Double implementation of the ratio correspondence by a market mechanism

Abstract

AbstraetTu ovcrcome deficils 01 lhe Lindahl solulion concepl when lhe econlJl1ly does nol exhibil conslanl relurns lo scale. Kaneko (1977a) introduced lhe concepl (lf a ratio equilibriulII. The ratio cOl'l'e.l'pOllllellCe sdects for each economy its sel 01' ralio equilibrium allocations. In Ihis papcr we provide a simple markel game lhal double illll'lel//t'nts lhe ratio con'espondence in Nash and strong equilibria.

Nash implementation with a private good

“…5 All of the above work, save Saijo (1988) and McKelvey (1989), focused specifically on either the constrained Walrasian or constrained Lindahl social choice rule, but later work has considered generalizations of the Walrasian and Lindahl rules. Corchón and Wilkie (1996) construct a continuous mechanism using reports of prices and allocations to implement the ratio equilibria, defined by Kaneko (1977a,b), in Nash and strong Nash equilibrium. Dutta, Sen, and Vohra (1995) investigate social choice rules satisfying local independence, a condition due to Nagahisa (1991), which dictates that the social optimality of an allocation depend only on the marginal rates of substitution of the agents at that allocation.…”

Double implementation of the Lindahl equilibrium by a continuous mechanism

“…The ratio equilibrium was proposed in Kaneko (1977) as an extension of the Lindahl solution to public goods economies whose production set may not satisfy additivity. The mechanism of Corchon and Wilkie (1990) is feasible and continuous. As pointed out by the referee of this paper, the main difference between the two papers is in the assumptions on the production sets: Corchon and Wilkie assume, as Kaneko, non-increasing returns to scale and separability (of the cost function), whereas we assume non-increasing returns to scale and additivity.…”

“…An Associate Editor of this journal sent me the paper Corchon andWilkie (1990, last revision May 1996), which provides a double implementation of the ratio equilibrium correspondence in Nash and strong equilibria. The ratio equilibrium was proposed in Kaneko (1977) as an extension of the Lindahl solution to public goods economies whose production set may not satisfy additivity.…”

“…As pointed out by the referee of this paper, the main difference between the two papers is in the assumptions on the production sets: Corchon and Wilkie assume, as Kaneko, non-increasing returns to scale and separability (of the cost function), whereas we assume non-increasing returns to scale and additivity. Furthermore, Corchon and Wilkie (1990) assume that the preferences are represented by utility functions and that there is only one private good.…”

Coalition-proof equilibria in a voluntary participation game

“…However, if participants play the mechanisms constructed by Hurwicz (1979), Walker (1981), and Corchon and Wilkie (1996), then the ratio allocation can be accomplished in the equilibria of the mechanisms.…”