Teams in Online Scheduling Polls: Game-Theoretic Aspects

TL;DR

This paper models online scheduling polls as a game where teams strategically declare availability to maximize their relative attendance, analyzing coalition formation, algorithmic solutions, and computational complexity of equilibria.

Contribution

It introduces a game-theoretic model for scheduling polls, provides an efficient algorithm for coalition optimization, and analyzes the computational complexity of coalition and equilibrium problems.

Findings

Efficient algorithm for coalition-based availability optimization.

NP-hardness of deciding coalition existence.

Polynomial-time computation of Nash equilibria for small teams.

Abstract

Consider an important meeting to be held in a team-based organization. Taking availability constraints into account, an online scheduling poll is being used in order to decide upon the exact time of the meeting. Decisions are to be taken during the meeting, therefore each team would like to maximize its relative attendance in the meeting (i.e., the proportional number of its participating team members). We introduce a corresponding game, where each team can declare (in the scheduling poll) a lower total availability, in order to improve its relative attendance---the pay-off. We are especially interested in situations where teams can form coalitions. We provide an efficient algorithm that, given a coalition, finds an optimal way for each team in a coalition to improve its pay-off. In contrast, we show that deciding whether such a coalition exists is NP-hard. We also study the existence of Nash equilibria: Finding Nash equilibria for various small sizes of teams and coalitions can be done in polynomial time while it is coNP-hard if the coalition size is unbounded.