Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published January 2012 | Published
Book Section - Chapter Open

Beyond myopic best response (in Cournot competition)

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.

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.

Attached Files

Published - p993-fiat.pdf

Files

p993-fiat.pdf
Files (563.0 kB)
Name Size Download all
md5:e5804e6e2f393649c427c24efc98c89a
563.0 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 17, 2023