Abstract
In this paper we introduce an (a, b)-generic 
valid utility system, a class of non-cooperative games with n players. The social utility of an outcome is measured by a submodular function. The private utility of a player is at most a times the change in social utility that would occur if the player declines to participate in the game. For any outcome, the total amount of the utility of all players is at most b times the social utility. We show that the price of anarchy of the system is at least \(\frac{a}{a+b}\) if there exist pure strategy Nash equilibria. For the case that there does not exist a pure strategy Nash equilibrium, we design a mechanism to output an outcome that gives a social utility within \(\frac{a}{2bn+a-b}\) times of the optimal.
This research was supported in part by the National Natural Science Foundation of China under grant number 12171444 and 11871442, and was also supported in part by the Natural Science Foundation of Shandong Province under grant number ZR2019MA052.
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Yang, Y., Nong, Q., Gong, S., Du, J., Liang, Y. (2021). The Price of Anarchy of Generic Valid Utility Systems. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_19
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