Empirical examples of mixed strategies are not very common, but randomizing one's actions?that is, adopting a mixed strategy?often makes sense in situations in which one party is monitoring the work effort, legal compliance, emissions reductions, or arms limitations of another. Here is an example. An employer agrees to pay a wage, w, to a worker who may then Work, expending a subjective cost of effort, e, or Not work, the payment of the wage being conditional on whether the worker has been detected Not working (table c). The employer can determine if the worker worked by paying an inspection cost of c. If the worker Works, revenues net of wage and inspection costs are y. Suppose the worker randomizes his actions, choosing the mixed strategy: Not work with probability , otherwise Work, and the employer chooses the strategy Monitor with probability , otherwise, Not monitor. The mixed strategy Nash equilibrium is a pair (?*, ?*) such that neither employer nor worker could gain higher expected pay-offs by adopting a different strategy.

1 Show that the mixed strategy Nash equilibrium for this game is o* = c/(2c + w) and u* = e/w 2 Explain why the equilibrium level of Not working varies inversely with the wage and the equilibrium level of Monitoring varies with the subject tive cost of effort 3 Define a strict Nash equilibrium and show that (o*, p*) cannot be strict. Show that the worker would do equally well by adopting any strategy, that is, choosing o over [0, 1], as long as the employer played the Nash equilibrium strategy, and that the analogous statement is true of the employer. 4 Why, nonetheless, might one expect to observe values in the neighbor- hood of o* and p*?TABLE C The Monitor and Work Game Employer Worker Monitor Not Monitor Not work 0, c Work W-G. V-WC W-G. V-WU