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Inverse game theory: learning utilities in succinct games. (English) Zbl 1404.91059
Markakis, Evangelos (ed.) et al., Web and internet economics. 11th international conference, WINE 2015, Amsterdam, The Netherlands, December 9–12, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-48994-9/pbk; 978-3-662-48995-6/ebook). Lecture Notes in Computer Science 9470, 413-427 (2015).
Summary: One of the central questions in game theory deals with predicting the behavior of an agent. Here, we study the inverse of this problem: given the agents’ equilibrium behavior, what are possible utilities that motivate this behavior? We consider this problem in arbitrary normal-form games in which the utilities can be represented by a small number of parameters, such as in graphical, congestion, and network design games. In all such settings, we show how to efficiently, i.e. in polynomial time, determine utilities consistent with a given correlated equilibrium. However, inferring both utilities and structural elements (e.g., the graph within a graphical game) is in general NP-hard. From a theoretical perspective our results show that rationalizing an equilibrium is computationally easier than computing it; from a practical perspective a practitioner can use our algorithms to validate behavioral models.
For the entire collection see [Zbl 1326.68026].

MSC:
91A43 Games involving graphs
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