Consider the following labor market game:

An employer sets a wage between $0 and $10 for a worker. The worker is paid the wage regardless of the worker's effort. After the wage is paid the worker chooses an effort level between 0 and 10. The cost of effort for the worker is $0.25 per unit of effort. The benefit of effort goes to the employer, who receives $3 for each unit of effort. 

a.  What is the subgame perfect equilibrium of this game?

b. Suppose this game is run for 10 rounds in an experiment, with pairs of subjects randomly re-matched after each round. What would you expect to observe in the experiment?

c. Suppose that you observe positive wages paid by the employer in the experiment? What kind of social preferences could account for observed positive wages? 

Suppose that the experiment is run with the same pair of subjects in each of 10 Funds (fixed matching), rather than having subjects randomly re-matched after each round. Sould you expect this to make any difference in outcomes? Why or why not?