[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83081-en":3,"doc-seo-83081-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83081,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Does Financial Trading Smooth Non-Convex Markets","Non-convex markets may fail to admit a competitive equilibrium, creating practical difficulties in real auction settings where uniform prices must be determined. The study analyzes whether introducing convex financial trading provides a smoothing effect that mitigates equilibrium-existence problems. A two-stage non-convex electricity market model (forward followed by spot) with convex arbitrageurs predicts smaller discriminatory side payments to sustain the cleared allocation. The prediction is tested using PJM’s 2020 transaction-fee policy.","arXiv :2607 .06316v1 [math .OC] 7 Jul 2026  \nDoes Financial Trading Smooth Non-Convex Markets?  \nNicolas Stevens∗†, Peter Cramton‡ and Martial Toniotti§  \nJuly 8, 2026  \nAbstract  \nIn non-convex markets, a competitive equilibrium may fail to exist. This turns out to be an important issue in real-world non-convex auction markets, such as electricity markets, as it complicates pricing and requires the auctioneer to resort to out-of-market discriminatory side payments to sustain an equilibrium. We investigate whether the introduction of convex financial trading induces a smoothing effect, mitigating the issues arising from non-convexities. We develop a two-stage non-convex market model (a forward market followed by a spot market) in which convex financial traders participate in the forward market. Our model predicts that financial trading reduces the magnitude of side payments required to support the cleared allocation. To test the prediction of our model, we examine the introduction of a transaction fee on financial traders in 2020 by PJM, the US’s largest electricity market. We show that the substantial decline in financial trading volume caused by this policy coincided with a significant increase in side payments, in line with our theoretical predictions.  \nKeywords: Nonconvex Markets, Financial Trading, Equilibrium Existence, Electricity Auctions  \n∗ Corresponding author.  \n†Max Planck Institute for Research on Collective Goods (Bonn, Germany) & Center for Operations Research and Econometrics, UCLouvain (Louvain-la-Neuve, Belgium). Email: [stevens@coll.mpg.de](stevens@coll.mpg.de)  \n‡Max Planck Institute for Research on Collective Goods (Bonn, Germany) & University of Maryland,  \nCollege Park, USA. Email: [pcramton@gmail.com](pcramton@gmail.com)  \n§ Center for Operations Research and Econometrics, UCLouvain, Louvain-la-Neuve, Belgium. Email: [martial.toniotti@uclouvain.be](martial.toniotti@uclouvain.be)  \n1 Introduction  \nIn a non-convex market, a competitive equilibrium may fail to exist. Several classical results show that this failure might not be too severe, at least on the large scale: Starr (1969) shows that when an equilibrium does not exist, the distance to an equilibrium (as measured by total excess supply or demand) is invariant with the number of market participants, while Aumann (1964) shows that when there is a continuum of traders, an equilibrium exists in spite of the non-convexities. Yet, despite these “asymptotic” positive results, nonconvexity remains problematic in real-world auctions where the auctioneer cannot simply overlook these complexities but must determine market-clearing prices (Milgrom, 2017) . There is an extensive literature which approaches this problem by designing mechanisms that accommodate non-convexities (see, for instance, Milgrom and Watt (2025), and the literature covered hereafter) . Instead of designing new mechanisms, we investigate whether the introduction of financial traders induces a smoothing effect which helps solve the issues arising from non-convexities. Two important features of financial traders are that (i) they use convex bids and (ii) they are arbitragers, thus they are expected to bid close to the market margin. We analyze how this addition of a large volume of convex bids close to the margin smooths the non-convexities present in the market and helps the auctioneer with price formation. We study this question in the context of electricity markets, which combine non-convex auction structures with active financial trading.  \nElectricity wholesale markets are typically organized as sealed-bid uniform-price auctions (Wilson, 2002; Cramton, 2017) . Most of these auctions involve non-convexities in the bidding language that enable the market participants, in particular the electricity producers, to represent the costs and constraints of operating a power plant directly into the auction. Focusing on the United States 1 , each power plant bids separately in the market, using ","cbCaitiB37VEJLOu","https://ap.wps.com/l/cbCaitiB37VEJLOu","pdf",2040371,1,34,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"Why can competitive equilibrium fail to exist in non-convex markets?\",\"answer\":\"In non-convex settings, surplus-maximizing allocations may not be supportable by a single uniform market-clearing price, so an equilibrium may not exist.\"},{\"question\":\"What role do convex financial traders play in the proposed theory?\",\"answer\":\"Convex financial traders submit convex bids close to the market margin and act as arbitragers, which smooths non-convexities and reduces the discriminatory side payments needed to sustain the allocation.\"},{\"question\":\"How does the PJM 2020 transaction-fee policy relate to the paper’s predictions?\",\"answer\":\"The paper examines how the fee reduced financial trading volume and finds that this coincided with a significant increase in side payments, matching the model’s theoretical 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can competitive equilibrium fail to exist in non-convex markets?","Question",{"text":75,"@type":76},"In non-convex settings, surplus-maximizing allocations may not be supportable by a single uniform market-clearing price, so an equilibrium may not exist.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What role do convex financial traders play in the proposed theory?",{"text":80,"@type":76},"Convex financial traders submit convex bids close to the market margin and act as arbitragers, which smooths non-convexities and reduces the discriminatory side payments needed to sustain the allocation.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the PJM 2020 transaction-fee policy relate to the paper’s predictions?",{"text":84,"@type":76},"The paper examines how the fee reduced financial trading volume and finds that this coincided with a significant increase in side payments, matching the model’s theoretical 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