## Specify conditions on the parameters of the model such that, with unobservability of workers’ effort, there exists an equilibrium where worker 1 is always hired but worker 2 never is.

A.In the context of Subsection 9.3.2 with effort unobservability, assume that (9.46) does not hold. Is there any subgame-perfect equilibrium where only one worker is hired every period? Discuss your answer.

B. Consider a context as described in Section 9.3, but with worker 1 being uniformly more productive than worker 2 for each scale of production, and suppose this fact is common knowledge. (That is, if yik denotes the productivity of worker when workers are employed by the firm, one has yyfor each = 12.) Specify conditions on the parameters of the model such that, with unobservability of workers’ effort, there exists an equilibrium where worker 1 is always hired but worker 2 never is.

### Prove that the hypothesis class of all conjunctions over d variables is PAC learnable and bound its sample complexity.

1.  In this question, we study the hypothesis class of Boolean conjunctions defined as follows. The instance space is X ={0,1}d and the label set is Y ={0,1}. A literal over the variables x1, . . ., xd is a….

### Show that for every probability distribution D, the Bayes optimal predictor fD is optimal, in the sense that for every classifier g from X to {0,1}, LD( fD) ≤ LD(g).

1. Let H be a hypothesis class of binary classifiers. Show that if H is agnostic PAC learnable, then His PAC learnable as well. Furthermore, if A is a successful agnostic PAC learner for H, then A is also a….

### . Show that the algorithm just described satisfies the requirements for being a RP solver for ERMH.

1. On the basis of the preceding, prove that for any k ≥ 3, the ERMHnk problem is NP-hard. 2 In this exercise we show that hardness of solving the ERM problem is equivalent….