Abstract
We study a sequential Bertrand game with one dominant market incumbent and multiple small entrants selling homogeneous products. Whilst the equilibrium for the case of a single entrant is well known from Gelman and Salop (1983), we derive properties of the N-firm equilibrium and present an algorithm that can be used to calculate this equilibrium. The algorithm is based on a recursive manipulation of polynomials that derive the optimisation problem that each of the market entrants is facing. Using this algorithm we derive the exact equilibrium for the cases of two and three small entrants. For more than three entrants only approximate results are possible. We use numerical results to gain further understanding of the equilibrium for an increasing number of firms and in particular for the case where N diverges to infinity. Similarly to the two-firm Judo equilibrium, we see that a capacity limitation for the small firms is necessary to achieve positive profits.
Highlights
Gelman and Salop [1] show that, in a sequential Bertrand competition between one entrant and a single market incumbent selling nondifferentiated products, capacity limitation is necessary for the entrant to be accommodated
We study the extension of Judo limitation of a single entrant to a market situation with multiple entrants
We have shown that the Judo limitation in capacities is an entry strategy for a single entrant competing with a dominant market incumbent and for the case of multiple small entrants
Summary
Gelman and Salop [1] show that, in a sequential Bertrand competition between one entrant and a single market incumbent selling nondifferentiated products, capacity limitation is necessary for the entrant to be accommodated. Because the small entrant uses the incumbent’s large size to its own advantage—it is somewhat bound to serve its large customer base at a single price—this entry strategy is called Judo economics [1]. This theoretical result has been confirmed by various studies found in the economic literature. Theoretical work has elaborated the original setting and introduced dynamics [4], an altered sequence of capacity and pricing decisions [5], or asymmetric firms [6]
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