The k-Egalitarian Myerson Values: Characterizations and Implementation

Network games under cooperative setups have gained significant attention due to their potential applications in various fields, involving humans, computers, and society. Players in such games generate values by forming networks under binding agreements. The challenge lies in identifying an appropriate allocation rule that can effectively distribute the generated value. Allocation rules are either player-based or link-based. The Equal Division rule and the Myerson value are two widely used player-based allocation rules, rooted in egalitarian and marginalistic principles, respectively. Egalitarianism emphasizes equality and fairness among individuals, while marginalism focuses on individuals’ additional involvement in a particular work and their inequalities. However, in many real situations, both these mechanisms are inadequate to deal with societal issues as egalitarianism attempts to establish equality, while marginalism highlights existing inequalities. Therefore, a trade-off between these two mechanisms has gained ample interest in recent years. In this paper, we propose two player-based allocation rules for network games that consolidate the Equal Division rule and the Myerson value. The first rule, the k-EM value allocates an equal share to each player in a component with a size not surpassing a specified number k, and assigns her marginal contributions in components with a size exceeding k. On the other hand, the k-DEM value, the dual of k-EM value, assigns marginal contributions in components up to size k and equal shares in larger ones. Further, we provide axiomatic characterizations and a bidding mechanism that implements the two allocation rules.