Laurence Kranich

CORE CONCEPTS FOR DYNAMIC TU GAMES

This paper is concerned with the question of how to define the core when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face a finite sequence of exogenously specified TU-games. Three different core concepts are presented: the classical core, the strong sequential core and the weak sequential core. The differences between the concepts arise from different interpretations of profitable deviations by coalitions. Sufficient conditions are given for nonemptiness of the classical core in general and of the weak sequential core for the case of two players. Simplifying characterizations of the weak and strong sequential core are provided. Examples highlight the essential difference between these core concepts.

Historical discrimination and optimal remediation

I consider a society which is jointly committed to ensuring equal opportunity and to increasing aggregate wealth but is faced with the vestiges of past discrimination in the form of a historically skewed distribution of social resources. Focusing on the problem of allocating the existing (fixed) quantity of social inputs, I consider two policy instruments: directly transferring resources from the advantaged to the disadvantaged or affording preferential treatment in employment to the disadvantaged group (affirmative action). After describing the general procedure for determining an optimal policy, I demonstrate by means of an example that either of the instruments might constitute an optimal remediation policy and I identify conditions which favor each.

Equal shadow wealth: A new concept of fairness in exchange economies

In this paper I introduce a new notion of fairness in exchange economies as well as a measure of unfairness. First, I consider the benchmark case in which agents have identical preferences, and I then extend the framework to allow for heterogeneous tastes. In both cases, I identify an appropriate egalitarian benchmark which requires that a numeraire commodity be distributed in such a way so as to offset differences in the holdings of other commodities. Inequality is then measured as the deviation between the actual distribution of the numeraire and such an ideal distribution. This renders a complete social ordering. Next, I contrast this notion of equal shadow wealth with the notion of no-envy (Foley, 1967) and with the envy-intensity measures proposed by Chaudhuri (1986) and Diamantaras and Thomson (1990). I also investigate conditions which ensure the existence of equitable and efficient allocations. The concepts developed here may be generalizable to a wide range of environments including economies with externalities and indivisible goods as well as relatively unstructured environments such as those involving abstract opportunity sets. In addition, this approach offers a simple method to measure multidimensional inequality.

The linear cost equivalent rule: A solution procedure for heterogeneous joint production problems

Abstract We propose an extension of the constant-returns-equivalent (CRE) solution for allocating joint costs/benefits among homogeneous contributors to environments in which contributors are heterogeneous. For the domain of quasilinear economies, we axiomatically characterize this solution by means of three axioms: efficiency, free access to linear economies, and a weak version of technological monotonicity which considers the different roles of the agents in generating the costs. Our proposal is also immune to arbitrary changes in the units of account of the various activities.

Manipulation of the Walrasian mechanism in production economies with unbounded short-selling

Abstract.Hurwicz (1979) and Otani and Sicilian (1982, 1990) characterized the Nash equilibrium allocations of the Walrasian demand manipulation game in successively more general exchange environments. In this paper, I extend the analysis to production economies with short-selling. First, I generalize Hurwicz’s and Otani and Sicilian’s theorem that any allocation at which each agent’s consumption bundle lies above her true offer curve can be supported in Nash equilibrium. I then show that for finite economies of any size the set of such allocations is often topologically large.