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DOI: 10.4230/LIPIcs.ITCS.2025.10

Algorithmic Collusion Without Threats

Authors: Eshwar Ram Arunachaleswaran, Natalie Collina, Sampath Kannan, Aaron Roth, and Juba Ziani

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

There has been substantial recent concern that automated pricing algorithms might learn to "collude." Supra-competitive prices can emerge as a Nash equilibrium of repeated pricing games, in which sellers play strategies which threaten to punish their competitors if they ever "defect" from a set of supra-competitive prices, and these strategies can be automatically learned. But threats are anti-competitive on their face. In fact, a standard economic intuition is that supra-competitive prices emerge from either the use of threats, or a failure of one party to correctly optimize their payoff. Is this intuition correct? Would explicitly preventing threats in algorithmic decision-making prevent supra-competitive prices when sellers are optimizing for their own revenue? No. We show that supra-competitive prices can robustly emerge even when both players are using algorithms which do not explicitly encode threats, and which optimize for their own revenue. Since deploying an algorithm is a form of commitment, we study sequential Bertrand pricing games (and a continuous variant) in which a first mover deploys an algorithm and then a second mover optimizes within the resulting environment. We show that if the first mover deploys any algorithm with a no-regret guarantee, and then the second mover even approximately optimizes within this now static environment, monopoly-like prices arise. The result holds for any no-regret learning algorithm deployed by the first mover and for any pricing policy of the second mover that obtains them profit at least as high as a random pricing would - and hence the result applies even when the second mover is optimizing only within a space of non-responsive pricing distributions which are incapable of encoding threats. In fact, there exists a set of strategies, neither of which explicitly encode threats that form a Nash equilibrium of the simultaneous pricing game in algorithm space, and lead to near monopoly prices. This suggests that the definition of "algorithmic collusion" may need to be expanded, to include strategies without explicitly encoded threats.

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Eshwar Ram Arunachaleswaran, Natalie Collina, Sampath Kannan, Aaron Roth, and Juba Ziani. Algorithmic Collusion Without Threats. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arunachaleswaran_et_al:LIPIcs.ITCS.2025.10,
  author =	{Arunachaleswaran, Eshwar Ram and Collina, Natalie and Kannan, Sampath and Roth, Aaron and Ziani, Juba},
  title =	{{Algorithmic Collusion Without Threats}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.10},
  URN =		{urn:nbn:de:0030-drops-226386},
  doi =		{10.4230/LIPIcs.ITCS.2025.10},
  annote =	{Keywords: Algorithmic Game Theory, Algorithmic Collusion, No-Regret Dynamics}
}

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DOI: 10.4230/LIPIcs.ITCS.2021.8

Pipeline Interventions

Authors: Eshwar Ram Arunachaleswaran, Sampath Kannan, Aaron Roth, and Juba Ziani

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract

We introduce the pipeline intervention problem, defined by a layered directed acyclic graph and a set of stochastic matrices governing transitions between successive layers. The graph is a stylized model for how people from different populations are presented opportunities, eventually leading to some reward. In our model, individuals are born into an initial position (i.e. some node in the first layer of the graph) according to a fixed probability distribution, and then stochastically progress through the graph according to the transition matrices, until they reach a node in the final layer of the graph; each node in the final layer has a reward associated with it. The pipeline intervention problem asks how to best make costly changes to the transition matrices governing people’s stochastic transitions through the graph, subject to a budget constraint. We consider two objectives: social welfare maximization, and a fairness-motivated maximin objective that seeks to maximize the value to the population (starting node) with the least expected value. We consider two variants of the maximin objective that turn out to be distinct, depending on whether we demand a deterministic solution or allow randomization. For each objective, we give an efficient approximation algorithm (an additive FPTAS) for constant width networks. We also tightly characterize the "price of fairness" in our setting: the ratio between the highest achievable social welfare and the social welfare consistent with a maximin optimal solution. Finally we show that for polynomial width networks, even approximating the maximin objective to any constant factor is NP hard, even for networks with constant depth. This shows that the restriction on the width in our positive results is essential.

Cite as

Eshwar Ram Arunachaleswaran, Sampath Kannan, Aaron Roth, and Juba Ziani. Pipeline Interventions. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arunachaleswaran_et_al:LIPIcs.ITCS.2021.8,
  author =	{Arunachaleswaran, Eshwar Ram and Kannan, Sampath and Roth, Aaron and Ziani, Juba},
  title =	{{Pipeline Interventions}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.8},
  URN =		{urn:nbn:de:0030-drops-135478},
  doi =		{10.4230/LIPIcs.ITCS.2021.8},
  annote =	{Keywords: Interventions for fairness, fairness in navigating life paths, social welfare, maximin welfare, budget-constrained optimization, hardness of approximation}
}

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Documents authored by Arunachaleswaran, Eshwar Ram

Algorithmic Collusion Without Threats

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Pipeline Interventions

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