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Inefficiency of multiplicative approximate Nash equilibrium for scheduling games

Author

Listed:
  • Zhuyinan Wang

    (Zhejiang University)

  • Chen Zhang

    (Zhejiang University)

  • Zhiyi Tan

    (Zhejiang University)

Abstract

This paper studies the inefficiency of multiplicative approximate Nash Equilibrium for scheduling games. There is a set of machines and a set of jobs. Each job could choose one machine and be processed by the chosen one. A schedule is a $$\theta $$ θ -NE if no player has the incentive to deviate so that it decreases its cost by a factor larger than $$1+\theta $$ 1 + θ . The $$\theta $$ θ -NE is a generation of Nash Equilibrium and its inefficiency can be measured by the $$\theta $$ θ -PoA, which is also a generalization of the Price of Anarchy. For the game with the social cost of minimizing the makespan, the exact $$\theta $$ θ -PoA for any number of machines and any $$\theta \ge 0$$ θ ≥ 0 is obtained. For the game with the social cost of maximizing the minimum machine load, we present upper and lower bounds on the $$\theta $$ θ -PoA. Tight bounds are provided for cases where the number of machines is between 2 and 7 and for any $$\theta \ge 0$$ θ ≥ 0 .

Suggested Citation

  • Zhuyinan Wang & Chen Zhang & Zhiyi Tan, 2025. "Inefficiency of multiplicative approximate Nash equilibrium for scheduling games," Journal of Combinatorial Optimization, Springer, vol. 49(3), pages 1-21, April.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:3:d:10.1007_s10878-025-01274-7
    DOI: 10.1007/s10878-025-01274-7
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