  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.
