Joseph Greenberg

THE EFFECT -OF ELECTORAL REWARDS IN MULTIPARTY COMPETITION WITH ENTRY

The authors elaborate a model of electoral competition for a fixed number of seats in a legislature. The novel feature of this model is that candidates (or parties) not only choose spatial locations as platforms but also determine whether to enter the contest at all. In most previous spatial models, the set of candidates is specified exogenously. Here, however, the spatial positions and the set of candidates are determined endogenously. An equilibrium in this context is defined and results are proved, suggesting that entry may disrupt spatial equilibria. Finally, the authors compare their treatment of spatial competition with entry to that of Palfrey.

Multiparty equilibria under proportional representation

The purpose of this article is to define and to prove formally the existence of an equilibrium under proportional representation, as well as partially to characterize it. Specifically, let m be the quota that represents the minimal number of voters necessary for a candidate to be elected. We show that there is a set of elected candidates, each choosing an alternative and each receiving at least m votes, such that no otherpotential candidate, by offering an additional alternative, can secure at least m votesfor himself. We then investigate the structure, at equilibrium, of the set of individuals who support a given candidate, as well as study stability properties of the equilibrium. We also provide necessary and sufficient conditions for the equilibrium to consist of a single candidate, thus generalizing Blacks medianvoter result.

THE RIGHT TO REMAIN SILENT

The paper points out that in dynamic games a player may be better-off if other players do not know his choice of strategy. That is, a player may benefit by not revealing (or not pre-determining) the choice of his action in an information set he (thereby) hopes will not be reached. He would be better-off by exercising his ``right to remain silent if he believes –- as the empirical evidence shows –- that players display aversion to ``Knightian uncertainty. In this case, a player who behaves strategically, may wish to avoid revealing his strategy. This is true under various interpretations of the notion of ``strategy profiles.

Cores of Convex Games Without Side Payments

This paper gives a short and direct proof that a convex game without side payments has a nonempty core. One setting in which such games arise is that of social choice, where the notion of equilibrium is in fact the core of the induced game.

Sophisticated) Stable Sets in Exchange Economies

Within the framework of (pure) exchange economies, we demonstrate that the von Neumann and Morgenstern stable set in the allocation space may differ from that in the corresponding utility space. Following Harsanyi (1974, Management Sci. 20, 1472-1495), we then define the notion of the sophisticated stable set and establish an equivalent theorem: like the core, the sophisticated stable set in the allocation space coincides with that in the utility space. We also show that the sophisticated stable set has the desirable property of individual rationality.

Existence of equilibria in atomless production economies with price dependent preferences

Abstract The existence of a competitive equilibrium for an economy with a measure space of agents is proved by reducing the economy to a three-person game and then applying Debreus lemma (1952). In addition to the relative simplicity and shortness of the proof, we generalize known results [Aumann (1966), Hildenbrand (1970), Schmeidler (1969)] by allowing both price dependent preferences and satiation.

Chapter 37 Coalition structures

Publisher Summary The study of stable coalition structures, or more generally of coalition formation, was conducted mainly within the framework of games in coalitional form. The most commonly used stability concept is the coalition-structure core, which extends individual stability to group stability. The best-known example of social environments whose associated games have a coalition-structure core is the central assignment game (in particular the marriage game). The basic result is that the game describing the following situation has a coalition-structure core: the set of players is partitioned into two disjoint groups. Each member of one group has to be matched with one member (or more) of the second. The fact that such games have a coalition structure core implies that it is possible to pair the players in such a way that there are no two players that prefer to be together over their current partners. Like firms and local jurisdictions, political parties can also be regarded as coalitions: each party (which is characterized by its political position) is identified with the set of voters supporting it. Multiparty equilibrium is, then, a stable partition of the set of voters among the different parties.

Quasi-equilibrium in abstract economies without ordered preferences

Abstract A definition and an existence proof for quasi-equilibrium in abstract economies is presented When applied to a standard economy this definition coincides with the regular notion of a quasi-equilibrium given by Debreu.

On the sensitivity of von Neumann and Morgenstern abstract stable sets: the stable and the individual stable bargaining set

The purpose of this paper is twofold: First, to study the properties of the notions of the “stable” and “individual stable” bargaining sets (SBS and ISBS). Second, to point out the sensitivity of the von Neumann and Morgenstern (vN&M) abstract stable set to the dominance relation that is being employed: Insisting that each member of the coalition be made better off yields the SBS, while requiring that at least one member of the coalition is better off and all others are not worse off yields the ISBS. Rather surprisingly, the SBS and the ISBS may have an empty intersection.We fully characterize both the SBS and the ISBS in 3-person games with transferable utilities, and we also show that in ordinally convex games these two sets coincide with the core. As a by-product we thus derive a new proof that such games have a nonempty core. The paper concludes with an open question.

Existence and Optimality of Equilibrium in Labour-managed Economies

Most general equilibrium models assume the a-priori existence of (a fixed number of) firms. In contrast, by explicitly introducing the classical entrepreneur into the model below, the resulting firm structure become endogenous. To this end, .. . a single class of inputs, labour, is singled out for special treatment. The distinctive features of Illyrian behaviour stem entirely from this fact (Ward (1958)). More specifically, we define labour to be a commodity that shares the following three properties: