A Membrane Computing Approach to the Generalized Nash Equilibrium

TL;DR

This paper introduces a novel approach to solving Generalized Nash Equilibrium problems using Membrane Computing techniques, specifically modeling GNE with P systems, which bridges evolutionary game theory and computational biology.

Contribution

It is the first to apply Membrane Computing to GNE problems, creating a new interdisciplinary modeling framework.

Findings

GNE problems can be effectively modeled with P systems.

The approach opens new avenues for solving complex equilibrium problems.

Bridges the gap between game theory and membrane computing.

Abstract

In Evolutionary Game Theory (EGT), a population reaches a Nash equilibrium when none of the agents can improve its objective by solely changing its strategy on its own. Roughly speaking, this equilibrium is a protection against betrayal. Generalized Nash Equilibrium (GNE) is a more complex version of this idea with important implications in real-life problems in economics, wireless communication, the electricity market, or engineering among other areas. In this paper, we propose a first approach to GNE with Membrane Computing techniques and show how GNE problems can be modeled with P systems, bridging both areas and opening a door for a flow of problems and solutions in both directions.