On hierarchical competition in oligopoly

Abstract

In this paper, we consider a hierarchical oligopoly model, in which firms compete on quantities of an homogeneous product. We provide a proof and an interpretation that under the three necessary and sufficient conditions of linear aggregate demand, constant and identical marginal costs, the strategy of leaders at any stage depends neither on the number of leaders who play after nor on the number of remaining stages. So, all firms behave as Cournotian oligopolists on the residual demand. We show that these three assumptions are not only sufficient but also necessary. Any departure from any of these assumptions rules out this property

Optimal Sequential Contests

“…We can use Taylor's theorem to express g(X) = [α − r g (X)](1 − X), where the remainder 49 For example, in the Stackelberg oligopoly with linear demand, the leader's quantity is independent of the number of followers. This observation has been made before, for example by Anderson and Engers (1992); Julien et al (2012). In fact, Julien et al (2012) derived this equilibrium characterization for arbitrary sequential oligopolies with linear demand (which implies α = 1 here).…”

“…For example, in the Stackelberg oligopoly with linear demand, the leader's quantity is independent of the number of followers. This observation has been made before, for example by Anderson and Engers (1992);Julien et al (2012). In fact,Julien et al (2012) derived this equilibrium characterization for arbitrary sequential oligopolies with linear demand (which implies α = 1 here).50 Equivalently, it is identical to n n in the first T − 1 periods, but all remaining players are collected into period T .…”

“…The only paper I am aware of that has studied sequential Tullock contests with more than two periods is Glazer and Hassin (2000), who characterized the equilibrium in the sequential threeplayer Tullock contest. The only class of contests where equilibria are fully characterized for sequential contests are oligopolies with linear demand (Daughety, 1990;Ino and Matsumura, 2012;Julien et al, 2012). Linear demand implies quadratic payoffs; this is the only case where the first-order conditions are linear in all variables and therefore the equilibrium is simple to characterize.…”

Judo Economics in Markets with Multiple Firms

“…This compares to Boyer and Moreaux [8], who study a Stackelberg game and show that production of each firm solely depends on the rank of the firm and not on the number of firms in the market. Julien et al [11] find a similar result in a multistage Stackelberg game with multiple firms in each stage. Output decisions in each stage only depend on the previous output decisions but do not depend on the number of followers or following periods.…”

Stackelberg Independence*

“…The model has been later used and extended by Anderson and Engers [1992]; Pal and Sarkar [2001]; Lafay [2010]; Julien et al . [2011, 2012]; and Ino and Matsumura [2012] to cover more than two periods and an arbitrary number of firms in each period. In all those papers, the model has the Stackelberg independence property.…”