LUDOVIC A. JULIEN
Professeur(e)
2023-22
Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem
Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic A. Julien, Damiano Turchet
- Abstract
- We consider a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Our main theorem shows that any sequence of Cournot-Nash allocations of the strategic market games associated with the partial replications of the exchange economy has a limit point for each trader and that the assignment determined by these limit points is a Walrasian allocation of the original economy. Instead of relying on restrictive assumptions on the characteristics of atoms, as in Busetto et al. (2017), our limit theorem relies on the characteristics of agents in the atomless part and their endogenously price-taking behavior.
- Mot(s) clé(s)
- Cournot-Nash equilibrium, Walras equilibrium, Asymptotic equivalence
2023-14
Pollution in strategic multilateral exchange: taxing emissions or trading on permit markets?
Ludovic A. Julien, Anicet Kabre, Louis de Mesnard
- Abstract
- We introduce polluting emissions in a sequential noncooperative oligopoly model of bilateral exchange. In one sector a leader and a follower use polluting technologies which create negative externalities on the payoffs of strategic traders who belong to the other sector. By modeling emissions as a negative externality, we show that the leader pollutes more (less) than the follower when strategies are substitutes (complements). Then, we consider the implementation of public policies to control the levels of emissions, namely two taxation mechanisms and a permit market. We study the effects of these public policies. Moreover, we determine the conditions under which these public policies can implement a Pareto-improving allocation.
- Mot(s) clé(s)
- Stackelberg competition; pollution; fiscal policy; permit market
2021-14
Noncooperative oligopoly equilibrium in markets with hierarchical competition
Ludovic A. Julien
- Abstract
- This paper deals with the existence of a non-cooperative sequential equilibrium in interrelated markets with heterogeneous atomic traders. Since this model features a rich set of strategic interactions, there are two kinds of problems associated with the existence of equilibrium. First, existence and uniqueness of followers' strategies are not guaranteed. Second, the no-trade equilibrium is always an equilibrium outcome. To overcome these two difficulties we consider a differentiable approach. We show that the set of equations which determines the strategies of followers is a variety with the required dimension, i.e. the vector mapping which defines this set is a local C²-diffeomorphism. The continuous differentiability of followers' strategies is critical for the existence of an interior equilibrium. Unlike the simultaneous move games, exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade. Some examples buttress the approach and discuss the assumptions made on the primitives.
- Mot(s) clé(s)
- Pure strategies, diffeomorphisms, Stackelberg-Nash equilibrium
2018-10
Existence and Optimality of Cournot-Nash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part
Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic A. Julien, Simone Tonin
- Abstract
- We consider a bilateral oligopoly version of the Shapley window model with large traders, represented as atoms, and small traders, represented by an atomless part. For this model, we provide a general existence proof of a Cournot-Nash equilibrium that allows one of the two commodities to be held only by atoms. Then, we show, using a corollary proved by Shitovitz (1973), that a Cournot-Nash allocation is Pareto optimal if and only if it is a Walras allocation.
- Mot(s) clé(s)
- Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium; Optimality
2017-22
Hierarchical competition and heterogeneous behavior in noncooperative oligopoly markets
Ludovic A. Julien
- Abstract
- In this paper, we consider a sequential bilateral oligopoly market which embodies a finite number of leaders and followers who compete on quantities. We define a noncooperative equilibrium concept for this two-stage market game with complete and perfect information, namely the Stackelberg-Nash equilibrium (SNE). Then, we study the existence of a SNE with trade. The existence proof requires some steps as this market game displays a rich set of strategic interactions. In particular, to show the existence of a pure strategy subgame perfect Nash equilibrium, we have to determine the conditions under which there exist well defined continuously differentiable best responses. Some examples buttress the approach and discuss the assumptions made on the primitives.
- Mot(s) clé(s)
- Best responses, Stackelberg-Nash equilibrium, trade, autarky
2016-13
On Noncooperative Oligopoly Equilibrium in the Multiple Leader-Follower Game
Ludovic A. Julien
- Abstract
- In this paper, we provide new proofs of existence and uniqueness of a Stackelberg market equilibrium for a multiple leader-follower noncooperative oligopoly model in which heterogeneous firms compete on quantities. To this end, we consider a two-step game of perfect and complete information in which many leaders interact strategically with many followers. The Stackelberg market equilibrium constitutes a pure strategy subgame perfect Nash equilibrium of this game. The existence (and uniqueness) problem is complexified in this framework since strategic interactions occur within each partial game but also between both partial games through sequential decisions. Then, to prove existence, we notably provide a new procedure to determine (the conditions under which) the optimal behavior of the followers (may be written) as functions of the leaders'strategy profile only. Some examples outline our procedure and discuss our assumptions.
- Mot(s) clé(s)
- Best response functions, existence, uniqueness.
2011-10
Do followers really matter in Stackelberg competition?
Ludovic A. Julien, Olivier Musy, Aurélien Saïdi
- Abstract
- In this note, we consider a generalized T−stage Stackelberg oligopoly. We provide
a proof and an interpretation that under the two necessary and sufficient conditions
of linear aggregate demand and identical constant marginal costs, followers
do not matter for leaders. Leaders act as rational myopic agents, voluntarily ignoring
the number of followers and remaining stages, thereby behaving as Cournotian
oligopolists. Strategies of incumbent firms are invariant to entry of new cohorts.
Their profits can be studied by the way of two discount factors: the first impacting
markup and the second impacting output supply. Some implications in terms of
welfare and convergence toward competitive equilibrium are derived. - Mot(s) clé(s)
- Leader’s markup discount factor; linear economy; follower’s output discount factor; myopic behavior
2008-29
Market Price Mechanisms and Stackelberg General Equilibria
Ludovic A. Julien, Fabrice Tricou
- Abstract
- This paper considers Stackelberg competition in a general equilibrium framework with production. The working of market power and the confi...gurations of strategic interactions are complexi...ed by the presence of an active leader. Two market price mechanisms are here studied: one is associated with the Stackelberg-Walras equilibrium, the other is linked to the Stackelberg-Cournot equilibrium. In the context of an exchange economy with a production sector, several results are obtained about equilibria mergings and about welfare comparisons.
- Mot(s) clé(s)
2006-6
Equilibres multiples avec chômage, coûts de transaction et concurrence monopolistique
Ludovic A. Julien, Nicolas Sanz
- Abstract
- The properties of WS-PS model are modified when trade activity is explicitly modelled. We introduce transaction costs on the output market to capture multiplicity whatever the degree of returns to scale. The price setting curve can become downward-sloping in the unemployment rate-real wage space. Trading externalities reinforce the effect of strategic complementarities between firms, leading to multiple unemployment equilibria. Moreover, a positive shock on the bargaining power of workers decreases the unemployment rate and the real wage at the low equilibrium, but increases both of them at the high equilibrium.
- Mot(s) clé(s)
- multiple unemployment equilibria, transaction costs, monopolistic competition
2006-3
A note on price-taking and price-making behaviours in pure exchange economies
Ludovic A. Julien, Fabrice Tricou
- Abstract
- This paper explores the rationale of price-taking and price-making behaviours in the context of Walrasian and Cournotian pure exchange economies. Beside the influence of the number of agents, we underline the role of the structure of preferences in the definition and in the working of market power. Through three equilibrium variations of the same basic economy, we obtain several results about price manipulation, about asymptotic identifications for large economies and for degenerate preferences, and about welfare comparisons. Perfect competition does not only correspond to the case of large economies, but may also concern economies where fundamental market powers are more or less equivalent.
- Mot(s) clé(s)
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