Gabrielle Demange

Group formation in economics : networks, clubs, and coalitions

Broad and diverse ranges of activities are conducted within and by organized groups of individuals, including political, economic and social activities. These activities have become a subject of intense interest in economics and game theory. Some of the topics investigated in this collection are models of networks of power and privilege, trade networks, co-authorship networks, buyer–seller networks with differentiated products, and networks of medical innovation and the adaptation of new information. Other topics are social norms on punctuality, clubs and the provision of club goods and public goods, research and development and collusive alliances among corporations, and international alliances and trading agreements. While relatively recent, the literature on game theoretic studies of group formation in economics is already vast. This volume provides an introduction to this important literature on game-theoretic treatments of situations with networks, clubs, and coalitions, including some applications.

FAIR ALLOCATION OF INDIVISIBLE GOODS AND CRITERIA OF JUSTICE

A set of n objects and an amount M of money is to be distributed among m people. Example: the objects are tasks and the money is compensation from a fixed budget. An elementary argument via constrained optimization shows that for M sufficiently large the set of efficient, envy free allocations is nonempty and has a nice structure. In particular, various criteria of justice lead to unique best fair allocations that are well behaved with respect to changes of M. This is in sharp contrast to the usual fair division theory with divisible goods. Copyright 1991 by The Econometric Society.

On Group Stability in Hierarchies and Networks

A hierarchical structure is a widespread organizational form in many areas. My aim in this paper is to provide a rationale for this fact based on two premises. First, a group organizes itself so as to achieve efficient coordination. Second, efficient coordination is achieved only if subgroups as well as individuals agree to cooperate. Even in situations in which there are gains to coordination, the agreement of each possible subgroup may be impossible to reach, resulting in instabilities. I argue that a hierarchical organization avoids such instabilities by distributing in an optimal way autonomy and blocking power to a restricted set of subgroups. Comparisons with nondirected networks are drawn.

Single-peaked orders on a tree

Inada (1969) and Sen and Pattanaik (1969) have characterized the sets of preference orders which ensure the transitivity of the strict majority rule, no matter how each voter selects his own order in the set. But a problem remains untouched: which domains of orders guarantee the existence of a majority winner without necessarily ensuring the transitivity of the strict majority rule. We provide in this paper domains, called sets of single-peaked linear orders on a tree, which enjoy such a property. They appear as a generalization of the well-known sets of single-peaked linear orders.

Algorithms for proportional matrices in reals and integers

LetR be the set of nonnegative matrices whose row and column sums fall between specific limits and whose entries sum to some fixedh > 0. Closely related axiomatic approaches have been developed to ascribe meanings to the statements: the real matrixf ∈ R and the integer matrixa ∈ R are “proportional to” a given matrixp ≥ 0.These approaches are described, conditions under which proportional solutions exist are characterized, and algorithms are given for finding proportional solutions in each case.

Social Security and Demographic Shocks

This paper examines the sharing of risks between generations in the framework of an overlapping generations model of social security with shocks to the productivity of labor and capital and demographic shocks. The study focused on stationary long run allocations. The concept of interim optimality was utilized, which amounts to standard Pareto optimality once the state of the world in which the agents are born is known. The set of interim optimal allocations was characterized and the equilibria associated with various institutional forms of social security from the point of view of the optimal criterion were also studied. In addition, the analogs of two traditional welfare theorems of microeconomic theory were obtained.

A further note on the stable matching problem

Using a lemma of J.S. Hwang we obtain a generalization of a theorem of Dubins and Freedman. It is shown that the core of the matching game is non-manipulable in a suitable sense by coalitions consisting of both men and women. A further strong stability property of the core is derived.

Social Security, Optimality, and Equilibria in a Stochastic Overlapping Generations Economy

Social security institutions implement intergenerational transfers and distribute risks over time. To compare various social security designs, we study an overlapping generations model with demographic shocks. Production takes place through a neoclassical production function subject to productivity shocks. We give a near characterization of optimal allocations. We study rational expectations equilibria when contributions are mandatory, based on labor and capital income. We also describe the equilibria of an economy with a voluntary pay-as-you-go social security fund, and show that they have a long-run optimality property. An example with Cobb-Douglas production and utility functions illustrates the results. Copyright 2000 by Blackwell Publishing Inc.

Contagion in financial networks: A threat index

This paper proposes to measure the spillover effects that cross liabilities generate on the magnitude of default in a system of financially linked institutions. Based on a simple model and an explicit criterion-the aggregate debt repayments-the measure is defined for each institution, affected by its characteristics and links to others. These measures-one for each institution-summarize relevant information on the interaction between the liabilities structure and the shocks to resources, and they can be useful to determine optimal intervention policies. The approach is illustrated to evaluate the consolidated foreign claims of 10 European Union countries. This paper was accepted by Amit Seru, finance.

Reforming Incentive Schemes Under Political Constraints: The Physician Agency

In many developed countries attempts to reform physicians payment schemes have failed. To analyze some of the difficulties, this paper studies reforms of payment schemes in situations such as the physician agency, where the quality of the good produced is imperfectly observable by the payer. We first study the situation, common in many countries, where physicians face a single scheme. We identify conditions under which no reform can both obtain the consent of a large proportion of physicians (political constraints) and improve patients welfare. We then study whether a menu of contracts, with or without cross subsidies, may solve the difficulties generated by the heterogeneity of producers practice.