Implicit quantification for modal reasoning in large games.
Reasoning about equilibria in normal form games involves the study of players’ incentives to deviate unilaterally from any profile. In the case of large anonymous games, the pattern of reasoning is different. Payoffs are determined by strategy distributions rather than strategy profiles. In such a g...
| Publicado en: | Synthese Vol. 201; no. 5; pp. 1 - 35 |
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| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
May2023
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=163402161&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 163402161 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: May2023 vid: 201 iid: 5 pid: 237 pub: Springer Nature artinfo: ui: 163402161 10.1007/s11229-023-04156-9 ppf: 1 ppct: 34 formats: fmt: – @attributes: type: T – @attributes: type: P size: 422KB tig: atl: Implicit quantification for modal reasoning in large games. aug: au: Das, Ramit Padmanabha, Anantha Ramanujam, R. affil: The Institute of Mathematical Sciences and Homi Bhabha National Institute, Chennai, India DI ENS, ENS, CNRS, PSL University & Inria, Paris, France Azim Premji University University, Bengaluru, India sug: keyword: Decidability Implicit quantification Improvement dynamics Large games Modal logic Strategy distributions ab: Reasoning about equilibria in normal form games involves the study of players’ incentives to deviate unilaterally from any profile. In the case of large anonymous games, the pattern of reasoning is different. Payoffs are determined by strategy distributions rather than strategy profiles. In such a game each player would strategise based on expectations of what fraction of the population makes some choice, rather than respond to individual choices by other players. A player may not even know how many players there are in the game. Logicising such strategisation involves many challenges as the set of players is potentially unbounded. This suggests a logic of quantification over player variables and modalities for player deviation, but such a logic is easily seen to be undecidable. Instead, we propose a propositional modal logic using player types as names and implicit quantification over players. With modalities for player deviation and transitive closure, the logic can be used to specify game equilibrium and interesting patterns of reasoning in large games. We show that the logic is decidable and present a complete axiomatisation of the valid formulas. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2023. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2023 holdings: @attributes: islocal: N |
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