Flexibility in a Stackelberg leadership with differentiated goods

Abstract

We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.Keywords: game theory; Stackelberg model; demand uncertainty; differentiation; perfect Bayesian equilibrium AMS Subject Classifications: 91A15; 91A80 IntroductionThe Stackelberg model [1] is one of the most widely used models in industrial organization to analyse the behaviour of the firms in a competitive environment. It models the strategic situation where firms sequentially choose their output levels in a market. The belief of firstmover advantage was widely held among entrepreneurs and venture capitalists, but is now questioned by numerous practitioners. There are examples of successful and unsuccessful pioneering firms as described, for instance, in Liu [2]: Dell was the first to introduce the direct-sale business model into the PC market, and it achieved great success; however, during the dot-com booming era, Pets.com, Webvan.com, Garden.com and eToys.com were all unsuccessful first movers in their respective market segments. The probability of success of pioneering in a market clearly depends on many factors, including technology, marketing strategy, market demand and product differentiation (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). Liu [2] studied the effect of uncertainty in demand systems where only the leading firm is facing uncertainty in the demand parameter α that is considered to be uniformly distributed on an interval α0, α1 . In this paper, we add the dimension of product differentiation to Liu's model and we show among other results that if their products are sufficiently differentiated, even with small uncertainty about the demand, the follower can achieve higher profits than the leader.Our study focus on the influence of two parameters: the product differentiation 0 < γ ≤ 1 and demand uncertainty θ ≥ 1. When γ is close to one we have small

Price competition in the Hotelling model with uncertainty on costs

“…Therefore, the pair ( p z A , p w B ) satisfies property (i) and so ( p z A , p w B ) is a local optimum price strategy. Let us prove that p z A and p w B satisfy inequalities (16). By Equation (14),…”

“…Our main goal is to study the price formation in the second subgame with incomplete information in the production costs of both firms. The incomplete information consists in each firm of knowing its production cost but being uncertain about the competitor cost as usual in oligopoly theory (see [16][17][18][19][20][21][22][23][24][25]). We show that the first and second moments of probability distribution in the production costs are the only relevant information for price formation and all other relevant economic quantities.…”