Contenu du sommaire : On perfect competition : definitions, usages and foundations

Two perspectives on the price system are examined, as a method of valuation represented by Walrasian equilibrium and as a means of appropriation represented by “perfectly competitive equilibrium.” The stronger requirements of perfectly competitive equilibrium emphasize that valuation is driven by appropriation. Similarities between the full appropriation property of perfectly competitive equilibrium and efficient incentive compatible mechanism design are demonstrated.

We discuss the traditional interpretation of Edgeworth's conception of competition neo-Walrasian authors developed following the Debreu-Scarf 's theorem legacy. This interpretation presents Edgeworth as the forerunner of the cooperative-games approach based on the notion of the core as a solution concept. We appraise those notions using Edgeworth's texts. This allows us to plead in favour of Edgeworth's originality and of the need to rescue his theory of perfect competition from a misleading way. Textual evidence allows us to assert that the language of the cooperative game theory, and the subsequent modern theory of the core, do not correspond to Edgeworth's theory. The modern notion of coalition seems to be an interpretation of Edgeworth's concept of “combination” and of “cooperative associations.” Both notions deeply differ from the traditional concept of coalition when one examines them more carefully. Edgeworth clearly establishes a difference between a group of agents entering in a series of bilateral contract relations and a “combination.” The logic of the former is purely individual in the sense of an individual improvement accepting bilateral contracts within a new group rather than the bilateral contracts she have formerly agreed within another group. In fact, within the new improving-group all contracts continue to be bilaterally established and, more important, these kind of association does not necessary imply giving up all previous exchanges outside this group. From this alternative interpretation about Edgeworth's notion of “combination” we extract a completely different conclusion than that implied by the coalitional formation presented in the cooperative game theoretical framework. In this framework, the core of an economy is simply reduced by the presence of an increasing number of agents forming this kind of coalitions. From the Egeworthian point of view, the number of agents does not per se guaranteed the increasing of competition when this kind of cooperative arrangement is the rule.

In developing their pure-exchange equilibrium models, Jevons [1871], Walras [1874-77], and Edgeworth [1881] make use of some version of a law, called law of indifference (or principle of uniformity) by Jevons and Edgeworth and often referred to as the law of one price in connection with Walrasian economics. Edgeworth, in particular, shares with Jevons the idea that the law of indifference must be regarded as an equilibrium property; unlike his predecessor, however, he denies the validity of the law in all economies with a finite number of traders: for him, price uniformity can only emerge and a Jevonsian or Walrasian or competitive equilibrium can only be established when the traders' number grows unboundedly large. About one century later, Negishi [1982] resumes the time-honoured discussion about the law, striving to prove that, contrary to Edgeworth's original conjecture, a competitive equilibrium can be attained even in small economies, provided that the true driving force underlying Jevons's law of indifference, namely, its implicit arbitrage mechanism, be allowed to operate and carry its effects through. In this paper, after reconstructing Jevons's, Walras's, and Edgeworth's respective positions, we critically discuss Negishi's critique of Edgeworth's stance on Jevons's law of indifference, Walras's equilibrium, and the role of large numbers, showing that his central claim is unsubstantiated.

A problematic issue in economic theory is the study of price determination. Two distinct approaches to this difficult topic have been taken: (i) in Bertrand competition it is assumed sellers enter the market with a commitment to supply all demand forthcoming from buyers (ii) in Edgeworth competition sellers quote prices with no commitment to supply more than their competitive supply. Both these types of market contract struggle to provide credible pricemaking foundations for perfect competition. In this paper we outline an alternative approach to contract formation with combines Bertrand's [1883] insight regarding price competition with Edgeworth's [1881] notion of recontracting. The result is that we can provide a price-making analogue of the Debreu-Scarf [1963] showing that in large markets price-making contracts are ‘close' to the competitive equilibrium.

We address the asymptotic convergence of active Nash equilibria of strategic market games to Walrasian ones for general sequences of economies whose distribution of characteristics has compact support.

In the economic literature of the nineteenth and twentieth centuries, perfect competition rests on essentially two different types of foundations, the distinction of which has not always been emphasized enough. According to the first type, perfect competition prevails when the agents, small relative to the market, completely lack the power to influence their environments, be it in a cooperative or a non-cooperative context. According to the second, perfect competition results from the agents' normal conduct, independently of their size: either peaceful price taking or, on the contrary, aggressive undercutting. The paper reviews and compares briefly these different categories of foundations.