the better employee is necessary for production. This assumption implies that ex-post
competition between employees takes an extreme form: ex post only one employee is
valuable5.
With probability ɑɪ employee 1 is the "good" employee and contributes a total value
of V1 — /(λlog(l + fe)), and employee 2 is the "bad" employee with a total value of
V2 = /(υ) = V. Vice-versa, with probability α2, V1 = f(v) = V_ and V2 ≡≈ /(Alog(l+fc)).
We take λ to be large enough that A log(l + fc) > υ for all relevant choices of k. Also, for
convenience we shall use the notation V for the higher value of the two employees and V
for the lower value.
Outside Ownership
Under outside ownership negotiations now involve four parties: the two employees, the
owner and the client. As before, the employees can in principle offer their services without
using the firm’s asset. The total surplus of this exchange would be lower but the owner
would then be cut out of the deal. This possibility provides the employees with an outside
option in their negotiations with the owner. Similarly, the owner, one of the employees
and the customer can freeze out the other employee. The only party that cannot be
excluded is the customer.
To model this potentially complicated negotiation game we proceed as follows. As
explained in section II. we capture the outside options principle in this multilateral bar-
gaining game with competition by Specihdng a simple two-stage game: in the first stage,
the owner makes a take-it-or-leave-it offer to the two emplθ}*ees and the customer. If the
offer is accepted, the game ends. If the offer is rejected, the game goes to a second and
final stage, where the two employees make take-it-or-leave-it offers simultaneously to the
customer. If the customer accepts one of the offers, the game ends. If the customer rejects
all the offers, every player gets a zero payoff and the game ends.
Without loss of generality, suppose that employee Ei is ex-post more capable than
employee S2. Then, we use backward induction and start from the second stage of the
bargaining game to find the solution of the overall bargaining game.
In the second stage, both employees compete for the customer à la Bertrand and the
equilibrium offers are v . At that offer, the customer picks the better employee. Therefore,
5In addition, an implicit assumption in these functional forms is that human capital investment only
adds value for the employee who is best ex post. This assumption is inessential when there is only one
customer. It will be relaxed when we consider the case of multiple customers.