Boolean Observation Games Article Swipe
Hans van Ditmarsch
,
Sunil Simon
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1613/jair.1.15248
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1613/jair.1.15248
We introduce Boolean Observation Games, a subclass of multi-player finite strategic games with incomplete information and qualitative objectives. In Boolean observation games, each player is associated with a finite set of propositional variables of which only it can observe the value, and it controls whether and to whom it can reveal that value. It does not control the given, fixed, value of variables. Boolean observation games are a generalization of Boolean games, a well-studied subclass of strategic games but with complete information, and wherein each player controls the value of its variables. In Boolean observation games, player goals describe multi-agent knowledge of variables. As in classical strategic games, players choose their strategies simultaneously and therefore observation games capture aspects of both imperfect and incomplete information. They require reasoning about sets of outcomes given sets of indistinguishable valuations of variables. An outcome relation between such sets determines what the Nash equilibria are. We present various outcome relations, including a qualitative variant of ex-post equilibrium. We identify conditions under which, given an outcome relation, Nash equilibria are guaranteed to exist. We also study the complexity of checking for the existence of Nash equilibria and of verifying if a strategy profile is a Nash equilibrium. We further study the subclass of Boolean observation games with ‘knowing whether’ goal formulas, for which the satisfaction does not depend on the value of variables. We show that each such Boolean observation game corresponds to a Boolean game and vice versa, by a different correspondence, and that both correspondences are precise in terms of existence of Nash equilibria.
Related Topics
Concepts
Generalization
Best response
Outcome (game theory)
Nash equilibrium
Mathematics
Boolean data type
Perfect information
Complete information
Mathematical economics
Value (mathematics)
Computer science
Discrete mathematics
Boolean function
Set (abstract data type)
Theoretical computer science
Statistics
Mathematical analysis
Programming language
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1613/jair.1.15248
- https://jair.org/index.php/jair/article/download/15248/27005
- OA Status
- diamond
- Cited By
- 1
- References
- 60
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4391399691
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4391399691Canonical identifier for this work in OpenAlex
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https://doi.org/10.1613/jair.1.15248Digital Object Identifier
- Title
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Boolean Observation GamesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-01-29Full publication date if available
- Authors
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Hans van Ditmarsch, Sunil SimonList of authors in order
- Landing page
-
https://doi.org/10.1613/jair.1.15248Publisher landing page
- PDF URL
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https://jair.org/index.php/jair/article/download/15248/27005Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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diamondOpen access status per OpenAlex
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https://jair.org/index.php/jair/article/download/15248/27005Direct OA link when available
- Concepts
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Generalization, Best response, Outcome (game theory), Nash equilibrium, Mathematics, Boolean data type, Perfect information, Complete information, Mathematical economics, Value (mathematics), Computer science, Discrete mathematics, Boolean function, Set (abstract data type), Theoretical computer science, Statistics, Mathematical analysis, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
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2024: 1Per-year citation counts (last 5 years)
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60Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| publication_date | 2024-01-29 |
| publication_year | 2024 |
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