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Author
Date
2021-04-08Type
- Master Thesis
ETH Bibliography
yes
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Abstract
A main concern of game theory involves predicting the behaviour of players from their underlying utilities. While the utilities of the players are often unknown, their behaviour is generally observable. This motivates the formulation of the static inverse problem which aims to infer the underlying utilities from an observed Nash equilibrium. By means of inverse optimization we recast the static inference problem as an optimization problem, which we solve via linear programming under mild assumptions on the utility function. We extend the static inference problem to address dynamic games by leveraging the concept of a better-response dynamics. The dynamical inference problem aims to identify the underlying utilities from an observed sequence of actions between players that follow a better-response dynamics. Under mild assumptions on the utility function it can be solved efficiently via linear programming. The solution to the static inference problem respective to the dynamical inference problem is a polyhedron which contains all utility function parameters that best rationalize the observed behaviour. We introduce two measures based on the Löwner-John ellipsoid and the maximum volume inscribed ellipsoid to capture the coarseness of the solution set in relation to the parameter space. To illustrate our approach we cast the classic example of demand estimation under Bertrand- Nash competition as a static inference problem and a dynamical inference problem, where the observed prices constitute a Nash equilibrium and a better-response dynamics, respectively. In numerical simulations we show that if the observed prices are an exact Nash equilibrium the static inference method recovers the true underlying parameters of the demand function and observing only a few price pairs are sufficient to achieve a very refined solution set. Furthermore, our results are consistent with other papers on demand estimation. Equivalent results are obtained by the dynamical inference method if the observed prices follow an exact better-response dynamics. We further validate the dynamic inference method by estimating the demand of Coke and Pepsi from their observed prices from 1968-1986. A distinguishing feature of our dynamic inference method is that it applies to dynamic games, which have not yet necessarily converged to an equilibrium but it is merely based on the assumption that players aim to improve their utilities with respect to previous actions. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000485983Publication status
publishedContributors
Examiner: Pagan, Nicolo
Examiner: Belgioioso, Giuseppe
Examiner: Balabdaoui, Fadoua
Examiner: Dörfler, Florian
Publisher
ETH ZurichOrganisational unit
09478 - Dörfler, Florian / Dörfler, Florian
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ETH Bibliography
yes
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