Roy Gardner

Shapley value and disadvantageous monopolies

Abstract At least one monopoly in a two-sector model must be advantageous, according to the Shapley value. If the elasticity of substitution is a constant at least equal to one, then each monopoly has an advantage if the other sector is not monopolized. For elasticity of substitution less than one, monopoly may be disadvantageous, depending on the distribution parameter.

Liberal paradox, game equilibrium, and Gibbard optimum

ConclusionsOur analysis of a game-theoretic model of liberal rights had two main purposes: First, we gave a characterization of Gibbards solution to the liberal paradox in terms of a game equilibrium. Secondly, we asked for preference restrictions that can guarantee the existence of a Pareto-optimal equilibrium in this ‘game of liberalism’. As one of our main results it turned out that voluntary cooperation between players does not by itself eliminate the possible occurrence of the liberal paradox if this is, in the cooperative context, defined as the emptiness of the core. Rather, we derived a sufficient condition that guaranteed a non-empty core of the cooperative game as well as a Pareto-optimal Nash equilibrium in the non-cooperative game: At least n — 1 of the n players must deem their own issue more important than all the other issues taken together.However, several important questions remain open. First, the relationship between Gibbards social choice function f* and Arrows famous conditions (1963, Chap. 3) has not been investigated. Although f* satisfies nondictatorship and the Pareto condition, it is likely that it fails both collective rationality and the independence condition. Finally, there is the question of whether other familiar SCFs, e.g. Condorcets rule or Bordas rule, agree with f*. In so far as they do not, credence is lent to the view that certain aspects of a persons life are not to be put to a vote. This also makes libertarian antipathy to majority rule more understandable.

Repressed inflation in the Soviet Union: A temporary equilibrium approach

Abstract The Soviet economy is modeled by means of temporary general equilibrium theory. Three temporary equilibrium states are distinguished. In Walrasian equilibrium, all markets clear. Under repressed inflation, there is excess consumer demand for goods marketed by the state, while consumer demand is deficient in the underconsumption regime. The dynamics of these temporary equilibrium states are studied and the dynamic adjustment equations fitted to Soviet data. Simulation of the model offers an explanation for the tendency of the inventories/cash balances ratio to fall since 1965.

The Borda Game

Recently, a number of authors have constructed axiomatic defences of Bordas rule [2, 4, 8], In every case, it Is assumed that voters mark their ballots honestly, in accordance with their preferences. That this assumption may be unrealistic was known to Borda himself [ij. Elsewhere • [3, 5], it has been shpwn how Bordas rule can reward misrepresented pref erences on the part of individual voters. This result is in the same spirit as, but not a consequence of, the Gibbard-Satterthwaite theorem [6, 7], since Bordas rule allows ties. This is in marked contrast to Condorcets rule, where such misrepresentation is not rewarded.

The strategic inconsistency of Paretian liberalism

In this paper, the problem of the Paretian liberal is cast as a preference revelation game whose outcome function satisfies Gibbards libertarian condition and strong Pareto optimality. Strategic consistency requires that the equilibrium of the game agree with the sincere outcome. It is shown that, whether viewed in a cooperative or non-cooperative context, the liberal social choice function is strategically inconsistent. This result suggests that, from a strategic standpoint, a different resolution of the liberal paradox is desirable.

Core and value for a public-goods economy: An example

Abstract An example of a public-goods economy with a continuum of agents is presented in which the Shapley value does not lie in the core.

Variation of the electorate: Veto and purge

In the paradigm social choice problem, there is a fixed set of alternatives and a fixed set of voters. This essay considers variations of the electorate when some subset of voters has a special voice on some subset of alternatives. We formalized such a situation by means of the veto function. We focus on stable veto functions, exhibit a stable liberal social choice function and promotion mechanism, and investigate a notion of stability for groups whose membership itself is the social state.