Current Projects

Suppose that a monopolist with a convex production technology must determine price and quantity by eliciting consumer demand. We know well how to proceed when the objective is to maximize profits. But how can we proceed if the objective is instead to maximize consumer surplus, subject to the monopolist not losing money? This can happen if the monopolist is regulated, is a cooperative, or if the buyers are organized as a cartel. 

We characterize the class of mechanisms available to the regulated monopolist. Across those that moreover guarantee ex-post voluntary participation to both the consumers and the monopolist, we find that a novel class of mechanisms maximize consumer surplus. This latter class involves subsidies to consumers who purchase nothing. 

Status: revising draft

The literature on value capture examines situations where a few economic agents engage in trade with one another. The final prices of these trades depend on a variety of non-observed variables, such as the bargaining abilities of the agents involved. The concept of the core from cooperative game theory provides a set of possible allocations and corresponding prices that can result from these bargaining processes. It also takes into account the competitive advantage of the various agents, which is determined by their outside options. An agent is said to have a competitive advantage if they can extract value regardless of their bargaining ability.

The literature has examined and interpreted various conditions that guarantee a competitive advantage, and how to measure it. This paper generalizes the conditions proposed by MacDonald and Ryall (2004) and Montez et al. (2018). The condition is based on the new concept of "balanced renegotiation": an agent has a competitive advantage if, when assigned low payments, they can initiate a series of counterproposals to various groups that ultimately makes it impossible to divide the value created. The renegotiation process is considered "balanced" when all other agents are involved the same number of times in the process. The paper provides examples related to collusion and R&D cooperation, and suggests strategies for increasing the competitive advantage.

Status: writing initial draft

We consider a version of the classic job scheduling problem in which all machines are identical, but in which jobs must be processed before a deadline. We study this problem using cooperative game theory, focusing on the question of how to divide the total cost between the agents. We consider both a simple version of the problem, in which all jobs have the same length, and a more general version where jobs of different lengths either need to be processed continuously on one machine or may be interrupted and processed on several machines at the same time. In all these versions the core may be empty. We therefore focus on stability and fairness and define two allocation mechanisms that satisfy the core constraints and either the most favorable scenario lower bounds or the egalitarian fair lower bounds. For the simple version we also provide necessary and sucient conditions for the core to be non-empty and for the general version we provide sufficient conditions.

Status: revising draft

Suppose that a group of agents are connected to a source via a pipeline. The flow in the pipeline creates a negative local externality, that can be interpreted as pollution or risk of a spill. We first examine the problem of determining the optimal flow in the pipeline, balancing the consumption gains with the negative externalities. We then examine how to share the benefits generated by the pipeline. To do so, we define an optimistic and a pessimistic version of the problem (depending if a coalition consumes before or after the other agents). We explore the resulting cores. Given that the optimal use of the pipeline typically implies that some agents will restrict their consumption for the benefits of the group, we consider providing them with compensation for this sacrifice.

Status: writing initial draft and presenting initial results

Semi-convex games (with E. Bahel and H. Wang)

In a convex game, the marginal contribution of a player is an increasing (with respect to set inclusion) function of the coalition joined by that player. We define below a new family of TU games for which the players’ marginal contributions do not necessarily satisfy this property. In a k-semiconvex TU game, the marginal contribution of a player i to a coalition T containing at least n−k+1 players is weakly higher than i’s marginal contribution to a subset of T and the reverse inequality must hold for coalitions T that contain at most n−k players (and their nonempty subsets S). We show a necessary condition for such games to have a non-empty core, by defining a core allocation that generalizes the Shapley value. Multiple applications are provided.

   Status: writing initial draft

Queueing problems when users can move (with A. Atay)

We study the situation where we have a finite set of machines that can process jobs, and users that are assigned to their local machine. However, if they are impatient and the queue at their local machine, they can travel to a neighboring machine, at a cost. Using a cooperative game theory framework, we study how this option of moving affects stability and cost sharing. We consider optimistic (where a coalition of agents could use all machines without the presene of others) and pessimistic (where others have already arrived at the machines) approaches to determine bounds, and compare the two approaches. We show that the optimistic approach is more demanding, but it is always possible to find allocations in which no coalition does better than the best case scenario of the optimistic approach.

Status: gathering results

Optimistic and pessimistic approaches in cooperative games (with A. Atay)

In many settings, the value that a coalition can obtain when it "stands alone" depends on the behavior of other agents. This has lead many to consider two opposite approaches when defining a cooperative game. In the optimistic approach, other agents act in a way that is helpful to the coalition in question, most often in a passive way, by being present or not, depending if they generate a positive or negative externality. By opposition, the pessimistic approach supposes that while the others are acting rationally, they do so in a way that hurts the coalition.

As an example, in a public goods game, the pessimistic approach supposes that others are not contributing to the public good, while the optimistic approach supposes that others have contributed to the public good in a manner that maximizes their own joint benefits. 

After observing that the optimistic approach provides an upper bound on the value that a coalition should obtain, and the pessimistic approach a lower bound, we argue that the optimistic anti-core is a valid concept if we are interested in stability: no coalition should receive more than in their best case scenario, given by the optimistic approach.

We then show that the two approaches are usually not dual to each other; in fact the optimistic anti-core is more restrictive than the pessimistic core, and the former is thus a subset of the latter. Thus, if we can show that the optimistic anti-core is non-empty, so is the pessimistic core. We revisit multiple applications, from minimum cost spanning trees to queueing problems, and show the relevance of the result.

Status: submitted

Monotonicity and the value of a language (with G. Bergantiños)

Using the axiomatic approach, we examine how to determine the value of languages. We propose a different family of functions then Alcade-Unzu et al. (2022), characterized by using a different monotonicity axiom. Various applications are discussed. 

Status: working paper out

Scheduling with divisible jobs (with S. Banerjee)

Traditionally, scheduling problems suppose that agents have jobs of various lengths to be processed on a machine. When we have more than one machine, it matters whether we suppose that the jobs are divisible (we can process them simultaneously on multiple machines) or not. The divisible case, unexplored so far, is the subject of the paper. We define optimistic (coalitions have priority access to the machines) and pessimistic (coalitions have access to the machine after the complement set of agents) games, and study the optimistic anticore and the pessimistic core. We study their Shapley values, providing closed-form expressions. We also study the serial allocation rule, and show that it is in the pessimistic core.