Tight Bounds for the Price of Anarchy and Stability in Sequential Transportation Games

TL;DR

This paper studies the efficiency of sequential transportation games by establishing bounds on the Price of Anarchy and Stability for various social cost functions, including a new one, in both metric and non-metric cases.

Contribution

It introduces a sequential version of transportation games and provides tight bounds for the Price of Anarchy and Stability across multiple social cost functions.

Findings

Bounds for Sequential Price of Stability and Anarchy are established.

Analysis includes a new social cost function based on total player distances.

Results cover both metric and non-metric instances.

Abstract

In this paper, we analyze a transportation game first introduced by Fotakis, Gourv\`es, and Monnot in 2017, where players want to be transported to a common destination as quickly as possible and, in order to achieve this goal, they have to choose one of the available buses. We introduce a sequential version of this game and provide bounds for the Sequential Price of Stability and the Sequential Price of Anarchy in both metric and non-metric instances, considering three social cost functions: the total traveled distance by all buses, the maximum distance traveled by a bus, and the sum of the distances traveled by all players (a new social cost function that we introduce). Finally, we analyze the Price of Stability and the Price of Anarchy for this new function in simultaneous transportation games.