Tadelis 211 Youre a sprinter and in practice today you fell

(Tadelis 2.11). You\'re a sprinter, and in practice today you fell and hurt your leg. An x-ray suggests that it\'s broken with probability 0.2. Your problem is whether you should participate in next week\'s tournament. If you run, you think you\'ll win with probability 0.1. If your leg is broken and you run, then it will be further damaged and your payoffs are as follows:

+100 if you win the race and your leg isn\'t broken

+50 if you win and your leg is broken

0 if you lose and your leg isn\'t broken

-50 if you lose and your leg is broken

0 if you don\'t run and your leg isn\'t broken

-10 if you don\'t run and your leg is broken

Compute E[v(run)] - E[v(not run)], the difference in expected payoffs from running and not running, respectively.

Solution

Probability of leg broken = 0.2

Probability of leg not broken = 1-0.2 = 0.8

Probability of winning race = 0.1

Probability of not winning race = 1- 0.1 = 0.9

P(win the race and leg isn\'t broken) = 0.1 * 0.8

P(win the race and leg is broken) = 0.1 * 0.2

P(loose the race and leg isn\'t broken) = 0.9 * 0.8

P(loose the race and leg is broken) = 0.9 * 0.2

Therefore,

E[v(run)]= 100 *0.1*0.8 + 50 *0.1 *0.2 + 0*0.9*0.8 + (-50)*0.9*0.2 = 0

E[v(not run)]= 0*0.8+ (-10)*0.2 = -2

E[v(run)] - E[v(not run)] = 0 - (-2) = 2 Answer