Rationalizability and Monotonocity in Games with Incomplete Information Article Swipe
This paper examines games with strategic complements or substitutes and incomplete information, where players are uncertain about the opponents' parameters. We assume that the players' beliefs about the opponent's parameters are selected from some given set of beliefs. One extreme is the case where these sets only contain a single belief, representing a scenario where the players' actual beliefs about the parameters are commonly known among the players. Another extreme is the situation where these sets contain all possible beliefs, representing a scenario where the players have no information about the opponents' beliefs about parameters. But we also allow for intermediate cases, where these sets contain some, but not all, possible beliefs about the parameters. We introduce an assumption of weakly increasing differences that takes both the choice belief and parameter belief of a player into account. Under this assumption, we demonstrate that greater choice-parameter beliefs leads to greater optimal choices. Moreover, we show that the greatest and least point rationalizable choice of a player is increasing in their parameter, and these can be determined through an iterative procedure. In each round of the iterative procedure, the lowest surviving choice is optimal for the lowest choice-parameter belief, while the greatest surviving choice is optimal for the highest choice-parameter belief.
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Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2501.15548
- https://arxiv.org/pdf/2501.15548
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4406880772
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4406880772Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2501.15548Digital Object Identifier
- Title
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Rationalizability and Monotonocity in Games with Incomplete InformationWork title
- Type
-
preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-01-26Full publication date if available
- Authors
-
Joep van SlounList of authors in order
- Landing page
-
https://arxiv.org/abs/2501.15548Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2501.15548Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2501.15548Direct OA link when available
- Concepts
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Rationalizability, Complete information, Mathematical economics, Computer science, Economics, Nash equilibriumTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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