Incentives in Planning Procedures for the Provision of Public Goods

In the past few years several studies have addressed the problem of designing decentralized mechanisms for determining an efficient allocation of resources in the presence of public goods. A crucial feature of such mechanisms is the incentives that are provided for the participants to supply correct information about their preferences, since, unless proper incentives are present, self-interested behaviour may frustrate the realization of efficiency. As has long been recognized, the study of such self-interested, strategic behaviour and of incentive problems in general must be essentially game-theoretic in nature. However, there are many possible specifications of the game that arise when agents under such a mechanism can decide whether or not to reveal their preferences correctly. Each such specification yields a different formalization of such concepts as self-interest and incentive compatibility. Correspondingly, very different patterns of behaviour may emerge under different formulations of the game of preference revelation. In this note we will be concerned with one aspect of this problem, namely, the specification of the pay-off functions in the context of planning procedures with public goods. The games we will consider will be non-cooperative ones in which the players are the agents (consumers) in the process and the strategy sets consist of messages the agents can send regarding what their preferences are. (These messages may, in fact, be complete preference orderings.) This much is more or less common to most studies of incentive questions. However, in many iterative planning procedures, a proposed allocation is generated at each iteration. This gives rise to a choice as to the pay-off functions in the game. On the one hand, one might hypothesize that agents will be concerned only with what they will finally receive. This leads to specifying the pay-off to each player as the utility to him under his true preferences of the final allocation selected. We will refer to the game with this pay-off as the global game. Alternatively, one might argue that it is more reasonable to suppose that agents simply try to do as well as they can for themselves at each iteration. This then leads to consideration of a separate game at each iteration, with the pay-offs being the change in the utilities associated with the adjustment of the proposed allocation. We call games with this pay-off local or instantaneous. Both these alternatives have been considered in the literature. Samuelson's initial discussion of the public good problem would seem to be in terms of the former, global, criterion. Hurwicz adopted this approach in his pathbreaking analysis of incentives [6] and most of the rapidly growing literature on the topic has followed this line. On the other hand, Dreze and de la Vallee Poussin [3] and Malinvaud [8] have employed the local or instantaneous game in their analyses of the incentives under their planning procedure for public goods. Use of these different modellings has led to strongly contrasting results. Hurwicz showed that even in the context of simple exchange economies there could not exist a mechanism for selecting individually rational Pareto optima which was incentive compatible in the sense that correct revelation was always a Nash equilibrium in the global game. On the other side, Dreze and de la Vallee Poussin showed that under correct