Pure Nash Equilibrium and Coordination of Players in Ride Sharing Games

TL;DR

This paper models ride sharing as a game with externalities, investigates conditions for pure Nash equilibria, and explores coordination methods to improve efficiency and reduce the price of anarchy.

Contribution

It introduces a framework for ride sharing games with externalities, establishes conditions for pure Nash equilibria, and demonstrates coordination techniques to enhance social welfare.

Findings

Ride sharing games can have finite improvement properties and pure Nash equilibria under certain conditions.

Coordination via signaling can improve the price of anarchy in ride sharing games.

First analysis of equilibrium existence and coordination effects in ride sharing game models.

Abstract

In this study, we formulate positive and negative externalities caused by changes in the supply of shared vehicles as ride sharing games. The study aims to understand the price of anarchy (PoA) and its improvement via a coordination technique in ride sharing games. A critical question is whether ride sharing games exhibit a pure Nash equilibrium (pNE) since the PoA bound assumes it. Our result shows a sufficient condition for a ride sharing game to have a finite improvement property and a pNE similar to potential games. This is the first step to analyze PoA bound and its improvement by coordination in ride sharing games. We also show an example of coordinating players in ride sharing games using signaling and evaluate the improvement in the PoA.