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<p>In the realm of graph-restricted games, the underlying network structure plays a pivotal role, enforcing a key constraint: communication between agents is possible only if a valid path connecting them exists within the network. This constraint strongly shapes the dynamics and strategic considerations, particularly in value allocation settings. The Myerson value and the position value are two prominent allocation rules in such contexts. While classical axiomatic characterizations of these rules often rely on structural assumptions, such as component additivity of the value function or restrictions on the network, these assumptions limit their applicability in general, non-additive environments. We provide new axiomatic characterizations of both values that apply to arbitrary (including non-additive) value functions. Our key axiom specifies how an allocation rule should respond when a source network <i>g</i> and all its supergraphs experience a uniform perturbation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\epsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>, which may represent either an increase or a decrease in value. For the Myerson value, this perturbation is shared equally among the agents with links in <i>g</i> (EDBA). For the position value, it is shared equally among the links in <i>g</i> and then split between their endpoints (EDBL). Combined with a null-game property, each axiom uniquely identifies its respective value. This parallel axiomatization highlights the fundamental contrast between agent-oriented and link-oriented allocation and extends both values beyond previously assumed structural restrictions.</p>

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A comparison of the Myerson value and the position value

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Ayşe Mutlu Derya

摘要

In the realm of graph-restricted games, the underlying network structure plays a pivotal role, enforcing a key constraint: communication between agents is possible only if a valid path connecting them exists within the network. This constraint strongly shapes the dynamics and strategic considerations, particularly in value allocation settings. The Myerson value and the position value are two prominent allocation rules in such contexts. While classical axiomatic characterizations of these rules often rely on structural assumptions, such as component additivity of the value function or restrictions on the network, these assumptions limit their applicability in general, non-additive environments. We provide new axiomatic characterizations of both values that apply to arbitrary (including non-additive) value functions. Our key axiom specifies how an allocation rule should respond when a source network g and all its supergraphs experience a uniform perturbation \(\epsilon \) ϵ , which may represent either an increase or a decrease in value. For the Myerson value, this perturbation is shared equally among the agents with links in g (EDBA). For the position value, it is shared equally among the links in g and then split between their endpoints (EDBL). Combined with a null-game property, each axiom uniquely identifies its respective value. This parallel axiomatization highlights the fundamental contrast between agent-oriented and link-oriented allocation and extends both values beyond previously assumed structural restrictions.