Incentives in the Generalized MDP Procedure for the Provision of Public Goods

Abstract

Malinvaud (1970-1971) and Dreze and de la Vallee Poussin (1971) have independently proposed a well-defined planning procedure for an economy with public goods. This procedure, which has come to be called the MDP procedure, has several desirable properties given correct revelation of each participant's preference. If each individual truthfully announces his marginal rates of substitution between public goods and a private good, every trajectory of the process lies entirely in the space of feasible allocations and monotonically converges to an individually rational Pareto optimum. Moreover, as is shown in Champsaur (1976), given correct revelation, this procedure is neutral to any kind of distributional value judgements in the sense that every individually rational Pareto optimum can be attained as a limit of some trajectory defined by the process. In connection with the problem of whether the participants in the MDP procedure reveal their correct preferences, little literature has so far been written. There are now results available which have been derived by Dreze and de la Vallee Poussin (1971) and Roberts (1979) that (i) at every iterative stage telling the truth is a maximin strategy for each individual and, at an equilibrium of the process, is a Nash equilibrium strategy, and that (ii) correct revelation produces a dominant strategy equilibrium at every instant if a society consists of just two individuals. Nevertheless, maximin strategies are played only because of the rather restricted assumption on each participant's behaviour, while confinement to the case of a two-person society is too severe to give meaningful implications for reality. In either case, one might be fully justified in believing that truthful revelation will hardly appear in the MDP procedure. Fortunately, almost all the properties of the MDP procedure can be preserved under circumstances where the agents misrepresent their marginal rates of substitution; Henry (1979) and Roberts (1979) have shown that, as long as each individual chooses a Nash-type strategy at each instant, the process maintains the same properties as in the case of correct revelation, except that the adjustment speeds of public goods are significantly reduced. This result implies the MDP procedure is implementable under game theoretic circumstances, but at the same time, it exposes serious problems in several respects. In the first place, since the Nash equilibrium strategy of each agent is not necessarily the truthful announcement, the virtue of honesty is no longer of positive significance in the MDP procedure. Secondly, for the validity of its solution concept, if each agent plays a Nash equilibrium strategy at all, he must have complete knowledge relating to the possible strategies chosen by all the other agents. Clearly, this supposition