From Nash games to vector equilibrium problems

Cotrina J.; García Y.; Marechal M. · Decisions in Economics and Finance (2026) · DOI: 10.1007/s10203-026-00601-9

Resumen

In this paper, we study a recently introduced vector-valued version of the Nikaidô–Isoda bifunction that allows Nash games to be reformulated as strong vector equilibrium problems. We show that classical assumptions in Nash equilibrium theory, such as the quasiconvexity of the players’ payoff functions, naturally translate into generalized convexity properties of the vector Nikaidô–Isoda bifunction. This correspondence does not generally hold for the scalar Nikaidô–Isoda bifunction, since it is defined through summation and quasiconvexity is not preserved under sums. Based on this reformulation, we investigate the existence of solutions to strong vector equilibrium problems by means of the finite intersection property and transfer lower continuity, thereby extending and unifying several results in the literature. We further analyze the main properties of the vector Nikaidô–Isoda bifunction and identify classes of games for which this bifunction satisfies generalized quasiconvexity and generalized monotonicity assumptions. Finally, we establish a connection between the classical notion of weak transfer lower continuity in games and the transfer lower continuity of the vector Nikaidô–Isoda bifunction. © The Author(s), under exclusive licence to Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2026.

Instituciones: Universidad del Pacífico