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· Clearing Supply and Demand Under Bilateral Constraints, with Olivier Bochet, Herve Moulin and Jay Sethuraman, October 2010 (first version: November 2009) (download maxflow15.pdf) (Under 2^nd round revision at Theoretical Economics)

Abstract: In a moneyless market, a non storable, non transferable homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. Transfers between a supplier and a demander are feasible only if they are linked, and the links form an arbitrary bipartite graph. Typically, supply is short in one segment of the market, while demand is short in another. Information about individual preferences is private, and so is information about feasible links: an agent may unilaterally close one of her links if it is in her interest to do so. Our egalitarian transfer solution rations only the long side in each market segment, equalizing the net transfers of rationed agents as much as permitted by the bilateral constraints. It elicits a truthful report of both preferences and links: removing a feasible link is never profitable to either one of its two agents. Together with efficiency, and a version of equal treatment of equals, these properties are characteristic.

· Egaliterianism Under Earmark Constraints, with Olivier Bochet and Herve Moulin, August 2010 (first version: September 2009) (download Earmark15.pdf)

Abstract: We consider a model in which a homogeneous commodity (the resource) is shared by several agents with single-peaked preferences, but the resource is coming from any number of different suppliers, under arbitrary bilateral feasibility constraints: each supplier can only deliver to a certain subset of agents. Examples include balancing the workload of machines, sharing earmarked funds between different projects, and assigning students to schools under geographic constraints. Unlike in the one supplier model (Sprumont, 1991), that we generalize, in a Pareto optimal allocation agents who get more than their peak typically coexist with agents who get less. A variant of the Gallai-Edmonds decomposition (see Ore, 1962) identifies these two subsets of agents, that we call respectively the over-demanded and the under-demanded side of the market. Like in the one supplier model, there is a Lorenz dominant Pareto optimal allocation. We call it the egalitarian solution, and characterize it by the combination of strategyproofness (truthful revelation of peaks) and a variant of equal treatment of equals. The proof relies on submodular optimization techniques as in Dutta and Ray (1989).

· Allocation Rules on Networks, with Çağatay Kayı, September 2009 (first version: April 2008) (download ARN.pdf)

Abstract: Given geographical or infrastructure constraints, it is important to understand how scarce resources should be allocated. An example where such network constraints are critical is water resources. We depict the water distribution infrastructure as a network between sources and cities which are linked by rivers and pipelines. In a stylized model, we assume that sources are only connected to cities and cities are only connected to sources. We define the constrained proportional rule, the constrained equal awards and the constrained equal losses rules and give algorithms how to calculate these allocation rules. The objective is to identify allocation rules that are well-behaved from the normative viewpoint. In addition to efficiency, we look for distributional fairness. We give axiomatic characterizations of the constrained proportional rule and the constrained equal awards rule.

· Cournot Competition on a Network of Markets and Firms, January 2009 (first version: October 2008) (download CN.pdf)

Abstract: Suppose markets and firms are connected in a bipartite network, where firms can only supply to those markets they are connected to. Firms compete a la Cournot and decide how much to supply to each market  they have a link with. We assume that markets have linear inverse demands and firms have convex quadratic costs. We show there exists a unique equilibrium in any given network of firms and markets. We provide a formula which expresses the quantities at equilibrium as a function of a network centrality measure. Next, we study the impact of a merger between two firms. We find that in contrast to a simple Cournot model the merger affects the consumers and rival firms asymmetrically. Some consumers and rivals might be hurt from the merger while others benefit. Moreover, we analyze how a cartel including all the firms in the network would behave to maximize its total profit. We show that the cartel segments the markets among its members. Each firm operates only in the markets allocated to it and refuses to supply to others.

· A Noncooperative Definition of Pairwise Stability, February 2010 (first version: June 2004) (download TP.pdf)

Abstract: This paper examines a normal form game of network formation due to Myerson (1991). All players simultaneously announce the links they wish to form. A link is created if and only if there is mutual consent for its formation. The empty network is always a Nash equilibrium of this game. I define a refinement of Nash equilibria that I call trial perfect. Trial perfect equilibria contains the set of proper equilibria. I show that the set of networks which can be supported by a pure strategy trial perfect equilibrium coincides with the set of pairwise-Nash equilibrium networks, for games with link-responsive payoff functions.