Trey, Cactus, and Leo are all going to start up new businesses in town. They are all making their decisions simultaneously, and they know the profits they can earn depend on their choice and on the choices of the other two individuals. Trey is going to either start a concrete business, landscaping business, or become an architect; Cactus is going to either start a bar, start a restaurant, or start a boutique; and Leo is going to build small houses, build mid-sized houses, or build large houses.

Solve for the Nash equilibrium (equilibria) of this game. You should do this by first finding the dominant strategies or by using the iterated deletion of dominated strategies. Is the Nash equilibrium (or multiple Nash equilibria) Pareto efficient?

(Treys payoff, Cactuss payoff, Leos payoff)

						Leo
		Builds small houses			Builds mid-sized houses			Builds large houses
		Cactus			Cactus			Cactus
		Run bar	Run restaurant	Run boutique	Run bar	Run restaurant	Run boutique	Run bar	Run restaurant	Run boutique
Trey	Concrete business	(-1,3,-2)	(2,0,2)	(0,0,2)	(4,2,0)	(3,1,3)	(0,0,1)	(-1,1,-1)	(0,-2,1)	(0,-2,2)
	Landscaping business	(1,2,0)	(1,1,0)	(1,1,1)	(1,4,2)	(2,2,1)	(1,2,1)	(1,4,2)	(1,1,2)	(1,3,1)
	Architect	(1,2,-2)	(1,1,-1)	(1,1,1)	(2,3,3)	(5,3,0)	(1,2,1)	(3,4,2)	(2,5,1)	(1,2,1)

Show your work & All steps if possible, please!

Leo (Trey's payoff, Cactus's payoff, Leo's payoff) Builds small houses Builds mid-sized houses Builds large houses Run bar (-1,3,-2) Cactus Run Run restaurant boutique (2,0,2) (0,0,2) Run bar (4,2,0) Cactus Run restaurant (3,1,3) Run boutique (0,0,1) Run bar (-1,1,-1) Cactus Run restaurant (0,-2,1) Run boutique (0,-2,2) Concrete business Trey Landscaping business Architect (1,2,0) (1,2,-2) (1,1,0) (1,1,-1) (1,1,1) (1,1,1) (1,4,2) (2,3,3) (2,2,1) (5,3,0) (1,2,1) (1,2,1) (1,4,2) (3,4,2) (1,1,2) (2,5,1). (1,3,1) (1,2,1) Leo (Trey's payoff, Cactus's payoff, Leo's payoff) Builds small houses Builds mid-sized houses Builds large houses Run bar (-1,3,-2) Cactus Run Run restaurant boutique (2,0,2) (0,0,2) Run bar (4,2,0) Cactus Run restaurant (3,1,3) Run boutique (0,0,1) Run bar (-1,1,-1) Cactus Run restaurant (0,-2,1) Run boutique (0,-2,2) Concrete business Trey Landscaping business Architect (1,2,0) (1,2,-2) (1,1,0) (1,1,-1) (1,1,1) (1,1,1) (1,4,2) (2,3,3) (2,2,1) (5,3,0) (1,2,1) (1,2,1) (1,4,2) (3,4,2) (1,1,2) (2,5,1). (1,3,1) (1,2,1)