Oligopoly with a large number of competitors: asymmetric limit result

Abstract

Stackelberg game, Cournot game, Limit result, Marginal-cost advantage, Arrow effect, L11, L12, L13,

How Many Firms Should Be Leaders? Beneficial Concentration Revisited*

“…22 22 P ( X *( X L , n )) uniformly converges to min { C ′(0), P ( X L )} ( P with a price ceiling at C ′(0)) on . The proof is similar to in section 3.2 of Ino and Kawamori (2009). This implies that converges to zero as n →∞ for any sequence { Y ( n )} where .…”

“…For an application of the Stackelberg model with free entry of followers to innovation and trade policy, see Etro (2004, 2011). For the limit result when an infinite number of followers enter the market, see Ino and Kawamori (2009). For the implications of public policy in free‐entry markets, see Davidson and Mukherjee (2007), Brandão and Castro (2007), Mukherjee and Mukherjee (2008), and Marjit and Mukherjee (2008).…”

“…However, we provide certain qualifications for our results regarding beneficial concentration with respect to an integer problem. If it is assumed that the number of firms is an integer, in both the SP and WP models, counterexamples can be presented wherein beneficial concentration does not occur (these counterexamples are available in Ino and Matsumura, 2009). Although general properties of the integer problem are rather complicated to identify, we have found the following positive aspects for this problem: When the number of followers entering the market is sufficiently large ( f is sufficiently small), if the leader’s marginal cost is slightly less than that of the followers (it must also be noted that this condition holds regardless of how small the cost difference may be), then the welfare of the Stackelberg equilibrium must exceed that of the Cournot equilibrium in both the SP and the WP models, even under the integer constraint.…”

“…20 20 This is because the leader’s profit is continuous in its strategy since the followers’ reactions are continuous in the leader’s strategy by Berge’s maximum theorem. See Ino and Kawamori (2009). …”

Bargaining outcomes in patent licensing: Asymptotic results in a general Cournot market

“…Kamien and Tauman (2002) extended his model to a Cournot oligopoly market. With a general demand function and convex cost, Ino and Kawamori (2009) examined whether or not a cost-reducing innovation is profitable for the incumbent patent holder in a large oligopolistic market, and showed that a partial-monopoly market, in which the incumbent patent holder chooses his output as a price maker while the other firms produce as price takers, arise when he does not license his (non-drastic) patented technology. It is left for a future research to study bargaining outcomes in the case of an incumbent patent holder.…”