Question

Consider two neighbors embroiled in a property dispute. Neighbor 1 (let’s call her Shelly) believes Neighbor 2’s (let’s call him Bob) maple tree crosses her property line and wants to cut it down. Bob believes that Shelly is mistaken about the position of her property line and warns her to leave his tree alone. Shelly can negotiate with Bob or sue him (presumably to pay for tree removal). Bob can either negotiate with Shelly or sue her (presumably to block her from cutting the tree down). Legal fees to sue someone are $2000.

If both negotiate, neither loses anything or gains anything. If Bob sues while Shelly negotiates, Bob must pay $2000 in legal fees, but because Shelly failed to develop a legal defense (choosing instead to negotiate), she will certainly lose the case and have to pay a $5000 to Bob. The opposite is true if Shelly sues while Bob negotiates. (Shelly pays $2000 in legal fees while Bob pays $5000 to Shelly).

If Shelly and Bob BOTH sue each other, the case goes to court and an impartial judge has a 50/50 chance of ruling against either one. If the judge rules against someone in this kind of case, they have to pay $10,000 to the other person (both still have to pay legal fees regardless of the decision).

a) Draw this strategic interaction as a mixed game (a game with both simultaneous and sequential elements).

b) Is this game zero sum or non-zero sum?

c) Find the Nash equilibrium of this game by any method you choose