Solutions of partition function-based TU games for cooperative communication networking
Giovanni Rossi

TL;DR
This paper introduces a novel method for distributing surpluses in cooperative network games based on partition functions, utilizing lattice solutions with M"obius inversion on atoms, leading to new sharing rules and insights into the core.
Contribution
It proposes a new lattice-based solution approach for partition function TU games, focusing on atom-level M"obius inversion and alternative edge-sharing rules.
Findings
New lattice solutions with M"obius inversion on atoms.
Two alternative edge-sharing methods derived from the solution.
Analysis of core non-emptiness beyond supermodularity.
Abstract
In networked communications nodes choose among available actions and benefit from exchanging information through edges, while continuous technological progress fosters system functionings that increasingly often rely on cooperation. Growing attention is being placed on coalition formation, where each node chooses what coalition to join, while the surplus generated by cooperation is an amount of TU (transferable utility) quantified by a real-valued function defined on partitions -or even embedded coalitions- of nodes. A TU-sharing rule is thus essential, as how players are rewarded determines their behavior. This work offers a new option for distributing partition function-based surpluses, dealing with cooperative game theory in terms of both global games and games in partition function form, namely lattice functions, while the sharing rule is a point-valued solution or value. The…
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Taxonomy
TopicsGame Theory and Voting Systems · Game Theory and Applications · Advanced Algebra and Logic
