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