Nash equilibrium

Dan and Neil are playing Settlers of Catan. Dan has rolled a seven and just put the stopper on a Field which touches one of Neil’s Settlements. Since Dan is a real jerk store, he decides to steal one of Neil’s two cards. Neil has a Grain and a Wool resource card. Neil holds one card in his left hand and the other card in his right hand face down. Dan chooses one of Neil’s cards. This is a one shot game where Dan takes an unknown card from Neil’s left or right hand. Dan really wants the Grain resource card, his payoff for picking the Grain card is 10 life points. Dan does not particularly want the Wool resource card, his payoff for picking the Wool card is 3 life points. For Neil, if Dan selects Grain, Neil loses 1 life point. If Dan selects Wool Neil loses 2 life points. Additionally, Dan is an Anti-Leftite, he hates going left, whenever he picks Neil’s left hand he loses 2 life points no matter which card he gets. Neil gets great joy from seeing Dan in pain, if Dan picks Neil’s left hand, Neil gains 4 life points no matter which card Dan gets.

a. Draw a payoff matrix for Neil and Dan

b. Does Dan have a dominant strategy?

c. Does Neil have a dominant strategy?

d. What is the Nash equilibrium for the one-shot game?