Fair Incentives for Early Arrival in 0-1 Cooperative Games
Yaoxin Ge, Yao Zhang, Dengji Zhao
TL;DR
This paper addresses fairness for early arrival in online cooperative games, where a single realized arrival order should yield allocations close to the Shapley value. It introduces the Shapley distance as a per-order fairness metric and proposes the Weighted Value-Sharing Mechanism (WVS), with Egalitarian Value-Sharing (EVS) as a constant-weight instantiation, to minimize distance while preserving SF, OIR, I4EA, and MOS in $0$-$1$ monotone games. The authors prove that EVS maximizes egalitarian welfare among contributing players and minimizes the expected SD across random orders, offering a mechanism that improves per-order fairness without sacrificing the core fairness guarantees. The work provides formal mechanisms and proofs, enabling fairer incentive design for early participation in online cooperative settings with practical relevance to startup formation and dynamic coalitions. Overall, EVS offers a principled approach to balancing early-arrival incentives with per-order fairness in online cooperative games.
Abstract
Incentives for early arrival (I4EA) was recently proposed for studying online cooperative games. In an online cooperative game, players arrive in an unknown order, and the value increase after each player arrived should be distributed immediately among all the arrived players. Although there is only one arriving order in the game, we also hope that the value distribution is equal to their Shapley value in expectation. To achieve these goals, the early solutions ignored the fairness in each single arriving order. More specifically, an important player may receive nothing in a game, which seems unfair in reality. To combat this, we propose refined fairness in this paper and design new solutions in 0-1 value games. Specifically, we compute the distance of the distribution in each order to the Shapley value and aim to minimize it. We propose a new mechanism called Egalitarian Value-Sharing (EVS) to do so. We also show that the mechanism can maximize the egalitarian welfare among all the players who made contributions.