Model of Competition in a Two-seller Market

In this model of sellers' competition we are concerned with the transition from a single-seller market to a two-seller market, the effects of transition on the first seller, his likely reactions and the thereby changed market situation that awaits the entering competitor. The decision variables considered in this model are the sizes of the two sales forces. We show that the enterer should not view the market as it stands prior to his entry, but as changed by the first seller to accommodate or oppose his entry. Upon the entrance of the competitor, both sellers must increase their sales forces to attain the levels of profit anticipated prior to entry, if indeed these can be attained. Equilibrium strategies are shown to be maximal sales effort on the part of the first seller and either maximal sales effort or abstention from entry on the part of the enterer. A finite series is derived to express the exact expectation of a class of rational functions of a binomially distributed random variable.