Towards Formal Foundations for Game Theory
| Autor: | Cezary Kaliszyk, Julian Parsert |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Computer science
0102 computer and information sciences 02 engineering and technology 01 natural sciences TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES 010201 computation theory & mathematics Order (business) 0202 electrical engineering electronic engineering information engineering Independence (mathematical logic) 020201 artificial intelligence & image processing Game theory Mathematical economics Expected utility hypothesis Axiom |
| Zdroj: | Interactive Theorem Proving-9th International Conference, ITP 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 9-12, 2018, Proceedings Interactive Theorem Proving ISBN: 9783319948201 ITP Lecture Notes in Computer Science Lecture Notes in Computer Science-Interactive Theorem Proving |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-319-94821-8_29 |
| Popis: | Utility functions form an essential part of game theory and economics. In order to guarantee the existence of these utility functions sufficient properties are assumed in an axiomatic manner. In this paper we discuss these axioms and the von-Neumann-Morgenstern Utility Theorem, which names precise assumptions under which expected utility functions exist. We formalize these results in Isabelle/HOL. The formalization includes formal definitions of the underlying concepts including continuity and independence of preferences. We make the dependencies more precise and highlight some consequences for a formalization of game theory. |
| Databáze: | OpenAIRE |
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