Game Theory

Acompany decides whether and how to induce a manager to put in high effort to increase the chances that the project succeeds. Unfortuantely, the manager's effort is unoloservalole the value of a suceessful project is $$2$ million; the probability of sucess given high effort is $0\mathrm{.}4$ the probability of success given low effort is $0\mathrm{.}2,$ the manager's utility is the square rout compensation $($measured in millions of dollars$)$ and his disutity from exerting high effort is $0\mathrm{.}1.$ The reservation luage of the manager is $$160,000.$

The company should offer $ if it wants only low effe the manager. When it induces low managerial effor t$,$ the Profit to the company is $