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Beyond myopic best response (in Cournot competition)

Fiat, Amos and Koutsoupias, Elias and Ligett, Katrina and Mansour, Yishay and Olonetsky, Svetlana (2012) Beyond myopic best response (in Cournot competition). In: Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM , Philadelphia, PA, pp. 993-1005. ISBN 9781611972108. https://resolver.caltech.edu/CaltechAUTHORS:20120615-115818156

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Abstract

A Nash Equilibrium is a joint strategy profile at which each agent myopically plays a best response to the other agents' strategies, ignoring the possibility that deviating from the equilibrium could lead to an avalanche of successive changes by other agents. However, such changes could potentially be beneficial to the agent, creating incentive to act non-myopically, so as to take advantage of others' responses. To study this phenomenon, we consider a non-myopic Cournot competition, where each firm selects whether it wants to maximize profit (as in the classical Cournot competition) or to maximize revenue (by masquerading as a firm with zero production costs). The key observation is that profit may actually be higher when acting to maximize revenue, (1) which will depress market prices, (2) which will reduce the production of other firms, (3) which will gain market share for the revenue maximizing firm, (4) which will, overall, increase profits for the revenue maximizing firm. Implicit in this line of thought is that one might take other firms' responses into account when choosing a market strategy. The Nash Equilibria of the non-myopic Cournot competition capture this action/response issue appropriately, and this work is a step towards understanding the impact of such strategic manipulative play in markets. We study the properties of Nash Equilibria of non-myopic Cournot competition with linear demand functions and show existence of pure Nash Equilibria, that simple best response dynamics will produce such an equilibrium, and that for some natural dynamics this convergence is within linear time. This is in contrast to the well known fact that best response dynamics need not converge in the standard myopic Cournot competition. Furthermore, we compare the outcome of the non-myopic Cournot competition with that of the standard myopic Cournot competition. Not surprisingly, perhaps, prices in the non-myopic game are lower and the firms, in total, produce more and have a lower aggregate utility.


Item Type:Book Section
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http://dl.acm.org/citation.cfm?id=2095195PublisherArticle
http://resolver.caltech.edu/CaltechAUTHORS:20190312-141425964Related ItemJournal Article
ORCID:
AuthorORCID
Ligett, Katrina0000-0003-2780-6656
Additional Information:© 2012 SIAM. This research was supported in part by the Google Interuniversity center for Electronic Markets and Auctions and in part by a grant from the Israeli Science Foundation. Research supported in part by an NSF Mathematical Sciences Postdoctoral Fellowship. This research was supported in part by the Google Interuniversity center for Electronic Markets and Auctions, by a grant from the Israel Science Foundation, by a grant from United States-Israel Binational Science Foundation (BSF), and by a grant from the Israeli Ministry of Science (MoS). We are very grateful to Andrzej (Andy) Skrzypacz who very kindly help us overcome our ignorance and gave us critical references regarding strategic delegation.
Funders:
Funding AgencyGrant Number
Google Interuniversity center for Electronic Markets and AuctionsUNSPECIFIED
Israeli Science FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)UNSPECIFIED
Ministry of Science (Israel)UNSPECIFIED
NSF Postdoctoral FellowshipUNSPECIFIED
Record Number:CaltechAUTHORS:20120615-115818156
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120615-115818156
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31919
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:18 Jun 2012 15:46
Last Modified:03 Oct 2019 03:56

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