Two co-workers, Chris and Rene, have a dispute over who should get a massive $10,000 Christmas bonus offered by their company's headquarters to the employee considered most instrumental in the company's success this past year. The co-workers are allowed to divide this bonus however they decide. However, headquarters has decided that the local company boss will decide who gets the bonus if the co-workers cannot agree. Both employees are risk averse and both have the same utility function U= , where X = the amount of bonus received. Both workers consider that their boss will either give the bonus entirely to one worker or the other, but not split it. Thus, if the workers cannot agree on how to divide the bonus, then each will either get $0 or the full $10,000 bonus.

a) Assuming both Chris and Rene feel the boss will just flip a coin to decide who gets the bonus (i.e., 50% chance of getting the $0 or the full $10,000 bonus), what is the minimum amount of the bonus that each worker would accept in a voluntarily agreement to avoid the risk of what the boss might choose to do in deciding who gets the bonus?