#### (Solved): Two Drivers Are Barreling Down I-94 Trying To Get Home As Fast As Possible. Suppose They Are Travell ...

Two drivers are barreling down I-94 trying to get home as fast as possible. Suppose they are travelling side by side at a high rate of speed when they come to a construction project that forces the two lanes to merge into a single lane. Suppose each driver has two actions they could take: i) continue at the same high rate of speed, ii) slow down and yield to the other driver if necessary. A driver that slows down gets a payoff of 0. A driver that continues to go fast gets a payoff of 1 if the other driver slows down. However, if both drivers go fast they cause an accident and received payoffs of (c1, c2) with ci<0, c2<0. a) Solve for the mixed strategy equilibrium if ci and ca are known. b) Now suppose that (ci, cz) are unknown but each is an independent draw from a uniform distribution on (0,2). Suppose that each driver plays a cutoff rule strategy: if C c drive fast, otherwise drive slow. Solve for the symmetric Bayesian Nash equilibrium in cutoff rule strategies.

a)Amixed strategy Nash equilibrium. involves at least one player playing a randomizedstrategyand no player being able to increase his or her expected payoff by playing an alternatestrategy.
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