When Nash Meets Stackelberg

This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a Stackelberg game where a leader optimizes a (parametrized) linear objective function subject to linear constraints while its followers solve convex quadratic problems subject to the standard optimistic assumption. Although we prove that deciding if a NASP instance admits a Nash equilibrium is generally a Sigma2p-hard decision problem, we devise two exact and computationally-efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We apply NASPs to model the hierarchical interactions of international energy markets where climate-change aware regulators oversee the operations of profit-driven energy producers. By combining real-world data with our models, we find that Nash equilibria provide informative, and often counterintuitive, managerial insights for market regulators.