In the context of oligopoly, firms do not have to worry about strategic behaviour as do monopolies, as far as consumers are concerned. Nonetheless, as they face competition from a few other firms, strategies in terms of price-setting and quantity-setting are of prime importance. What we want to look at in this essay is the range of the different strategies a duopolistic firm (i.e. an oligopoly that faces only one competitor) might choose, in a non-cooperative quantity-setting context. We want to introduce the concept of conjectural variations in that analysis, as it helps understanding the divergence between the two main models of duopolistic quantity-setting, Cournot and Stackelberg. By doing so, we will be able to compare these two approaches to duopolistic profit-maximizing firms and to determine why firms should adopt one strategy or the other.
[...] Therefore, reaction functions in Cournot and Stackelberg models have different meanings: while they reflect expectations of both firms about their respective competitor's output in Cournot, they picture the actual follower's reactions to be anticipated by the leader in Stackelberg. Looking at conjectural variations allows us to quantify these conjectures. These divergences about firm's beliefs are anything but futile, as they result in different outcomes for the firms while completely shaping their strategies. Conjectural variations are assumptions made by the firms: how to decide which ones to make? [...]
[...] So there is no stable equilibrium and several options emerge: either one of the firm is influent enough to win this fight, and the industry ends up in a Stackelberg equilibrium that benefits this powerful firm; or none of them is dominant enough and the industry tends toward a Cournot equilibrium where both firms produce on their own reaction functions and thus maximise their profits to the extent they can afford given what the other produces which they cannot affect; finally they could collude and maximise their joint profits. [...]
[...] We have seen that in a context of non- cooperative quantity-setting duopoly, a firm is better-off if it produces at the Stackelberg Leader's level. However, this requires it to be dominant enough to get to move first. We can think about big firms like Microsoft, whose competitors would tend to wait for it to announce its strategy before entering the game. A firm whose only competitor is similar to itself won't manage to produce QL* as it would not allow it to maximise its profits: Stackelberg Leader's level of production is a stable equilibrium only if there is two firms, of which one is a follower. [...]
[...] In contrast, the Stackelberg approach to duopoly is one of sequential quantity setting, pictured by the concept of “leader-follower”. In short, a Stackelberg firm leader might choose first the amount it will produce, but it must take into account that his choice will affect that of its competitor follower. Both duopolies are particular oligopolies: they keep general features of that structure of market. Firms are price-makers, behave strategically; they also count some more specific assumptions: firms produce homogenous products and face identical and constant costs. [...]
[...] Chapter 11, Hard Problems: “Game Theory, Strategic Behaviour, and Oligopoly” at http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_11/PThy_C hapter_11.html Explain ‘conjectural variation' in Cournot duopoly, evaluate its impacts and discuss the policy implication” at http://www.nedprod.com/NeoCapitalism/EC3201%20Essay.pdf Le duopole et la concurrence en quantité at http://yildizoglu.u- bordeaux4.fr/micro2web/node33.html E. Kalai and W. Stanford, “Conjectural variations strategies in dynamic Cournot games with fast reactions”, September 1983, available at http://www.kellogg.northwestern.edu/research/math/papers/575.pdf . K. Hinde, Cournot with conjectural variations available at http://kevinhinde.com/Micro2/ . E. Kalai and W. Stanford J. Black, Oxford dictionnary of Economics, "conjectural variation" p.76 Varian, at 491. [...]
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