We train two neural networks adversarially to play normal-form games. At each iteration, a row and column network take a new randomly generated game and output individual mixed strategies. The parameters of each network are independently updated via stochastic gradient descent to minimize expected regret given the opponent's strategy. Our simulations demonstrate that the joint behavior of the networks converges to strategies close to Nash equilibria in almost all games. For all 2×2 and in 80% of 3×3 games with multiple equilibria, the networks select the risk-dominant equilibrium. Our results show how Nash equilibrium emerges from learning across heterogeneous games.

@techreport{condorellifurlan2024, address = {}, author = {Condorelli, Daniele and Furlan, Massimiliano}, institution = {}, series = {}, type = {Working Paper}, number = {}, title = {Deep Learning to Play Games}, year = {2024}, }

We simulate behavior of independent reinforcement learning algorithms playing the Crawford and Sobel (1982) game of strategic information transmission. We show that a sender and a receiver training together converge to strategies close to the ex-ante optimal equilibrium of the game. Hence, communication takes place to the largest extent predicted by Nash equilibrium. The conclusion is robust to alternative specifications of the learning hyperparameters and of the game. We discuss implications for theories of equilibrium selection in information transmission games, for work on emerging communication among algorithms in computer science and for the economics of collusions in markets populated by artificially intelligent agents.

@techreport{condorellifurlan2023, address = {}, author = {Condorelli, Daniele and Furlan, Massimiliano}, institution = {}, series = {}, type = {Working Paper}, number = {}, title = {Cheap Talking Algorithms}, year = {2023}, }

In bidding markets, suppliers with uncertain costs compete to sell to a single buyer. Let supplier surplus be the total rent obtained by suppliers. If procurement is efficient, a single seller maximizes supplier surplus, although a trade-off exists between cost efficiency and less competition. Instead, multiple suppliers maximize supplier surplus if the buyer runs an optimal auction (i.e., has buyer power) and a condition on the cost distribution holds. We use this result to study entry. When an upstream firm licenses suppliers, incentives to exclude following a merger between one supplier and the upstream firm are smaller with buyer power.

@techreport{condorellipadilla2022Bidding, address = {}, author = {Condorelli, Daniele and Padilla, Jorge}, institution = {}, series = {}, type = {Working Paper}, number = {}, title = {Buyer Power and Entry in Bidding Markets}, year = {2022}, }

A platform matches a unit-mass of sellers, each owning a single product of heterogeneous quality, to a unit-mass of buyers with differing valuations for unit-quality. After matching, sellers make take-it-or-leave-it price-offers to buyers. Initially, valuations of buyers are only known to them and the platform, but sellers make inferences from the matching algorithm. The efficient matching is positive-assortative, but buyer-optimal matchings are, often, stochastically negative-assortative (i.e., compared to lower-quality sellers, high-quality ones are matched to buyers with lower expected valuation). Albeit everyone trades, generating rents for the side lacking bargaining power results in inefficient matching.

@techreport{condorelliszentes2023, address = {}, author = {Condorelli, Daniele and Szentes, Balazs}, institution = {}, series = {}, type = {Working Paper}, number = {}, title = {Buyer-Optimal Platform Design}, year = {2023}, }

Many goods are allocated via resale networks, reaching their final buyer through a sequence of exchanges. We study a model where a single good is traded by a potentially infinite number of traders who have private valuations for the good and are connected in a random network that determines resale possibilities. Whoever holds the good has bargaining power. We show that large resale networks allocate efficiently in the no-discounting limit, even if resale opportunities are locally-limited. When the network is a stationary random tree, the limiting equilibrium is inefficient if and only if the network is a chain of monopolists.

@techreport{condorelligaleottirenou2022, address = {}, author = {Condorelli, Daniele and Galeotti, Andrea and Renou, Ludovic}, institution = {}, series = {}, type = {Working Paper}, number = {}, title = {On the Efficiency of Large Resale Networks}, year = {2022}, }

An ecosystem comprises all downstream products that employ a certain upstream input. In many cases, final consumers make irreversible investments to join an ecosystem before downstream prices are set. By committing to buy products that use the specific ecosystem input, they are at risk of being held-up. Unable to observe future prices, consumers base their decisions on what they observe about the market structure within each ecosystem, including vertical contracts signed by the upstream firms. By entering into vertical agreements with multiple competing downstream firms, thus creating a credible expectation of lower prices, an upstream firm is able to mitigate consumers' hold-up problem and, as a result, increase ecosystem demand. Our main observation is that, in contrast to conventional wisdom, an upstream monopolist merging with one of its downstream affiliates will find it profitable to continue to serve downstream competitors, even when products sold downstream are homogeneous.

@article{https://doi.org/10.1111/joie.12377, author = {Condorelli, Daniele and Padilla, Jorge and Sohn, Youngji}, title = {Vertical Mergers in Ecosystems with Consumer Hold-Up*}, journal = {The Journal of Industrial Economics}, volume = {n/a}, number = {n/a}, pages = {}, doi = {https://doi.org/10.1111/joie.12377}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/joie.12377}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/joie.12377}, }

We present a theory of monopoly protection by means of entry in adjacent markets that have a common customer base (i.e., envelopment). A firm dominant in its market enters a datarich secondary market and engages in predatory pricing and privacy-policy tying. We define the latter as conditioning service provision to the subscription of a privacy-policy that allows bundling of user data across all sources. Acquiring data from the secondary market confers an advantage in the data-intensive primary market that shields the dominant firm from entry, thus harming consumers. We discuss potential remedies, including data unbundling and portability.

@article{10.1093/ej/uead090, author = {Condorelli, Daniele and Padilla, Jorge}, title = "{Data-Driven Envelopment with Privacy-Policy Tying}", journal = {The Economic Journal}, volume = {134}, number = {658}, pages = {515-537}, year = {2023}, month = {10}, issn = {0013-0133}, doi = {10.1093/ej/uead090}, url = {https://doi.org/10.1093/ej/uead090}, eprint = {https://academic.oup.com/ej/article-pdf/134/658/515/56444291/uead090.pdf},}

If demand is log-concave, a monopolist obtains at least 1/e of the area under the demand.

@article{CONDORELLI2022110178, author = {Daniele Condorelli}, title = {A lower-bound on monopoly profit for log-concave demand}, journal = {Economics Letters}, volume = {210}, pages = {110-178}, year = {2022}, issn = {0165-1765}, doi = {https://doi.org/10.1016/j.econlet.2021.110178}, }

We characterize equilibria of oligopolistic markets where identical firms with constant marginal cost compete a' la Cournot. For given maximal willingness to pay and maximal total demand, we first identify all combinations of equilibrium consumer and producer surplus that can arise from arbitrary demand functions. Then, as a further restriction, we fix the average willingness to pay above marginal cost (i.e., first best surplus) and identify all possible triples of consumer surplus, producer surplus and deadweight loss.

@article{https://doi.org/10.3982/TE3849, author = {Condorelli, Daniele and Szentes, Balazs}, title = {Surplus Bounds in Cournot Competition}, journal = {Theoretical Economics}, volume = {17}, number = {3}, pages = {0-0}, year = {2022} }

We analyze a bilateral trade model where the buyer can choose the probability distribution of her valuation for the good. The seller, after observing the buyer's choice of the distribution but not the realized valuation, makes a take-it-or-leave-it offer. If the buyer's choice of the distribution is costless, the price and the payoffs of both the buyer and the seller are shown to be 1/e in the unique equilibrium outcome. The equilibrium distribution of the buyer's valuation generates a unit-elastic demand and trade is ex-post efficient. These two properties are shown to be preserved even when different distributions are differentially costly as long as the cost is monotone in the dispersion of the distribution.

@article{doi:10.1086/704574, author = {Condorelli, Daniele and Szentes, Balazs}, title = {Information Design in the Holdup Problem}, journal = {Journal of Political Economy}, volume = {128}, number = {2}, pages = {681-709}, year = {2020}, doi = {10.1086/704574}, }

We study private value auctions in which bidders may collude without using side-payments. In our model, bidders coordinate their actions to achieve an outcome that interim-Pareto dominates the noncooperative outcome. We characterize auctions that are collusion-proof in the sense that no such coordination opportunities exist, and show that the efficient and revenue maximizing auctions are not collusion-proof unless all bidders exhibit a concave distribution of valuations. We then solve for revenue maximizing collusion-proof auctions. If distributions of valuations are symmetric and single-peaked, the optimal selling mechanism is a standard auction with a minimum bid, followed by sequential negotiation in case no bidder bids above the minimum bid.

@article{CHE2018398, author = {Yeon-Koo Che and Daniele Condorelli and Jinwoo Kim}, title = {Weak cartels and collusion-proof auctions}, journal = {Journal of Economic Theory}, volume = {178}, pages = {398-435}, year = {2018}, issn = {0022-0531}, doi = {https://doi.org/10.1016/j.jet.2018.09.005}, }

We endogenize intermediaries' choice to operate as agents or merchants in a market where there are frictions due to asymmetric information about consumption values. A seller has an object for sale and can reach buyers only through intermediaries. Intermediaries can either mediate the transaction by buying and reselling-the merchant mode-or refer buyers to the seller for a fee-the referral mode. When the seller has a strong bargaining position and can condition the asking price to the intermediaries' business model choice, all intermediaries specialize in agency. The seller's and intermediaries' joint profits equal the seller's profits when he has access to all buyers. When the seller does not have such bargaining power, the level of the referral fee and the degree of competition among intermediaries determine the business mode adoption. A hybrid agency-merchant mode may be adopted in equilibrium. Banning the referral mode can decrease welfare because the merchant mode is associated with additional allocative distortions due to asymmetric information.

@article{https://doi.org/10.1111/jems.12251, author = {Condorelli, Daniele and Galeotti, Andrea and Skreta, Vasiliki}, title = {Selling through referrals}, journal = {Journal of Economics \& Management Strategy}, volume = {27}, number = {4}, pages = {669-685}, year = {2018} doi = {https://doi.org/10.1111/jems.12251}, }

In many markets, goods flow from initial producers to final customers travelling through many layers of intermediaries and information is asymmetric. We study a dynamic model of bargaining in networks that captures these features. We show that the equilibrium price demanded over time is non-monotonic, but the sequence of transaction prices declines over time, with the possible exception of the last period. The price dynamic is, therefore, reminiscent of fire-sales and hot-potato trading. Traders who intermediate the object arise endogenously and make a positive profit. The profit-earning intermediaries are not necessarily traders with many connections; for the case of multilayer networks, they belong to the path that reaches the maximum number of potential buyers using the minimal number of intermediaries. This is not necessarily the path of the network that maximizes the probability of consumption by traders who value the most the object (i.e. welfare).

@article{10.1093/restud/rdw034, author = {Condorelli, Daniele and Galeotti, Andrea and Renou, Ludovic}, title = "{Bilateral Trading in Networks}", journal = {The Review of Economic Studies}, volume = {84}, number = {1}, pages = {82-105}, year = {2016}, month = {07}, issn = {0034-6527}, doi = {10.1093/restud/rdw034}, }

A number of identical objects is allocated to a set of privately informed agents. Agents have linear utility in money. The designer wants to assign objects to agents that possess specific traits, but the allocation can only be conditioned on the willingness to pay and on observable characteristics. I solve for the optimal mechanism. The choice between market or non-market mechanisms depends on the statistical linkage between characteristics valued by the designer and willingness to pay.

@article{CONDORELLI2013582, author = {Daniele Condorelli}, title = {Market and non-market mechanisms for the optimal allocation of scarce resources}, journal = {Games and Economic Behavior}, volume = {82}, pages = {582-591}, year = {2013}, issn = {0899-8256}, doi = {https://doi.org/10.1016/j.geb.2013.08.008}, }

I study the ex-ante efficient allocation of a set of quality-heterogeneous objects to a number of heterogeneous risk-neutral agents. Agents have independent private values, which represent the maximum cost they are willing to sustain to obtain an object of unitary quality. The designer faces a trade-off between allocative efficiency and cost of screening, because the cost sustained is wasted. The optimal mechanism ranks agents based on their marginal contribution to social surplus and distributes objects to higherranked agents. The ranking is independent of the scarcity of objects or the extent of their heterogeneity. If the hazard rates of the distributions of values are increasing, agents are ranked according to their expected values. If hazard rates are decreasing and agents are symmetric, the objects are allocated to the agents that sustain the highest costs. In general, optimal mechanisms combine both pooling and screening of values.

@article{CONDORELLI2012613, author = {Daniele Condorelli}, title = {What money can't buy: Efficient mechanism design with costly signals}, journal = {Games and Economic Behavior}, volume = {75}, number = {2}, pages = {613-624}, year = {2012}, issn = {0899-8256}, doi = {https://doi.org/10.1016/j.geb.2012.02.018}, }

We revisit the economics of "platform envelopment strategies," whereby a dominant platform (the enveloper) operating in a multi-sided market (the origin market) enters a second multi-sided market (the target market) by leveraging the data obtained from its shared user relationships. In particular, we analyze the logic and effects of "privacy policy tying," a strategy whereby the enveloper requests consumers to grant their consent to combining their data in both origin and target markets. This may allow the enveloper to fund the services offered to all sides of the target market by monetizing data in the origin market, monopolize the target market, and entrench its dominant position in the origin market. We conclude by considering a range of possible policy interventions that may serve to limit such potential anticompetitive effects, while preserving the efficiencies generated by conglomerate platforms.

@article{10.1093/joclec/nhaa006, author = {Condorelli, Daniele and Padilla, Jorge}, title = "{Harnessing Platform Envelopment in the Digital World}", journal = {Journal of Competition Law & Economics}, volume = {16}, number = {2}, pages = {143-187}, year = {2020}, month = {04}, issn = {1744-6414}, doi = {10.1093/joclec/nhaa006}, }

This chapter surveys a set of papers that analyze strategic intermediation in networks. In all these papers, the architecture of the network, by determining the level of competition and outside options of traders, has an impact on how surplus is shared across trading parties. We emphasize the insights that are most recurrent in the literature.

@incollection{condorelligaleotti2016, author = "Condorelli, Daniele and Galeotti, Andrea", title = "Strategic Models of Intermediation Networks", editor = "Bramoull{\'e}, Y. and Galeotti, A. and Rogers, B.W.", booktitle = "The Oxford Handbook of the Economics of Networks", publisher = "Oxford University Press", address = "Oxford", year = 2016, pages = "", chapter = 27, }

This paper studies slot allocation at congested airports in Europe. First, I discuss the inefficiencies of the current regulation, introduced as part of the liberalisation process of the air transport market. Then, I consider three marked based methods which are suitable to achieve a more efficient allocation of slots to airlines: congestion pricing, auctions and secondary trading. These methods are examined in terms of their ability to improve efficiency and in terms of their implications on the distribution of slots' scarcity rents. Special attention is drawn to complementarities between slots. Finally, I propose to auction slots periodically, allowing secondary trading well before the first auction takes place. By selling slots before the first auction incumbents can be partially compensated for the subsequent withdrawal of their slots.

@Article{Condorelli2007, author={Daniele Condorelli}, title={{Efficient and Equitable Airport Slot Allocation}}, journal={Rivista di Politica Economica}, year=2007, volume={97}, number={1}, pages={81-104}, month={01}, doi={}, }