Skip to main content


Equilibria under the probabilistic serial rule


Haris Aziz, Serge Gaspers, Simon Mackenzie, Nicholas Mattei, Nina Narodytska and Toby Walsh




The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address several fundamental questions regarding equilibria under PS. Firstly, we show that Nash deviations under the PS rule can cycle. Despite the possibilities of cycles, we prove that a pure Nash equilibrium is guaranteed to exist under the PS rule. We then show that verifying whether a given profile is a pure Nash equilibrium is coNP-complete, and computing a pure Nash equilibrium is NP-hard. For two agents, we present a linear-time algorithm to compute a pure Nash equilibrium which yields the same assignment as the truthful profile. Finally, we conduct experiments to evaluate the quality of the equilibria that exist under the PS rule, finding that the vast majority of pure Nash equilibria yield social welfare that is at least that of the truthful profile.

BibTeX Entry

    author           = {Aziz, Haris and Gaspers, Serge and Mackenzie, Simon and Mattei, Nicholas and Narodytska, Nina and
                        Walsh, Toby},
    month            = jul,
    year             = {2015},
    title            = {Equilibria Under the Probabilistic Serial Rule},
    booktitle        = {Proceedings of the 24th International Joint Conference on Artificial Intelligence},
    pages            = {1105-1112},
    address          = {Buenos Aires, Argentina}


Served by Apache on Linux on seL4.