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Prices of Anarchy, Information, and Cooperation in Differential Games

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Abstract

The price of anarchy (PoA) has been widely used in static games to quantify the loss of efficiency due to noncooperation. Here, we extend this concept to a general differential games framework. In addition, we introduce the price of information (PoI) to characterize comparative game performances under different information structures, as well as the price of cooperation to capture the extent of benefit or loss a player accrues as a result of altruistic behavior. We further characterize PoA and PoI for a class of scalar linear quadratic differential games under open-loop and closed-loop feedback information structures. We also obtain some explicit bounds on these indices in a large population regime.

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Authors and Affiliations

  1. Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1308 West Main Street, Urbana, IL, 61801, USA

    Tamer Başar & Quanyan Zhu

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  1. Tamer Başar
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  2. Quanyan Zhu
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Correspondence to Tamer Başar.

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Research supported in part by grants from AFOSR and DOE.

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Başar, T., Zhu, Q. Prices of Anarchy, Information, and Cooperation in Differential Games. Dyn Games Appl 1, 50–73 (2011). https://doi.org/10.1007/s13235-010-0002-3

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  • DOI: https://doi.org/10.1007/s13235-010-0002-3

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