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Verification with Common Knowledge of Rationality for Graph Games

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Theoretical Aspects of Computing – ICTAC 2024 (ICTAC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15373))

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Abstract

Realizability asks whether there exists a program satisfying its specification. In this problem, we assume that each agent has her own objective and behaves rationally to satisfy her objective. Traditionally, the rationality of agents is modeled by a Nash equilibrium (NE), where each agent has no incentive to change her strategy because she cannot satisfy her objective by changing her strategy alone. However, an NE is not always an appropriate notion for the rationality of agents because the condition of an NE is too strong; each agent is assumed to know strategies of the other agents completely. In this paper, we use an epistemic model to define common knowledge of rationality of all agents (CKR). We define the verification problem as a variant of the realizability problem, based on CKR, instead of NE. We then analyze the complexity of the verification problems for the class of positional strategies.

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Notes

  1. 1.

    The rationality in Definition 6 is called the strong notion of rationality [3].

  2. 2.

    For every NE \(\boldsymbol{s}\in S\), the epistemic model with a single world w where \(\boldsymbol{\sigma }(w)=\boldsymbol{s}\) satisfies \(w \in \mathop {\mathcal{C}\mathcal{K}}\nolimits RAT _{G,\boldsymbol{\alpha },M,S}\).

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Correspondence to Rindo Nakanishi .

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Nakanishi, R., Takata, Y., Seki, H. (2025). Verification with Common Knowledge of Rationality for Graph Games. In: Anutariya, C., Bonsangue, M.M. (eds) Theoretical Aspects of Computing – ICTAC 2024. ICTAC 2024. Lecture Notes in Computer Science, vol 15373. Springer, Cham. https://doi.org/10.1007/978-3-031-77019-7_14

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  • DOI: https://doi.org/10.1007/978-3-031-77019-7_14

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