Ned and Ruth love to play hide and seek. It is a simple game, but it continues to amuse. It goes like this. Ruth hides upstairs or downstairs. Ned can look upstairs or downstairs but not in both places. If he finds Ruth, Ned gets one scoop of ice cream and Ruth gets none. If he does not find Ruth, Ruth gets one scoop of ice cream. a) Fill in the payoffs in the matrix below:

b) Are there any Nash equilibria in pure strategies in this game, and if so, what are they? c) Find a Nash equilibrium in mixed strategies for this game.

		Ruth
		upstairs	downstairs
ned	upstairs
	downstairs