Prophet Inequality with Competing Agents

Tomer Ezra*, Michal Feldman, Ron Kupfer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We introduce a model of competing agents in a prophet setting, where rewards arrive online, and decisions are made immediately and irrevocably. The rewards are unknown from the outset, but they are drawn from a known probability distribution. In the standard prophet setting, a single agent makes selection decisions in an attempt to maximize her expected reward. The novelty of our model is the introduction of a competition setting, where multiple agents compete over the arriving rewards, and make online selection decisions simultaneously, as rewards arrive. If a given reward is selected by more than a single agent, ties are broken either randomly or by a fixed ranking of the agents. The consideration of competition turns the prophet setting from an online decision making scenario to a multi-agent game. For both random and ranked tie-breaking rules, we present simple threshold strategies for the agents that give them high guarantees, independent of the strategies taken by others. In particular, for random tie-breaking, every agent can guarantee herself at least 1k+1 of the highest reward, and at least 12k of the optimal social welfare. For ranked tie-breaking, the ith ranked agent can guarantee herself at least a half of the ith highest reward. We complement these results by matching upper bounds, even with respect to equilibrium profiles. For ranked tie-breaking rule, we also show a correspondence between the equilibrium of the k-agent game and the optimal strategy of a single decision maker who can select up to k rewards.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - 14th International Symposium, SAGT 2021, Proceedings
EditorsIoannis Caragiannis, Kristoffer Arnsfelt Hansen
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030859466
StatePublished - 2021
Event14th International Symposium on Algorithmic Game Theory, SAGT 2021 - Virtual, Online
Duration: 21 Sep 202124 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12885 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Symposium on Algorithmic Game Theory, SAGT 2021
CityVirtual, Online


FundersFunder number
Horizon 2020 Framework Programme740282, 866132
European Research Council
Israel Science Foundation317/17


    • Multi-agent system
    • Prophet inequality
    • Threshold-strategy


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