Blanket in the backward induction equilibrium

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Sam and Dan are twins who like playing tricks on each other. Sam is deciding wheter to take Dan's blanket. Sam has a utility of 0 if he doesn't tale Dan's blanket. If Sam takes Dan's blanket, there is a possibility of Dan retaliating by taking Sam's pillow, thereby earning Sam a utility of -5. If Dan doesn't retaliate, Sam gets a utility of 5. Dan has a utility of 10 if Sam doesn't take his blanket. If Same takes his blanket, Dan's utility is -10. Dan's utility changes by X if he retaliates.

a) Draw the game tree.

b) For what values of X would we observe Sam taking Dan's blanket in the backward induction equilibrium?

Reference no: EM131387635

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