Optimal Pricing for Linear-Quadratic Games with Nonlinear Interaction Between Agents

TL;DR

This paper investigates optimal pricing strategies in network games with nonlinear, concave interactions, demonstrating the importance of network structure knowledge for maximizing revenue and providing an efficient algorithm for strategy computation.

Contribution

It introduces a novel analysis of pricing in nonlinear network games, proving the uniqueness of Nash Equilibrium and showing the advantage of network-aware pricing strategies.

Findings

Optimal pricing depends on network structure.

Asymmetric networks yield higher revenue.

Network-aware strategies outperform network-agnostic ones.

Abstract

This paper studies a class of network games with linear-quadratic payoffs and externalities exerted through a strictly concave interaction function. This class of game is motivated by the diminishing marginal effects with peer influences. We analyze the optimal pricing strategy for this class of network game. First, we prove the existence of a unique Nash Equilibrium (NE). Second, we study the optimal pricing strategy of a monopolist selling a divisible good to agents. We show that the optimal pricing strategy, found by solving a bilevel optimization problem, is strictly better when the monopolist knows the network structure as opposed to the best strategy agnostic to network structure. Numerical experiments demonstrate that in most cases, the maximum revenue is achieved with an asymmetric network. These results contrast with the previously studied case of linear interaction function, where a network-independent price is proven optimal with symmetric networks. Lastly, we describe an efficient algorithm to find the optimal pricing strategy.