We investigate the application of Shapley value to quantifying contribution a tuple query answer. The is widely known numerical measure in cooperative game theory and many applications for assessing player coalition game. It has been established already 1950s, theoretically justified by being very single wealth-distribution that satisfies some natural axioms. While this investigated several are...

We consider a dynamic multiagent system in which several states succeed each other, following a Markov chain process. In each state, a different single stage game among the agents, or players, is played, and cooperation among subsets of players can arise in order to achieve a common goal. We assume that each coalition can ensure a certain value for itself. The Shapley value is a well known meth...

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists,...

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and ...

The Aumann–Shapley [Values of Non-atomic Games, Princeton University Press, Princeton] value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault [Coherent allocation of risk capital, J. Risk 4 (1) (2001) 1]. We obtain an explicit formula for the Aumann–Shapley value, when the risk measure is given by a d...

Ginsburgh and Zang [1] consider a revenue sharing problem for the museum pass program, in which several museums jointly offer museum passes that allow visitors an unlimited access to participating museums in a certain period of time. We consider a cost sharing problem that can be regarded as the dual problem of the above revenue sharing problem. We assume that all museums are public goods and h...

Three values for non-transferable utility games – the Harsanyi NTU-value, the Shapley NTU-value, and the Maschler–Owen consistent NTU-value – are compared in a simple example.

In this paper cost sharing problems are considered. We focus on problems on a rooted tree, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, we call these games irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games (Littlechil...

This paper presents a collection of four different classes of weighted Shapley levels values. All classes contain generalisations of the weighted Shapley values to cooperative games with a level structure. The first class is an upgrade of the weighted Shapley levels value in Gómez-Rúa and Vidal-Puga (2011), who use the size of components as weights. The following classes contain payoff vectors ...