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Author: Shereif Eid

Affiliation: Leibniz Information Center for Science and Technology (TIB), Hannover, Germany

Keyword(s): Cooperative Games, Weighted Voting, Shapley-Shubik Power Index, Infinite Games, Multi-Agent Systems.

Abstract: After we describe the waiting queue problem, we identify a partially observable 2n+1-player voting game with only one pivotal player; the player at the n-1 order. Given the simplest rule of heterogeneity presented in this paper, we show that for any infinite sequential voting game of size 2n+1, a power index of size n is a good approximation of the power index at infinity, and it is difficult to achieve. Moreover, we show that the collective utility value of a coalition for a partially observable anonymous game given an equal distribution of weights is n²+n. This formula is developed for infinite sequential anonymous games using a stochastic process that yields a utility function in terms of the probability of the sequence and voting outcome of the coalition. Evidence from Wikidata editing sequences is presented and the results are compared for 10 coalitions.

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Paper citation in several formats:
Eid, S. (2021). The Power Index at Infinity: Weighted Voting in Sequential Infinite Anonymous Games. In Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART; ISBN 978-989-758-484-8; ISSN 2184-433X, SciTePress, pages 475-482. DOI: 10.5220/0010178504750482

@conference{icaart21,
author={Shereif Eid.},
title={The Power Index at Infinity: Weighted Voting in Sequential Infinite Anonymous Games},
booktitle={Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART},
year={2021},
pages={475-482},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010178504750482},
isbn={978-989-758-484-8},
issn={2184-433X},
}

TY - CONF

JO - Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART
TI - The Power Index at Infinity: Weighted Voting in Sequential Infinite Anonymous Games
SN - 978-989-758-484-8
IS - 2184-433X
AU - Eid, S.
PY - 2021
SP - 475
EP - 482
DO - 10.5220/0010178504750482
PB - SciTePress

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