Strategic Games and Truly Playable Effectivity Functions

Valentin Goranko, Wojtek Jamroga, Paolo Turrini

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    Abstract

    A well known (and often used) result by Marc Pauly states that for every playable effectivity function E there exists a strategic game that assigns to coalitions exactly the same power as E, and vice versa. While the latter direction of the correspondence is correct, we show that the former does not always hold in the case of infinite game models. We point out where the proof of correspondence goes wrong, and we present examples of playable effectivity functions in infinite models for which no equivalent strategic game exists. Then, we characterize the class of truly playable effectivity func- tions, that does correspond to strategic games. Moreover, we discuss a construction that transforms any playable effec- tivity function into a truly playable one while preserving the power of most (but not all) coalitions. We also show that Coalition Logic is not expressive enough to distinguish be- tween playable and truly playable effectivity functions, and we extend it to a logic that can make this distinction while enjoying finite axiomatization and finite model property.
    Original languageEnglish
    Title of host publicationProceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS-2011)
    EditorsTumer, Yolum, Sonenberg and Stone
    Publication date2011
    Publication statusPublished - 2011
    EventInternational Conference on Autonomous Agents and Multiagent Systems - Taipei, Taiwan
    Duration: 1 Jan 2011 → …
    Conference number: 10

    Conference

    ConferenceInternational Conference on Autonomous Agents and Multiagent Systems
    Number10
    CityTaipei, Taiwan
    Period01/01/2011 → …

    Keywords

    • Correspondence
    • Cooperative games
    • Strategic reasoning

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