A question on assymetric information in game theory:

A worker's job consists of operating a machine. If the worker operates the machine as instructed (e l), then with probability 1/2 the level of output of 1 (s H) and the firm's revenue is > 0, and with probability 1/2 output and revenue are zero (s L). Alternatively, the worker can choose to use the machine for her own private purposes e 0), obtaining a private consumption value of 1/2 from doing so. If she does so, however, output and revenue are zero with certainty. The worker has utility u(y) = y (1/2) y2, where y is her disposable income, inclusive of any private value she obtain from the machine, i.e. y(w, e) w + (l e)/ 2, where w is the wage received from her employer and e e {0, l} is an indicator of how she uses the machine l: as intended; e 0, for private purposes). Employers operate under conditions of perfect competition, meaning that they must break even in expectations (zero expected profit). So, if their expected revenue is E(v) and the cost of using the machine is r, the expected wage paid, E(w), must be such that E(v) r E(w) 0. Assume 2 (1 r). VI/ hen c? 1, this implies r F/ 2 r 1, making the zero-profit condition: