arXiv subjects

Sanjeev Goyal

Publications and source records attributed to Sanjeev Goyal.

8 recordsLinked to original sources

arXiv2025

Interconnected Contests

We study a two-player model of conflict with multiple battlefields -- the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighboring battles. There exists a unique equilibrium in which the relative probability of a player winning a battle is the product of the ratio of the centrality of the battlefield in the two respective competing networks and the ratio of the relative cost of efforts of the two players. We study the design of networks and characterize networks that maximize total efforts and maximize total utility. Finally, we characterize the equilibrium of a game in which players choose both networks and efforts in the battles.

econ.TH↗

arXiv2024

Robust Market Interventions

When can interventions in markets be designed to increase surplus robustly -- i.e., with high probability -- accounting for uncertainty due to imprecise information about economic primitives? In a setting with many strategic firms, each possessing some market power, we present conditions for such interventions to exist. The key condition, recoverable structure, requires large-scale complementarities among families of products. The analysis works by decomposing the incidence of interventions in terms of principal components of a Slutsky matrix. Under recoverable structure, a noisy signal of this matrix reveals enough about these principal components to design robust interventions. Our results demonstrate the usefulness of spectral methods for analyzing imperfectly observed strategic interactions with many agents.

econ.TH↗

arXiv2022

Taxes and Market Power: A Principal Components Approach

Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked. Because of market power, the equilibrium is inefficient. We study how a policymaker should target a budget-balanced tax-and-subsidy policy to increase welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of eigenbundles -- orthogonal in the sense that a tax on any eigenbundle passes through only to its own price -- with pass-through coefficients determined by associated eigenvalues. Our basis permits a simple characterization of optimal interventions. A planner maximizing consumer surplus should tax eigenbundles with low pass-through and subsidize ones with high pass-through. The Pigouvian leverage of the system -- the gain in consumer surplus achievable by an optimal tax scheme -- depends only on the dispersion of the eigenvalues of the matrix of strategic interactions. We interpret these results in terms of the network structure of the market.

econ.TH↗

arXiv2021

Discord and Harmony in Networks

Consider a coordination game played on a network, where agents prefer taking actions closer to those of their neighbors and to their own ideal points in action space. We explore how the welfare outcomes of a coordination game depend on network structure and the distribution of ideal points throughout the network. To this end, we imagine a benevolent or adversarial planner who intervenes, at a cost, to change ideal points in order to maximize or minimize utilitarian welfare subject to a constraint. A complete characterization of optimal interventions is obtained by decomposing interventions into principal components of the network's adjacency matrix. Welfare is most sensitive to interventions proportional to the last principal component, which focus on local disagreement. A welfare-maximizing planner optimally works to reduce local disagreement, bringing the ideal points of neighbors closer together, whereas a malevolent adversary optimally drives neighbors' ideal points apart to decrease welfare. Such welfare-maximizing/minimizing interventions are very different from ones that would be done to change some traditional measures of discord, such as the cross-sectional variation of equilibrium actions. In fact, an adversary sowing disagreement to maximize her impact on welfare will minimize her impact on global variation in equilibrium actions, underscoring a tension between improving welfare and increasing global cohesion of equilibrium behavior.

econ.TH↗

arXiv2020

Targeting Interventions in Networks

We study games in which a network mediates strategic spillovers and externalities among the players. How does a planner optimally target interventions that change individuals' private returns to investment? We analyze this question by decomposing any intervention into orthogonal principal components, which are determined by the network and are ordered according to their associated eigenvalues. There is a close connection between the nature of spillovers and the representation of various principal components in the optimal intervention. In games of strategic complements (substitutes), interventions place more weight on the top (bottom) principal components, which reflect more global (local) network structure. For large budgets, optimal interventions are simple -- they involve a single principal component.

cs.GT↗

arXiv2019

Trading in Complex Networks

Global supply networks in agriculture, manufacturing, and services are a defining feature of the modern world. The efficiency and the distribution of surpluses across different parts of these networks depend on choices of intermediaries. This paper conducts price formation experiments with human subjects located in large complex networks to develop a better understanding of the principles governing behavior. Our first finding is that prices are larger and that trade is significantly less efficient in small-world networks as compared to random networks. Our second finding is that location within a network is not an important determinant of pricing. An examination of the price dynamics suggests that traders on cheapest -- and hence active -- paths raise prices while those off these paths lower them. We construct an agent-based model (ABM) that embodies this rule of thumb. Simulations of this ABM yield macroscopic patterns consistent with the experimental findings. Finally, we extrapolate the ABM on to significantly larger random and small world networks and find that network topology remains a key determinant of pricing and efficiency.

q-fin.GN↗

arXiv2016

Strategic Network Formation with Attack and Immunization

Strategic network formation arises where agents receive benefit from connections to other agents, but also incur costs for forming links. We consider a new network formation game that incorporates an adversarial attack, as well as immunization against attack. An agent's benefit is the expected size of her connected component post-attack, and agents may also choose to immunize themselves from attack at some additional cost. Our framework is a stylized model of settings where reachability rather than centrality is the primary concern and vertices vulnerable to attacks may reduce risk via costly measures. In the reachability benefit model without attack or immunization, the set of equilibria is the empty graph and any tree. The introduction of attack and immunization changes the game dramatically; new equilibrium topologies emerge, some more sparse and some more dense than trees. We show that, under a mild assumption on the adversary, every equilibrium network with $n$ agents contains at most $2n-4$ edges for $n\geq 4$. So despite permitting topologies denser than trees, the amount of overbuilding is limited. We also show that attack and immunization don't significantly erode social welfare: every non-trivial equilibrium with respect to several adversaries has welfare at least as that of any equilibrium in the attack-free model. We complement our theory with simulations demonstrating fast convergence of a new bounded rationality dynamic which generalizes linkstable best response but is considerably more powerful in our game. The simulations further elucidate the wide variety of asymmetric equilibria and demonstrate topological consequences of the dynamics e.g. heavy-tailed degree distributions. Finally, we report on a behavioral experiment on our game with over 100 participants, where despite the complexity of the game, the resulting network was surprisingly close to equilibrium.

cs.GT↗

arXiv2012

Competitive Contagion in Networks

We develop a game-theoretic framework for the study of competition between firms who have budgets to "seed" the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochastic diffusion process in the network. This framework yields a rich class of competitive strategies, which depend in subtle ways on the stochastic dynamics of adoption, the relative budgets of the players, and the underlying structure of the social network. We identify a general property of the adoption dynamics --- namely, decreasing returns to local adoption --- for which the inefficiency of resource use at equilibrium (the Price of Anarchy) is uniformly bounded above, across all networks. We also show that if this property is violated the Price of Anarchy can be unbounded, thus yielding sharp threshold behavior for a broad class of dynamics. We also introduce a new notion, the Budget Multiplier, that measures the extent that imbalances in player budgets can be amplified at equilibrium. We again identify a general property of the adoption dynamics --- namely, proportional local adoption between competitors --- for which the (pure strategy) Budget Multiplier is uniformly bounded above, across all networks. We show that a violation of this property can lead to unbounded Budget Multiplier, again yielding sharp threshold behavior for a broad class of dynamics.

cs.GT↗