Years and Authors of Summarized Original Work
2006; Bilò
2008, 2011; Epstein, Kleiman
Problem Definition
In bin packing games with selfish items, n items are to be packed into (at most) n bins, where each item chooses a bin that it wishes to be packed into. The cost of an item i of size 0 < s i  ≤ 1 is defined based on its size and the contents of its bin. Nash equilibria (NE) are defined as solutions where there is no item that can change its choice unilaterally and gain from this change. Bin packing games were inspired by the well-known bin packing problem [2]. In this problem, a set of items, each of size in (0, 1], is given. The goal is to partition (or pack) the items into a minimum number of subsets that are called bins. Each bin has unit capacity, and the load of a bin is defined to be the total size of items packed into it (where the load cannot exceed 1). The problem is NP-hard in the strong sense, and thus theoretical research has focused on studying and developing...
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Recommended Reading
Bilò V (2006) On the packing of selfish items. In: Proceedings of the 20th international parallel and distributed processing symposium (IPDPS2006). IEEE, Rhodes, Greece, 9pp
Coffman E Jr, Csirik J (2007) Performance guarantees for one-dimensional bin packing. In: Gonzalez TF (ed) Handbook of approximation algorithms and metaheuristics, chap 32. Chapman & Hall/CRC, Boca Raton, pp (32–1)–(32–18)
Dósa Gy, Epstein L (2012) Generalized selfish bin packing. CoRR, abs/1202.4080
Epstein L, Kleiman E (2011) Selfish bin packing. Algorithmica 60(2):368–394
Epstein L, Kleiman E, Mestre J (2009) Parametric packing of selfish items and the subset sum algorithm. In: Proceedings of the 5th international workshop on internet and network economics (WINE2009), Rome, Italy, pp 67–78
Han X, Dósa Gy, Ting HF, Ye D, Zhang Y (2013) A note on a selfish bin packing problem. J Glob Optim 56(4):1457–1462
Johnson DS, Demers AJ, Ullman JD, Garey MR, Graham RL (1974) Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J Comput 3(4):299–325
Miyazawa FK, Vignatti AL (2009) Convergence time to Nash equilibrium in selfish bin packing. Electron Notes Discret Math 35:151–156
Yu G, Zhang G (2008) Bin packing of selfish items. In: The 4th international workshop on internet and network economics (WINE2008), Shanghai, China, pp 446–453
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Epstein, L. (2016). Selfish Bin Packing Problems. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_494
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