Abstract
In this paper, we analyze a transportation game first introduced by Fotakis, Gourvès, and Monnot in 2017, where players want to be transported to a common destination as quickly as possible and, 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.
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Notes
More specifically, Uber Pool, where different users share the same car to reduce costs and, thus, the vehicle must pick up and deliver users in different locations.
The largest cost of a user is, in fact, the largest distance traveled by a bus.
By unbounded we mean that one can find a sequence of instances with a fixed number of players and buses where the ratio between the social cost of the best SPE and the optimal social cost goes to infinity.
That is, player 1 chooses bus 1, player 2 chooses bus 1 in the subgame where player 1 chooses bus 1, and chooses bus 2 in the subgame where player 2 chooses bus 2, and so on.
References
Angelucci A, Bilò V, Flammini M, Moscardelli L (2013) On the sequential price of anarchy of isolation games. In: International computing and combinatorics conference, pp 17–28 https://doi.org/10.1007/978-3-642-38768-5_4
Anshelevich E, Dasgupta A, Kleinberg J, Tardos E, Wexler T, Roughgarden T (2008) The price of stability for network design with fair cost allocation. SIAM J Comput 38(4):1602–1623. https://doi.org/10.1137/070680096
Bilò V, Flammini M, Monaco G, Moscardelli L(2012) Some anomalies of farsighted strategic behavior. In: International Workshop on approximation and online algorithms, pp 229–241 . https://doi.org/10.1007/978-3-642-38016-7_19
Cole R, Correa JR, Gkatzelis V, Mirrokni V, Olver N (2011) Inner product spaces for Minsum coordination mechanisms. In: Proceedings of the forty-third annual ACM symposium on theory of computing, pp 539–548 . https://doi.org/10.1145/1993636.1993708
Correa J, de Jong J, De Keijzer B, Uetz M (2019) The inefficiency of nash and subgame perfect equilibria for network routing. Math Oper Res 44(4):1286–1303. https://doi.org/10.1287/moor.2018.0968
de Jong J, Uetz M (2014) The sequential price of anarchy for atomic congestion games. In: International conference on web and internet economics, pp 429–434 https://doi.org/10.1007/978-3-319-13129-0_35
de Jong J, Uetz M, Wombacher A (2013) Decentralized throughput scheduling. In: International conference on algorithms and complexity, pp 134–145 . https://doi.org/10.1007/978-3-642-38233-8_12
Fotakis D, Gourvès L, Monnot J(2017) Selfish transportation games. In: International conference on current trends in theory and practice of informatics, pp 176–187 . https://doi.org/10.1007/978-3-319-51963-0_14
Furuhata M, Dessouky M, Ordóñez F, Brunet ME, Wang X, Koenig S (2013) Ridesharing: the state-of-the-art and future directions. Transp Res Part B: Methodol 57:28–46. https://doi.org/10.1016/j.trb.2013.08.012
Hassin R, Yovel U (2015) Sequential scheduling on identical machines. Oper Res Lett 43(5):530–533. https://doi.org/10.1016/j.orl.2015.08.003
Hoeksma R, Uetz M (2011) The price of anarchy for minsum related machine scheduling. In: International workshop on approximation and online algorithms, pp 261–273. https://doi.org/10.1007/978-3-642-29116-6_22
Koutsoupias E, Papadimitriou C (2009) Worst-case equilibria. Comput Sci Rev 3(2):65–69. https://doi.org/10.1016/j.cosrev.2009.04.003
Leme RP, Syrgkanis V, Tardos É(2012) The curse of simultaneity. In: Proceedings of the 3rd innovations in theoretical computer science conference, pp 60–67 . https://doi.org/10.1145/2090236.2090242
Roughgarden T (2009) Intrinsic robustness of the price of anarchy. In: Proceedings of the forty-first annual ACM symposium on Theory of computing, pp 513–522. https://doi.org/10.1145/1536414.1536485
Shoham Y, Leyton-Brown K (2008) Multiagent systems: algorithmic, game-theoretic, and logical foundations. Cambridge University Press, Cambridge
Zermelo E (1913) Über eine anwendung der mengenlehre auf die theorie des schachspiels. Proc Fifth Int Congr Math 2:501–504
Funding
This research was partially supported by the São Paulo Research Foundation (FAPESP) grants 2015/11937-9, 2016/01860-1, and 2017/05223-9; and the National Council for Scientific and Technological Development (CNPq) grants 308689/2017-8, 425340/2016-3, 314366/2018-0, 425806/2018-9, 311039/2020-0 and 313146/2022-5. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.
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Silva, F.J.M.d., Miyazawa, F.K., Romero, I.V.F. et al. Tight bounds for the price of anarchy and stability in sequential transportation games. J Comb Optim 46, 10 (2023). https://doi.org/10.1007/s10878-023-01073-y
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DOI: https://doi.org/10.1007/s10878-023-01073-y