Comparable axiomatizations of the average tree solution and the Myerson value

Özer Selçuk () and Takamasa Suzuki ()
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Özer Selçuk: University of the West of England
Takamasa Suzuki: Gifu Shotoku Gakuen University

International Journal of Game Theory, 2023, vol. 52, issue 2, No 1, 333-362

Abstract: Abstract Combination of a TU-game and an undirected graph representing cooperation restrictions among the players is called a TU-game with communication structure. For TU-games with communication structure, the average tree solution is defined as the average of the marginal contribution vectors corresponding to all spanning trees of the undirected graph. In this paper, we provide new characterizations for the average tree solution and the Myerson value on the class of TU-games with connected cycle-free communication structure. On this class of games, we show that the average tree solution is the unique solution satisfying linearity, efficiency, satellite symmetry, and satellite marginality. Together with linearity and efficiency, by using network symmetry and network marginality we also characterize the Myerson value and provide a comparison with the average tree solution.

Keywords: Transferable utility game; Communication structure; Spanning tree; Average tree solution; Myerson value; 90B18; 91A12; 91A43; C71 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00182-022-00817-0

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