 Potentials in quadratic Cournot cross-holding gamesZhigang Cao, Guopeng Li, Sixian Shen and Feng Zhu Journal of Mathematical Economics, 2025, vol. 119, issue C Abstract: Do firms in an oligopoly market behave “as if” they were maximizing a common fictitious objective function, as in perfect competition and monopoly? The answer is yes under certain mild technical conditions (Slade, 1994). That is, in terms of Monderer and Shapley (1996), the Cournot competition is a potential game. In this paper, we ask the same question for Cournot competition with quadratic payoff functions and cross-holdings, an important variant of the oligopoly market. We find that, for various potential functions, the question can be more easily understood from the structure of the influence network, which is constructed from the cross-holding network. Roughly, we find that the Cournot competition with cross-holdings is a potential game if and only if the influence network is symmetric in certain generalized sense. Extending the model to Cournot competition with both overlapping ownership and product differentiation, we find that the previous results still hold. We also provide two applications of our results. Keywords: Potential game; Cross-holding; Quadratic Cournot competition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:119:y:2025:i:c:s0304406825000527 DOI: 10.1016/j.jmateco.2025.103135 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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