Yet a widely cited 2019 paper<\/a> showed that algorithms could learn to collude tacitly, even when they weren\u2019t programmed to do so. A team of researchers pitted two copies of a simple learning algorithm against each other in a simulated market, then let them explore different strategies for increasing their profits. Over time, each algorithm learned through trial and error to retaliate when the other cut prices \u2014 dropping its own price by some huge, disproportionate amount. The end result was high prices, backed up by mutual threat of a price war.<\/p>\n Aaron Roth suspects that the pitfalls of algorithmic pricing may not have a simple solution. \u201cThe message of our paper is it\u2019s hard to figure out what to rule out,\u201d he said.<\/p>\n Implicit threats like this also underpin many cases of human collusion. So if you want to guarantee fair prices, why not just require sellers to use algorithms that are inherently incapable of expressing threats?<\/p>\n In a recent paper<\/a>, Roth and four other computer scientists showed why this may not be enough. They proved that even seemingly benign algorithms that optimize for their own profit can sometimes yield bad outcomes for buyers. \u201cYou can still get high prices in ways that kind of look reasonable from the outside,\u201d said Natalie Collina<\/a>, a graduate student working with Roth who co-authored the new study.<\/p>\n Researchers don\u2019t all agree on the implications of the finding \u2014 a lot hinges on how you define \u201creasonable.\u201d But it reveals how subtle the questions around algorithmic pricing can get, and how hard it may be to regulate.<\/p>\n \u201cWithout some notion of a threat or an agreement, it\u2019s very hard for a regulator to come in and say, \u2018These prices feel wrong,\u2019\u201d said Mallesh Pai<\/a>, an economist at Rice University. \u201cThat\u2019s one reason why I think this paper is important.\u201d<\/p>\n No Regrets<\/p>\n The recent paper studies algorithmic pricing through the lens of game theory, an interdisciplinary field at the border of economics and computer science that analyzes the mathematics of strategic competitions. It\u2019s one way to explore the failures of pricing algorithms in a controlled setting.<\/p>\n \u201cWhat we\u2019re trying to do is create collusion in the lab,\u201d said Joseph Harrington<\/a>, a University of Pennsylvania economist who wrote an influential review paper<\/a> on regulating algorithmic collusion and was not involved in the new research. \u201cOnce we do so, we want to figure out how to destroy collusion.\u201d<\/p>\n Natalie Collina and her colleagues discovered that high prices can arise in unexpected ways.<\/p>\n To understand the key ideas, it helps to start with the simple game of rock-paper-scissors. A learning algorithm, in this context, can be any strategy that a player uses to choose a move in each round based on data from previous rounds. Players might try out different strategies over the course of the game. But if they\u2019re playing well, they\u2019ll ultimately converge to a state that game theorists call equilibrium. In equilibrium, each player\u2019s strategy is the best possible response to the other\u2019s strategy, so neither player has an incentive to change.<\/p>\n In rock-paper-scissors, the ideal strategy is simple: You should play a random move each round, choosing all three possibilities equally often. Learning algorithms shine if one player takes a different approach. In that case, choosing moves based on previous rounds can help the other player win more often than if they just played randomly.<\/p>\n Suppose, for instance, that after many rounds you realize that your opponent, a geologist, chose rock more than 50% of the time. If you\u2019d played paper every round, you would have won more often. Game theorists refer to this painful realization as regret.<\/p>\n Researchers have devised simple learning algorithms that are always guaranteed to leave you with zero regret. Slightly more sophisticated learning algorithms called \u201cno-swap-regret\u201d algorithms also guarantee that whatever your opponent did, you couldn\u2019t have done better by swapping all instances of any move with any other move (say, by playing paper every time you actually played scissors). In 2000, game theorists proved<\/a> that if you pit two no-swap-regret algorithms against each other in any game, they\u2019ll end up in a specific kind of equilibrium \u2014 one that would be the optimal equilibrium if they only played a single round. That\u2019s an attractive property, because single-round games are much simpler than multi-round ones. In particular, threats don\u2019t work because players can\u2019t follow through.<\/p>\n One way to have regret is just to be kind of dumb. Historically, that hasn\u2019t been illegal.<\/p>\n Aaron Roth, University of Pennsylvania<\/p>\n In a 2024 paper<\/a>, Jason Hartline<\/a>, a computer scientist at Northwestern University, and two graduate students translated the classic results from the 2000 paper to a model of a competitive market, where players can set new prices every round. In that context, the results implied that dueling no-swap-regret algorithms would always end up with competitive prices when they reached equilibrium. Collusion was impossible.<\/p>\n However, no-swap-regret algorithms aren\u2019t the only pricing game strategies in the world of online marketplaces. So what happens when a no-swap-regret algorithm faces a different benign-looking opponent?<\/p>\n The Price Is Wrong<\/p>\n According to game theorists, the best strategy to play against a no-swap-regret algorithm is simple: Start with a specific probability for each possible move, and then choose one move at random every round, no matter what your opponent does. The ideal assignment of probabilities for this \u201cnonresponsive\u201d approach depends on the specific game you\u2019re playing.<\/p>\n![\"A](\"https:\/\/www.newsbeep.com\/us\/wp-content\/uploads\/2025\/10\/Aaron-Roth-cr-Courtesy-of-Aaron-Roth.webp.webp\")
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