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BPP Field Exam 2010 Answers (view source)
Revision as of 21:06, 29 March 2011
, 21:06, 29 March 2011→Question B1.3
====Question B1.3====
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 outputand 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.
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>.
I will now show that <math>A>C</math> and <math>B>C</math> -- in other words, working is better than shirking no matter what the other players do.
First, note that <math>B>C</math>. Algebraically, this flows naturally from the fact that <math>sum_{i\neq j} z(e_{j})+1>sum_{i\neq j} z(e_{j})</math>. Intuition: Note that the lotteries are identical except if
===Question C1: Agenda Control and Status Quo===
