On Colorful Bin Packing Games
Vittorio Bil\`o, Francesco Cellinese, Giovanna Melideo, Gianpiero, Monaco

TL;DR
This paper studies colorful bin packing games where selfish players pack items of multiple colors into bins, analyzing the existence, computation, and efficiency of Nash equilibria under different cost sharing rules.
Contribution
It introduces algorithms for computing Nash equilibria in colorful bin packing games and characterizes their efficiency, including bounds on the price of anarchy and stability.
Findings
Nash equilibria exist despite non-convergence in general.
Polynomial-time algorithms for equilibrium computation under certain conditions.
Unbounded price of anarchy when the number of colors exceeds two.
Abstract
We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash…
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