Simultaneous Penalization and Subsidization for Stabilizing Grand Cooperation
Lindong Liu, Xiangtong Qi, Zhou Xu
Operations Research · 2018 · Volume 66 · Issue 5
Abstract
In this paper we propose a new instrument, a simultaneous penalization and subsidization, for stabilizing the grand coalition and enabling cooperation among all players of an unbalanced cooperative game. The basic idea is to charge a penalty z from players who leave the grand coalition, and at the same time provide a subsidy ω to players who stay in the grand coalition. To formalize this idea, we establish a penalty-subsidy function ω ( z ) based on a linear programming model, which allows a decision maker to quantify the trade-off between the levels of penalty and subsidy. By studying function ω ( z ), we identify certain properties of the trade-off. To implement the new instrument, we design two algorithms to construct function ω ( z ) and its approximation. Both algorithms rely on solving the value of ω ( z ) for any given z , for which we propose two effective solution approaches. We apply the new instrument to a class of machine scheduling games, showing its wide applicability. The e-companion is available at https://doi.org/10.1287/opre.2018.1723 .
Keywords
cooperative game, grand coalition stability, simultaneous penalization and subsidization, parallel machine scheduling game
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