Targeting in networks under costly agreementsJournal articleMohamed Belhaj, Frédéric Deroian et Shahir Safi, Games and Economic Behavior, Volume 140, pp. 154-172, 2023

We consider agents organized in an undirected network of local complementarities. A principal with a fixed budget offers costly bilateral contracts in order to increase the sum of agents' effort. We study contracts rewarding effort exceeding the effort made in the absence of the principal. First, targeting a subgroup of the whole society becomes optimal under substantial contracting costs, which significantly increases the computational complexity of the principal's problem. In particular, under sufficiently low intensity of complementarities, a correspondence is established between optimal targeting and an NP-hard problem. Second, for any intensities of complementarities, the optimal unit returns offered to all targeted agents are positive for all contracting costs and in general heterogeneous, even though networks are undirected. Yet, heterogeneity never leads to negative returns, which implies that, with these linear payment schemes, coordination is never an issue for the principal.

The value of network information: Assortative mixing makes the differenceJournal articleMohamed Belhaj et Frédéric Deroian, Games and Economic Behavior, Volume 126, pp. 428-442, 2021

A monopoly sells a network good to a large population of consumers. We explore how the monopoly's profit and the consumer surplus vary with the arrival of public information about the network structure. The analysis reveals that, under homogeneous preferences for the good, degree assortativity ensures that information arrival increases both profit and consumer surplus. In contrast, heterogeneous preferences for the good can create a tension between consumer surplus and profit.

Group targeting under networked synergiesJournal articleMohamed Belhaj et Frédéric Deroian, Games and Economic Behavior, Volume 118, Issue C, pp. 29-46, 2019

A principal targets agents organized in a network of local complementarities, in order to increase the sum of agents' effort. We consider bilateral public contracts à la Segal (1999). The paper shows that the synergies between contracting and non-contracting agents deeply impact optimal contracts: they can lead the principal to contract with a subset of the agents, and to refrain from contracting with central agents.

Targeting the key player: An incentive-based approachJournal articleMohamed Belhaj et Frédéric Deroian, Journal of Mathematical Economics, Volume 79, Issue C, pp. 57-64, 2018

We consider a network game with local complementarities. A policymaker, aiming at minimizing or maximizing aggregate effort, contracts with a single agent on the network to trade effort change against transfer. The policymaker has to find the best agent and the optimal contract to offer. Our study shows that for all utilities with linear best-responses, it only takes two statistics about the position of each agent on the network to identify the key player: the Bonacich centrality and the self-loop centrality. We also characterize key players under linear quadratic utilities for various contractual arrangements.

Efficient networks in games with local complementaritiesJournal articleMohamed Belhaj, Sebastian Bervoets et Frédéric Deroian, Theoretical Economics, Volume 11, Issue 1, pp. 357-380, 2016

We address the problem of a planner looking for the efficient network when agents play a network game with local complementarities and links are costly. We show that for general network cost functions, efficient networks belong to the class of Nested-Split Graphs. Next, we refine our results and find that, depending on the specification of the network cost function, complete networks, core-periphery networks, dominant group architectures, quasi-star and quasi-complete networks can be efficient.

Network games under strategic complementaritiesJournal articleMohamed Belhaj, Yann Bramoullé et Frédéric Deroian, Games and Economic Behavior, Volume 88, Issue C, pp. 310-319, 2014

We study network games under strategic complementarities. Agents are embedded in a fixed network. They choose a positive, continuous action and interact with their network neighbors. Interactions are positive and actions are bounded from above. We first derive new sufficient conditions for uniqueness, covering all concave as well as some non-concave best responses. We then study the relationship between position and action and identify situations where a more central agent always plays a higher action in equilibrium. We finally analyze comparative statics. We show that a shock may not propagate throughout the entire network and uncover a general pattern of decreasing interdependence.

Competing Activities in Social NetworksJournal articleMohamed Belhaj et Frédéric Deroian, The B.E. Journal of Economic Analysis & Policy, Volume 14, Issue 4, pp. 36, 2014

We consider a society in which each agent has one unit of a resource to allocate between two activities. Agents are organized in a social network, and each activity generates complementarities between neighbors. We find multiplicity of equilibrium for high intensity of interaction, and we characterize equilibria in terms of specialization and polarization. Overall, results reveal the crucial role played by network geometry. The results also suggest that the structure of the social network should be taken into account for the design of a public policy in favor of a specific activity.

Risk-Taking and Risk-Sharing Incentives under Moral HazardJournal articleMohamed Belhaj, Renaud Bourlès et Frédéric Deroian, American Economic Journal: Microeconomics, Volume 6, Issue 1, pp. 58-90, 2014

This paper explores the effect of moral hazard on both risk-taking and informal risk-sharing incentives. Two agents invest in their own project, each choosing a level of risk and effort, and share risk through transfers. This can correspond to farmers in developing countries, who share risk and decide individually upon the adoption of a risky technology. The paper mainly shows that the impact of moral hazard on risk crucially depends on the observability of investment risk, whereas the impact on transfers is much more utility dependent.

Production Efforts in Large Indian Cities: A Network-based ApproachJournal articleSebastian Bervoets et Frédéric Deroian, Journal of Interdisciplinary Economics, Volume 25, Issue 1-2, pp. 117-145, 2013

In this article we construct a network of roads connecting large Indian cities and we evaluate this network’s overall performance. We consider a model where the production efforts of connected cities are strategic complements, and we relate the equilibrium effort profile to a well known centrality measure, the Katz-Bonacich centrality. We then make use of this result to compute the level of efforts of different cities in the current network and identify which city contributes most to overall efforts, which existing road is the most influential and which new road should be constructed in priority. Our results shed light on the importance of relatively small cities on aggregate efforts. Our exercise illustrates how network details might generate unexpected effects.
JEL: C72, D85

Strategic interaction and aggregate incentivesJournal articleMohamed Belhaj et Frédéric Deroian, Journal of Mathematical Economics, Volume 49, Issue 3, pp. 183-188, 2013

We consider a model of interdependent efforts, with linear interaction and lower bound on effort. Our setting encompasses asymmetric interaction and heterogeneous agents’ characteristics. We examine the impact of a rise of cross-effects on aggregate efforts. We show that the sign of the comparative static effects is related to a condition of balancedness of the interaction. Moreover, we point out that asymmetry and heterogeneous characteristics are sources of non-monotonic variation of aggregate efforts.