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arXiv · 2610.11690

Epistemic Disturbance in the Graph Model for Conflict Resolution: State-Preserving Actions, Four-Valued Assessments, and the Distinction between Capability and Intention

Yukiko Kato
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Abstract

In the graph model for conflict resolution (GMCR), a decision maker (DM) either moves the conflict to another state or does nothing. The basic definitions leave inaction implicit, so every action that leaves the state unchanged is treated as doing nothing. Yet announcements, exercises, leaks and selective disclosures are neither moves nor inaction: they leave the state unchanged but change what other DMs believe about which moves are available and which moves others would want to make. We introduce such state-preserving actions by augmenting states with the DMs' epistemic states: a physical move changes the physical state, a state-preserving action changes only the epistemic state, and inaction is the absence of a transition. Actions generate evidence through observer-specific interpretation maps. Building on a four-valued extension of GMCR from the author's earlier work, which separates evidence for and against, we show that evidence for a move can only enable perceived moves and evidence against can only disable them, that two of the four reduction operators ignore one kind of evidence, and that contradictory assessments are absorbing under monotone accumulation. With the monotonicity of stability in move sets, this fixes the direction in which any action moves a DM's stability judgements and characterizes when actions can enable provocation or deterrence. Capability assessments affect all sanction-based stability concepts, and on the DM's own side also Nash stability, whereas intention assessments affect only sequential stability. Hedging between two candidate types weakly expands or shrinks an observer's sequentially stable set according to how it reads contradiction. In the 1995 DVD format negotiation, general metarationality cannot distinguish its phases, since the computer industry group could always sanction; sequential stability, which asks whether it would, can.

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Yukiko Kato. 2026-10-08. Epistemic Disturbance in the Graph Model for Conflict Resolution: State-Preserving Actions, Four-Valued Assessments, and the Distinction between Capability and Intention. https://arxiv.org/abs/2610.11690

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