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 and 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?

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						Leo
(Trey’s payoff, Cactus’s payoff, Leo’s payoff)
		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)

Answer rating: 100% (QA)

To find the Nash equilibrium in this game we will use the concept of iterated deletion of dominated ... View the full answer