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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 and a <math>1-\frac{1}{N}</math> chance of getting zero. I will now show that irrespective of what other players are doing, the dominant strategy is to work.

If employee works but others aren't, the lottery is triggered and employee i's utility is <math>B=\frac{1}{N}(1-\exp[-\rho(\sum_{i\neq j} z(e_{j})+z(e_{i})-1)])</math>.

First, note that <math>B>C</math>. Within the algebra, note that the utilities are identical except for the exponents. Note that <math>\sum_{i\neq j} z(e_{j})+z-1>\sum_{i\neq j} z(e_{j})</math> because <math>z-1>0</math>. As such, we know that the inequality always holds. As for the intuition: Note that the lotteries are identical except for the payoff in <math>\frac{1}{N}</math> of the time. If he works, this value is higher, so he prefers to work.

In the above RHS expression, we know that the numerator is smaller than the denominator, so the fraction is less than 1. We know that <math>N>1</math>, so the inequality always holds.