrix

	Robber
Cop	Rob	Don't Rob
patrol	(1, -1)	(-1, 1)
don't patrol	(-1, 1)	(0, 0)

This is an example of a zero-sum game, where one player's gain is exactly equal to the other player's loss. The game illustrates the concept of mixed strategies and a mixed strategy Nash equilibrium.