DOI: https://doi.org/10.24963/ijcai.2021/25Aug 11, 2021Proceedings Paper

On a Competitive Secretary Problem with Deferred Selections

Tomer EzraMichal Feldman

Abstract

We study the secretary problem in multi-agent environments. In the standard secretary problem, a sequence of arbitrary awards arrive online, in a random order, and a single decision maker makes an immediate and irrevocable decision whether to accept each award upon its arrival. The requirement to make immediate decisions arises in many cases due to an implicit assumption regarding competition. Namely, if the decision maker does not take the offered award immediately, it will be taken by someone else. We introduce a novel multi-agent secretary model, in which the competition is explicit. In our model, multiple agents compete over the arriving awards, but the decisions need not be immediate; instead, agents may select previous awards as long as they are available (i.e., not taken by another agent). If an award is selected by multiple agents, ties are broken either randomly or according to a global ranking. This induces a multi-agent game in which the time of selection is not enforced by the rules of the games, rather it is an important component of the agent's strategy. We study the structure and performance of equilibria in this game. For random tie breaking, we characterize the equilibria of the game, and show that the expected...Continue Reading

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