The name is absent

Ei gets у — и and the customer v, while Eq gets zero. These equilibrium pawffs are their
outside options in the first round of bargaining with the owner. Therefore the outside
owner will make an offer of υ — y to Ei and y to the customer and keeps the residual
V — υ. Thus, under outside ownership the bargaining solution in our simple extensive
form bargaining game is given by:

Lemma 1 Under the outside ownership, the bargaining solution is given by:

Agent: employee Ei employee E⅛ outside owner 0 customerC
share:     v — у          0            V — v           y.

While this extensive form game may appear to be somewhat ad hoc. it does capture
in a simple and stark way the effects of competition between employees. It also captures
in an intuitive way the outside options principle. It is possible to allow' for richer (finite)
bargaining games with alternating offers and counter-offers which give unique bargaining
solutions identical to the one above (see e.g. Bolton and Whinston (1993)). These bar-
gaining games may appear to be more satisfactory and general but they are no less ad
hoc than the one considered here.

Given that Eiand Eq each has respectively an ɑɪ and ɑɔ chance of being the better
employee ex post, their ex-ante expected gross payoffs are α,(υ — υ) for г = 1,2 under
outside ownership. Thus, employee E_i (i = 1,2) chooses his initial investment in human
capital k_i given a Iewel kj chosen by employee Ej to maximize:

max{θi(λ log(l + k_i) — y) — fc_t}                          (.4)

We thus obtain the following result:

Lemma 2 For A large enough, ex-ante (symmetric) equilibrium investment levels under
outside ownership are:

⅛f^,=α_iλ-l. i = l,2.

Since we are considering a model where ex-post values of individual investments are
stochastic we obtain a very simple solution for the optimal choice of human capital in-
vestments for the two employees. In particular, we need not consider mixed strategy
equilibria in the investment stage, as in de Meza and Lockwood (1997) and Rajan and
ZingaIes (1997).

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