Papers

We develop a network game model with higher-order interactions. In our model, agents interact through hyperedges: the externality received by an agent depends on the joint activity of pairs of other agents rather than on individual neighbors in isolation. We represent the interaction structure by a nonnegative tensor and establish existence and uniqueness of an interior Nash equilibrium under a tensor spectral-radius condition. We then show that the equilibrium is the lower envelope of Katz-Bonacich centrality vectors generated by a family of induced ordinary networks. This representation clarifies how triadic interactions differ from bilateral ones: influence is transmitted through neighbor pairs and depends on third-party complementarities. We use this structure to derive comparative statics and study key-player problems in which the higher-order network game and the bilateral network game on its clique expansion may identify different key players.

This paper studies how a monopolist acquires consumer-level influence data to personalize prices in a market with positive network externalities. For any acquired dataset, the firm's profit depends on an effective data variance measuring the resolved influence heterogeneity. The optimal untargeted set therefore forms an interval: the monopolist leaves intermediate types unidentified while targeting one or both tails of the influence distribution. The value of influence data is higher in denser or more dispersed networks, and the targeted set expands as data become cheaper or network effects become stronger. The acquisition technology is consequential. Compared with representative random sampling which induces an all-or-nothing acquisition strategy, targeting supports partial acquisition and raises both profit and aggregate consumer surplus when data are costly; When data are cheap, targeting benefits the firm but reduces consumer surplus, yielding an ambiguous welfare impact.

In a favor exchange (informal risk-sharing) environment, we distinguish an opportunity network from an endogenously activated subnetwork, the former captures pairs of agents who can potentially help each other while the latter represents those who actually provide assistance in equilibrium. We show that an activated subnetwork normally consists of like friends, each having a moderate and similar number of activated links, even when they have diverse degrees in the opportunity network. We find that trees and preferential-attachment networks are generally ineffective for risk-sharing. We also show that an increase in the intensity of negative shocks does not necessarily lead to a decline in social welfare.

This paper investigates how a monopolist strategically acquires information from networked consumers with correlated preferences using discriminatory or uniform pricing schemes. Under uniform pricing, the optimal information acquisition problem can be efficiently solved in polynomial time by iteratively selecting consumers with the highest Katz-Bonacich centrality. By contrast, under discriminatory pricing, the problem is generally NP-hard. However, in typical networks, such as complete bipartite, core-periphery, and nested-split networks, the optimal targeted group can be characterized in a straightforward manner: the monopolist simply prioritizes consumers with higher degrees. A comparative analysis shows that the size of the optimal targeted group decreases with information cost but follows an inverted U-shape with respect to preference correlation. Allowing the monopolist to acquire information always reduces welfare under discriminatory pricing, whereas under uniform pricing, the impact is not necessarily negative.

Do firms in an oligopoly market behave “as if” they were maximizing a common fictitious objective function, as in perfect competition and monopoly? The answer is yes under certain mild technical conditions (Slade, 1994). That is, in terms of Monderer and Shapley (1996), the Cournot competition is a potential game. In this paper, we ask the same question for Cournot competition with quadratic payoff functions and cross-holdings, an important variant of the oligopoly market. We find that, for various potential functions, the question can be more easily understood from the structure of the influence network, which is constructed from the cross-holding network. Roughly, we find that the Cournot competition with cross-holdings is a potential game if and only if the influence network is symmetric in certain generalized sense. Extending the model to Cournot competition with both overlapping ownership and product differentiation, we find that the previous results still hold. We also provide two applications of our results.

We explore optimal monopoly pricing in the presence of local negative externalities among agents’ consumption. A monopolist first sets personalized prices, and consumers then simultaneously determine consumption levels. When network externalities are relatively small, the complement graph of the social network plays a key role in characterizing the equilibrium. Optimal prices are uniform when the production cost is linear and proportional to agents’ Katz-Bonacich centralities in the complement network when the production cost is convex. We further connect agents’ consumption with their degrees in several typical networks. The firm’s profit and total consumption decrease with network density, although the consumption of a specific agent may not decrease accordingly. Furthermore, in the context of directed networks, the monopolist charges higher prices to agents who generate substantial externalities for others without being reciprocally influenced. We also apply our model to the case involving large network externalities, where the monopolist exclusively sells products to consumers who constitute a maximum independent set.

We study Bayesian persuasion with local strategic substitutes in networks. A designer commits to a public signal to maximize total activity. Equilibria are characterized by the network’s maximum k insulated sets for each realization. We solve the optimal information structure and characterize beneficial persuasion. While agents individually prefer higher states, the designer’s payoff is non-monotonic in the posterior mean due to substitution effects. This provides a rationale for downplaying mechanisms—revealing low states truthfully and mixing signals when high. Moreover, for tree, nested split, and core-periphery networks, the designer strictly benefits if the prior mean insulated set size is less than the highest state set size.

There are two recognized classes of strategic-form symmetric games, both of which can be conveniently defined through the corresponding player symmetry groups. We investigate the basic properties of these groups and several related concepts. We generalize the notion of coveringness and adapt their results to characterize these player symmetry groups. We study the relationships between the coveringnesses of various symmetry groups. Our results demonstrate that these symmetry groups have rich mathematical structures that are of game theoretical and economic interests.