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Pareto optimal equilibria for selfish bin packing with uniform cost sharing

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Abstract

Bin packing problems deal with packing a set of items with sizes in (0, 1] into a minimum number of subsets, called bins, whose total sizes are no larger than 1. We study a class of bin packing games where the cost of an item packed into a bin with k items is \(\frac{1}{k}\), that is, the cost sharing of each bin is uniform. We study the quality of strictly Pareto optimal equilibria and weakly Pareto optimal equilibria for these games.

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References

  • Andelman N, Feldman M, Mansour Y (2009) Strong price of anarchy. Games Econ Behav 65(2):289–317

    Article  MathSciNet  MATH  Google Scholar 

  • Anshelevich E, Dasgupta A, Kleinberg JM, Tardos É, Wexler T, Roughgarden T (2008) The price of stability for network design with fair cost allocation. SIAM J Comput 38(4):1602–1623

    Article  MathSciNet  MATH  Google Scholar 

  • Aumann RJ (1959) Acceptable points in general cooperative n-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV. Annals of mathematics study 40. Princeton University Press, Princeton, pp 287–324

    Google Scholar 

  • Aumann Y, Dombb Y (2010) Pareto efficiency and approximate Pareto efficiency in routing and load balancing games. In: Proceedings of the 3rd international symposium on algorithmic game theory (SAGT’10), pp 66–77

  • Bilò V (2006) On the packing of selfish items. In: Proceedings of the 20th international parallel and distributed processing symposium (IPDPS’06). IEEE

  • Chien S, Sinclair A (2009) Strong and pareto price of anarchy in congestion games. In: Proceedings of the 36th international colloquium on automata, languages and programming (ICALP’09), pp 279–291

  • Coffman E Jr, Csirik J (2007) Chapter 32: Performance guarantees for one-dimensional bin packing. In: Gonzalez TE (ed) Handbook of approximation algorithms and metaheuristics. Chapman & Hall, Boca Raton, pp (32-1)–(32-18)

    Google Scholar 

  • Dósa Gy, Epstein L (2012) Generalized selfish bin packing. CoRR, arXiv:1202.4080

  • Dósa G, Epstein L (2016a) Quality of strong equilibria for selfish bin packing with uniform cost sharing. (Manuscript)

  • Dósa G, Epstein L (2016b) Selfish bin packing with general weights. (Manuscript)

  • Dósa G, Epstein L (2016c) The price of anarchy for selfish bin packing with uniform cost sharing. (Manuscript)

  • Dubey P (1986) Inefficiency of Nash equilibria. Math Oper Res 11(1):1–8

    Article  MathSciNet  MATH  Google Scholar 

  • Epstein L, Kleiman E (2011a) Selfish bin packing. Algorithmica 60(2):368–394

    Article  MathSciNet  MATH  Google Scholar 

  • Epstein L, Kleiman E (2011b) On the quality and complexity of pareto equilibria in the job scheduling game. In: Proceedings of the 10th international conference on autonomous agents and multiagent systems (AAMAS’11), pp 525–532

  • Epstein A, Feldman M, Mansour Y (2009) Strong equilibrium in cost sharing connection games. Games Econ Behav 67(1):51–68

    Article  MathSciNet  MATH  Google Scholar 

  • Epstein L, Kleiman E, Mestre J (2016) Parametric packing of selfish items and the subset sum algorithm. Algorithmica 74(1):177–207

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandes CG, Ferreira CE, Miyazawa FK, Wakabayashi Y (2011) Selfish square packing. Electron Notes Discrete Math 37:369–374

    Article  MathSciNet  MATH  Google Scholar 

  • Fiat A, Kaplan H, Levy M, Olonetsky S (2007) Strong price of anarchy for machine load balancing. In: Proceedings of the 34th international colloquium on automata, languages and programming (ICALP’07), pp 583–594

  • Galambos G (1988) Notes on Lee’s harmonic fit algorithm. Ann Univ Sci Bp Sect Comput 9:121–126

    MathSciNet  MATH  Google Scholar 

  • Holzman R, Law-Yone N (1997) Strong equilibrium in congestion games. Games Econ Behav 21(1–2):85–101

    Article  MathSciNet  MATH  Google Scholar 

  • Ieong S, McGrew B, Nudelman E, Shoham Y, Sun Q (2005) Fast and compact: a simple class of congestion games. In: Proceedings of the 20th national conference on artificial intelligence, pp 489–494

  • Johnson DS, Demers A, Ullman JD, Garey MR, Graham RL (1974) Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J Comput 3:256–278

    Article  MathSciNet  MATH  Google Scholar 

  • Koutsoupias E, Papadimitriou CH (1999) Worst-case equilibria. In: Proceedings of the 16th annual symposium on theoretical aspects of computer science (STACS’99), pp 404–413

  • Lee CC, Lee DT (1985) A simple online bin packing algorithm. J ACM 32(3):562–572

    Article  MATH  Google Scholar 

  • Luc DT (2008) Pareto optimality. In: Chinchuluun A, Pardalos PM, Migdalas A, Pitsoulis L (eds) Pareto optimality, game theory and equilibria. Springer, Berlin, pp 481–515

    Chapter  Google Scholar 

  • Ma R, Dósa Gy, Han X, Ting H-F, Ye D (2013) A note on a selfish bin packing problem. J Glob Optim 56(4):1457–1462

    Article  MathSciNet  MATH  Google Scholar 

  • Nash J (1951) Non-cooperative games. Ann Math 54(2):286–295

    Article  MathSciNet  MATH  Google Scholar 

  • Yu G, Zhang G (2008) Bin packing of selfish items. In: The 4th international workshop on internet and network economics (WINE’08), pp 446–453

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Authors and Affiliations

  1. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    György Dósa

  2. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

Authors
  1. György Dósa
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  2. Leah Epstein
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Correspondence to Leah Epstein.

Additional information

G. Dósa: Supported by VKSZ_12-1-2013-0088 “Development of cloud based smart IT solutions by IBM Hungary in cooperation with the University of Pannonia” and by National Research, Development and Innovation Office—NKFIH under the Grant SNN 116095.

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Dósa, G., Epstein, L. Pareto optimal equilibria for selfish bin packing with uniform cost sharing. J Comb Optim 37, 827–847 (2019). https://doi.org/10.1007/s10878-018-0323-5

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  • DOI: https://doi.org/10.1007/s10878-018-0323-5

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