On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

Abstract

1 We would like to thank Davide Dragone and Alessandro Tampieri for stimulating discussions and insightful suggestions. The usual disclaimer applies. AbstractWe characterise the subgame perfect equilibrium of a di¤erential market game with hyperbolic inverse demand where …rms are quantity-setters and accumulate capacity over time à la Ramsey. The related Hamilton-JacobiBellman are solved in closed form both on in…nite and on …nite horizon setups and the optimal strategies are determined. Then, we analyse the feasibility of horizontal mergers in both static and dynamic settings, and …nd appropriate conditions for their pro…tability under both circumstances. Static pro…tability of a merger implies dynamic pro…tability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.JEL Classi…cation: C73, L13

Differential Games in Industrial Economics

“…The Ramsey game in Cellini and Lambertini (1998) uses product di¤erentiation as in to investigate also Bertrand competition, showing that, if varieties are substitutes in demand, the Bertrand case collapses into the Ramsey golden rule in a wider parameter range than the Cournot one. More on capacity accumulation in a feedback oligopoly game can be found in Lambertini and Palestini (2014), where market demand is hyperbolic. Additional non-LQ games are considered in Jun and Vives (2004), Koulovatianos and Mirman (2007) and Dockner and Mosburger (2007).…”

Location choices with a non‐linear demand function

“…Interestingly, hyperbolic demand functions have been adopted also in other fields of research. For example, this kind of demand function has been widely adopted in the so-called 'rent-seeking' games (for example Szidarovsky and Okuguchi 1997;Chiarella and Szidarovsky 2002), in oligopoly models considering equilibrium (in)stability (Puu 1991(Puu , 1996(Puu , 2008 and differential oligopoly models (Lambertini 2010;Lambertini and Palestini 2014;Lamantia 2011). 8 A general demand function has been instead recently considered in a barbell model (Sun and Lai 2014), taking advantage from the fact that in the barbell model only two separate markets exist, in contrast with the infinite number of markets populating the Hotelling segment when the consumers are distributed all along the line.…”

“…Interestingly, hyperbolic demand functions have been adopted also in other fields of research. For example, this kind of demand function has been widely adopted in the so‐called ‘rent‐seeking’ games (for example Szidarovsky and Okuguchi ; Chiarella and Szidarovsky ), in oligopoly models considering equilibrium (in)stability (Puu , , ) and differential oligopoly models (Lambertini ; Lambertini and Palestini ; Lamantia ).…”