Endogenous Timing in Duopolies
Fecha
2021Autor
Basso-Sotz, Leonardo
Jara-Moroni, Pedro
UNIVERSIDAD DE CHILE
Institución
Resumen
In this thesis we aim to understand how does leadership emerge in duopolistic competitions.
In particular, we want to know which are the key features, of the rms and the market, that
explain that some interactions are simultaneous while others are sequential. In order to do
so, we develop a general model of duopolistic competition in which the timing of movements
is not exogenously given, but is part of the equilibrium, this is, depends on the actions of
the players. More precisely, we consider two rms that are absolutely identical except for
one single characteristic that makes them di erent. To x ideas, it is possible to think this
feature as the marginal cost or capacity of production. We interpret this di erence as the
consequence of di erent levels of investment made prior to the competition. This investment
variable might be tough or soft, which means that the total e ect of the investment on the
payo of the other player is negative or positive, respectively. After the investment, rms
engage in supermodular or submodular competition. This competition can be (a priori)
simultaneous or sequential, allowing us to endogenously obtain the timing of movements in
equilibrium. In order to do so, we use the extension models from Hamilton and Slutsky (1990),
namely, the Game with Observable Delay (GOD) and the Game with Action Commitment
(GAC). When there is multiple equilibria, we base our re nement on the risk dominance
concept from Harsanyi and Selten (1998).
For the supermodular case, we found that simultaneous competition is never the outcome
of the interaction, neither with GOD nor GAC. In the GOD extension model this result
comes from the fact that the existence theorem, in our setting, predicts that only sequential
play is an equilibrium. In the GAC model the result comes from the re nement process
based on risk considerations and the nature of the investment. Also, our results predict that,
when the investment variable is tough, the rm with the largest investment is more likely to
become the risk dominant leader, for both extension models. When the investment variable
is soft, we provide su cient (but not necessary) conditions for the leadership of the rm with
the largest investment. Regarding this last point, we still need to work further on nding
necessary hypotheses to characterize the leadership.
For the submodular case, we fully characterize which equilibrium will emerge when the
extension model is GOD: simultaneous competition. This result holds regardless of the type
nor level of investment. On the other hand, for the GAC extension model, we nd that the
simultaneous equilibrium is never the risk dominant (and therefore it should never emerge).
Also, when the investment variable is tough, the rm with the largest investment is more
likely to become the leader. In the case of soft investment, as with supermodular competition,
we give su cient conditions for the leadership of the player with the largest investment.
Considering the results obtained in this setting, we also provide an interpretation of the
di erences between both extension models, GOD and GAC, based on risk considerations.