플레이어 중요도 비교 및 순위 결정 게임
이 논문은 각 coalition의 절대적 가치 대신 coalition 간의 상대적 강도 정보만 주어지는 coalitional settings에서 player의 중요도를 평가하는 문제를 다룹니다. 모든 coalitional pseudo-games를 표현할 수 있는 유연한 framework를 도입하였으며, coalitional networks를 통해 제한적이거나 이질적인 비교 시나리오를 자연스럽게 수용합니다. 또한, Banzhaf value와 Shapley value 같은 semivalues를 특정 coalition comparison 차이의 가중합으로 계산할 수 있는 방법을 제시합니다.
arXiv:2606.31955v1 Announce Type: new Abstract: This work addresses the problem of assessing player importance in coalitional settings where the available information concerns the relative strength between pairs of coalitions, rather than the absolute worth of each coalition. We introduce a novel framework that is flexible enough to represent all coalitional pseudo-games and, through the use of coalitional networks, naturally accommodates scenarios with limited or heterogeneous coalition comparisons. Importantly, this framework still enables the computation of semivalues of pseudo-games, such as the Banzhaf and Shapley values, that can be expressed as weighted sums of differences in specific coalition comparisons, thus offering interpretations beyond traditional approaches. Furthermore, for ranking players rather than computing exact numerical attributions, we introduce the concept of a player's score, which simplifies the process of determining rankings based on semivalues, and shifts the perspective from average marginal contribution to average coalitional worth. This turns out to be particularly enlightening for the Banzhaf value.