The name is absent

Customer Cooperative

When the firm is owned by the customer the negotiation game reduces to a simple
trilateral bargaining game between the two employees and the owner-customer. As under
outside ownership we model bargaining as a two stage game where, in the first stage
the customer-owner offers a take-it-or-leave-it offer to the two employees, ɪf the offer is
accepted, the game ends. If the offer is rejected, the two employees can make take-it-
or-leave-it offers Simultaneoush^r to the customer-owner. As before, if the offer is rejected
every one gets a zero payoff and the game ends. Again proceeding by backward induction,
and assuming again that E↑ has a higher ex-post value the equilibrium payoffs in the
second stage are given by:

Agent: employee Ei employee E□ outside owner O customer C
share: V-V  OOV

The difference with the previous game is that now the customer can always secure the use
of the asset since he owns it. We highlight this result in the following lemma:

Lemma 3 The bargaining solution under customer cooperative is

Agent: employee Ei employee En outside owner 0 customer C

share:    V-V        0            0           V.

Given that each employee E_τ has an α₁∙ chance of being the better employee ex post,
employee E√s ex-ante expected gross payoff is : ɑi (V — V). and therefore each employee
chooses his investment level to maximize

max{α_i(∕(Λlog(l + ⅛_i)) - /(v)) - fc_j}.                     (5)

k₁>0

We, thus, obtain:

Lemma 4 The (symmetric) equilibrium investment levels under the customer cooperative
are:

fcf = a_i,∖f' - 1

It is easy to see here that the (Nash-equilibrium) investment incentives of each employee
coincide with the socially optimal investment incentives. Indeed, if the social objective is
to maximize total expected value, then the planner's ex-ante investment problem is:

max {[αι∕(z∖log(l + ⅛ι)) - ⅛ + [ɑa/(ʌlog(l ÷ ⅛)) - ⅛]}

fc₁ >0.⅛_a>Q

and we have obviously.

1.

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