The role of the non-productive players in cooperative games with transferable utilities: a survey. Issue 5 (4th July 2021) - Kakoty, Niharika
Abstract : Decision support systems apply the models of cooperative games with transferable utilities (TU games) for aggregating and ranking attributes based on their interdependent features. In TU games, players work together for a common goal under binding agreements. The contributions by the players to achieve this common goal generate some worth. A solution is a distribution of the total worth generated by all the players together. The Shapley value is the most popular solution of TU games. When cooperative game theoretic models are used in decision support systems, especially in Artificial Intelligence and Machine Learning models, the Shapley value is frequently used as a suitable solution, partly because it is easy to understand and partly because of its marginalistic approach. However, alternative criteria also exist in the literature that can be of interest to the practitioners. Most of the solutions based on these criteria differ by the property of a "non-productive player" whose contribution is marginal in different contexts of the game. We study how this property is used to characterize standard solution concepts of TU games. This, we believe will motivate the decision maker to explore possible alternative solutions that would treat the non-productive players differently from the Shapley assumptions.