Yves Sprumont

Population monotonic allocation schemes for cooperative games with transferable utility

Abstract An allocation scheme for a cooperative game specifies how to allocate the worth of every coalition. It is population monotonic if each players payoff increases as the coalition to which he belongs grows larger. We show that, essentially, a game has a population monotonic allocation scheme (PMAS) if and only if it is a positive linear combination of monotonic simple games with veto control. A dual characterization is also provided. Sufficient conditions for the existence of a PMAS include convexity and “increasing average marginal contributions.” If the game is convex, its (extended) Shapley value is a PMAS. Classification Number: 026.

Sharing a River

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. We are interested in efficiency, stability (in the sense of the core), and fairness (in a sense to be defined). We first show that the cooperative game associated with that problem is convex: its core is therefore large and easily described. Next, we propose the following fairness requirement: no group of agents should enjoy a welfare higher than what it could achieve in the absence of the remaining agents. We prove that only one welfare distribution in the core satisfies this condition: its marginal contribution vector corresponding to the ordering of the agents along the river. We discuss how it could be decentralized or implemented.

Strategyproof Collective Choice in Economic and Political Environments

This paper surveys some recent results characterizing strategyproof collective choice rules when preferences satisfy conditions that are meaningful in economic or political environments.

On the Testable Implications of Collective Choice Theories

We analyze collective choices in game forms from a revealed preference viewpoint. We call the joint choice behavior of n agents Nash- (respectively, Pareto-) rationalizable if there exist n preferences over the conceivable joint actions such that the joint actions selected from each game form coincide with the Nash equilibria (respectively, the Pareto optima) of the corresponding game. In the two-agent case, we show that every deterministic joint behavior which is Nash-rationalizable is also Pareto-rationalizable. The converse is false. We further identify general necessary and sufficient conditions for Nash-rationalizability of an n-agent joint choice behavior. We also define and characterize partial versions of the Nash- and Pareto-rationalizability requirements. Journal of Economic Literature Classification Numbers: C72, C92.

Ordering infinite utility streams

We reconsider the problem of ordering infinite utility streams. As has been established in earlier contributions, if no representability condition is imposed, there exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams. We examine the possibility of adding suitably formulated versions of classical equity conditions. First, we provide a characterization of all ordering extensions of the generalized Lorenz criterion as the only strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. Second, we offer a characterization of an infinite-horizon extension of leximin obtained by adding an equity-preference axiom to strong Pareto and finite anonymity.

Paretian Quasi-orders: The Regular Two-Agent Case

Abstract We characterize the “regular” two-agent Paretian quasi-orders. Journal of Economic Literature Classification Numbers: C60, D60, D71.

Rationalizability of choice functions on general domains without full transitivity

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. Such weakenings are particularly relevant in the context of social choice. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation. Furthermore, we discuss sufficient conditions and necessary conditions for rational choice on arbitrary domains. Transitive, quasi-transitive, and acyclical rationalizability are fully characterized for domains that contain all singletons and all two-element subsets of the universal set.

Non-Deteriorating Choice

We analyze an alternative to the standard rationalizability requirement for observed choices by considering non-deteriorating selections. A selection function is a generalization of a choice function where selected alternatives may depend on a reference (or status quo) alternative in addition to the set of feasible options. A selection function is non-deteriorating if there exists an ordering over the universal set of alternatives such that the selected alternatives are at least as good as the reference option. We characterize non-deteriorating selection functions in an abstract framework and in an economic environment.

Sharing the cost of a network: Core and core allocations

Abstract. This paper discusses the core of the game corresponding to the standard fixed tree problem. We consider the weighted adaptation of the constrained egalitarian solution of Dutta and Ray (1989). The core of the standard fixed tree game equals the set of all weighted constrained egalitarian solutions. Each weighted constrained egalitarian solution is determined (in polynomial time) as a home-down allocation, which creates further insight in the local behaviour of the weighted constrained egalitarian solution. The constrained egalitarian solution is characterized in terms of a cost sharing mechanism.

Welfare egalitarianism in non-rival environments

We study equity in economies where a set of agents commonly own a technology producing a non-rival good from their private contributions. A social ordering function associates to each economy a complete ranking of the allocations. We build social ordering functions satisfying the property that individual welfare levels exceeding a legitimate upper bound should be reduced. Combining that property with efficiency and robustness properties with respect to changes in the set of agents, we obtain a kind of welfare egalitarianism based on a constructed numerical representation of individual preferences.