Local Simple Games in Public Choice Mechanisms

Abstract

This paperinitiates an investigation of processes in wlhiclh cooperative games determine at each moment the directioni of motion of the social state. Attentioln is focused upoIn simple games, i.e., uponl games in which a coalitioni cani prevenit either every direction orno direction from beinig choseni. As motivation, conisider the problem of COInStlruCtinlg a planning pr^ocedule to allocate goods. Existing procedures, as surveyed in Tulkenis [1978], specify a local (instantaneous) game that determnines the direction of change of the allocation vector. For example, the MDP procedure of Malinvaud [1970-1] and Dreze and de la Valee Poussin [1971] specifies the direction of change at each moment as a function of reported marginal rates of substitution. Assuming that individuals are concerned only with mnaximizing thleir rates of utility increase, local games can be constructed so that their diiectionial equilibria will lead the allocation vector to the Pareto set. Various equiilibriuml concepts have been used. In MDP local games, for exanmple, maxmiin equilibria (Dreze and de la Valee Poussin [1971]), Nashi equilibria (Roberts [1979], SchoLumaker [1979]), and certain cooperative equilibria (Tulkens and Zamir [1979]) have been shown to cause convergence to the Pareto set. Whenever a procedure is actually to be implemented, account should be taken of the fact that it will be constrained by rules that are effective in the society. For example, in a dictatorship the social state must move in a direction that is most preferred by the dictator; the dictator will simply not abide by the equilibrium direction of a local game unless it is one of his most preferred directions. Less trivially, whenever unanimous disapproval of a motion can prevent its occurrence, the society will only agree to a procedure whose equilibrium direction of motion cannot be feasibly changed to a direction that increases everybody's utility at a greater rate. These two examples of constrainits on motion are not of the type that is usually imposed in the literature on allocation procedures and, furthermore, in areas like tax reform (e.g., Guesnerie [1977]) and majority rule dynamics (e.g., McKelvey [1976], Schofield [1978a]). The constraints oni motion in these studies call be viewed as resulting from a requirement that any motioni must increase the utility