## Publication: Strategic profit sharing between firms

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##### Publication date

2011-03-04

##### Defense date

2011-05-13

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##### Abstract

The purpose of our thesis "Strategic Profit Sharing Between Firms" is to
study the effects of the unilateral and unconditional profit sharing strategy
on firms' behavior. The basic model is a two-stage game. In the first stage,
firms decide simultaneously what part of their profits to give away to their
rival and then, in a second stage, the equilibrium price and quantities are
determined. Notice that the action of giving away profits is decided unilaterally and unconditionally in a non-cooperative framework. After the decision
to give profits is taken, the giving firm is commited to it. Our thesis contribution is to explore issues on collusion if the cross-ownership is the product
of this decision. The thesis is divided into two chapters. The first chapter "Strategic Profit Sharing Between Firms" starts by presenting the general model that shows
the direct (negative) and indirect (may be positive) effects of this strategy,
and, then, concentrate on the effects of its inclusion in some oligopolistic
models (Cournot, Bertrand, Hotelling). We show that giving away profits is
a rewarding strategy for firms in some (but not all) of the above oligopolistic competition models. Our analysis of the standard models shows that
firms may have incentives to share profits in equilibrium in the Bertrand and
Hotelling models (at least for some values of the parameters that define the
model) and not so much in the Cournot ones (requiring an unrealistic value
for the relevant parameter).
For the linear demand cases of study, and for the most standard assumptions on both Cournot and Bertrand models, a necessary (but not sufficient)condition to find a profit-sharing equilibrium is that strategies are complementary for substitutes goods. This, in turn, implies that profit sharing is never an equilibrium in the standard Cournot models. The complementarity
of the strategies is necessary for the equilibrium to internalize the effect on
the other firm's profits.
Chapter I finishes by relaxing the profit sharing key assumptions of our
model to understand the extent to which they are necessary conditions. We
first explore the possibility that only one firm has the possibility to share
profits. We show that profit sharing between firms is a winning and sustainable strategy only if both firms are sharing when competing in prices. We then explore how the profit sharing strategy may be concealed behind other
arrangements. In particular, we see that the implication of the firms in a
joint venture may be such a strategy. This is important, as the standard
profit sharing strategy may be easy to detect. The second chapter "Strategic Profit Sharing Leads to Collusion in Bertrand
Oligopolies" focuses on the Bertrand model with homogenous goods and adds
a first stage of profit sharing. We show that firms may be able to support
prices between the marginal cost and the monopoly price, thus obtaining
positive profits in almost all of the equilibria. This remarkable result, that
resembles a Folk theorem, is robust to the number of firms and to cost asymmetries. Furthermore, for a given equilibrium price, any share of the market can also be supported in a subgame perfect equilibrium. For the duopoly case we completely characterize the set of pure strategy equilibria. However, in the extension to more than two firms, and due to the increasing complication
in the multiplicity of equilibria, we only show the existence of the equilibria
in the subgames that is sufficient to support the desired equilibrium price

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##### Keywords

Beneficios, Equilibrio económico, Política de la competencia, Oligopolio, Incentivos económicos, Comportamiento empresarial