Changes

The CEO can design a scheme that exploits the risk aversion of the agents using chance. The contract would work like this: If all employees exert work, each worker will get an equal share <math>1/N</math> of the effort. However, if any single worker does NOT work, then the payoffs will be determined by a lottery in which each employee gets a <math>\frac{1}{N}</math> chance of getting 100% of the combined output. I will now show that irrespective of what other players are doing, the dominant strategy is to work.

Note that CARA utility is <math>u(c)=1-e^{-\rho c}</math>. The An employeei's utility from working (if others work) is <math>1-\exp[-\rho(\frac{1}{N}\sum_{i\neq j} z(e_{j})+\frac{1}{N}z(e_{i})-1)]</math>. An employee i's utility from working <i>if others are not working<i> is: <math>\frac{1}{N}(1-\exp[-\rho(\sum_{i\neq j} z(e_{j}...)])</math>. An employee i's utility from NOT working if others are not working is: <math>1-\exp[\frac{1}{N}\sum_{i\neq j} z(e_{j})+\frac{1}{N}z(e_{i})-1]</math>   If employee i does NOT work, the lottery is triggered and his utility is: <math>1-\exp[sum_{i\neq j} z(e_{j})]</math>. An employee i's utility from NOT working guarantees that the lottery will be triggered.