Finding Competitive Equilibria in Online Marketplaces with Platform Fees, Taxes, and Subsidies
Taihei Oki, Ryosuke Sato
AI 速览：研究在带平台费、税费、补贴等分段线性转移的多单位交易网络中，如何用升价算法计算最小均衡价格向量与均衡配置。
We study equilibrium computation in multi-unit trading networks with valuations satisfying generalized full substitutes and agent- and transaction-specific piecewise-linear transfer functions. These transfers model platform fees, taxes, subsidies, and membership discounts in online marketplaces. Our ascending procedure raises prices at different rates and reaches the minimum equilibrium price vector in finitely many iterations, each implementable in strongly polynomial time under our oracle and arithmetic models. An equilibrium allocation can then be recovered efficiently. The method extends primal-dual techniques developed for ascending auctions to handle complementarities between purchases and sales through a submodular flow formulation. In single-seller markets with substitutes and complements, our framework also extends the double-track auctions of Sun and Yang (2009) and Shioura and Yang (2015) to bidder- and good-specific transfers.
From signaling to interviews in random matching markets
Maxwell Allman, Itai Ashlagi, Amin Saberi, Sophie H. Yu
AI 速览：研究在带面试后冲击的集中式随机匹配市场中，申请人向有限数量偏好对象发送信号如何减少面试并影响临时稳定性。
In two-sided labor markets, interviews precede matches. Rising interview volumes in medical residency markets have motivated signaling mechanisms that let applicants express interest in a limited number of partners. We study how signaling reduces interviews in centralized random matching markets with post-interview shocks. We focus on interim stability, which ensures that agents do not regret not interviewing with each other. A matching is almost interim stable if it becomes interim stable after removing a vanishing fraction of agents. We consider markets with $n$ agents in which agents on the short side, long side, or both sides signal their top $d$ preferred partners. An interview occurs whenever at least one party signals the other. When the probability of a nonnegative interview shock is bounded away from zero and $d=ω(1)$, short-side signaling leads to almost interim stable matchings. Long-side signaling can fail in strongly imbalanced markets when pre-interview scores outweigh interview shocks. In balanced markets without interview shocks, both-side signaling fails to achieve almost interim stability when $d=o(\log n)$. For larger $d \ge Ω(\log^2 n)$, under the same probability condition, short-side signaling achieves perfect interim stability, while long-side signaling can fail in imbalanced markets. We extend these findings to propose a signaling mechanism for multi-tiered random markets and identify conditions for incentive compatibility. A technical contribution is the analysis of a message-passing algorithm for stable matchings on trees, together with local availability certificates used to study interim stability on general graphs.
We study a dynamic game where an expert sends probabilistic forecasts to a decision-maker. The decision-maker verifies these forecasts using a calibration test based on past data. How should the expert send forecasts to maximize her payoff while passing the test? For a stationary ergodic process, we characterize the optimal forecasting strategy by reducing the dynamic game to a static persuasion problem. Calibration restricts long-run forecast distributions to mean-preserving contractions of the distribution of truthful forecasts. We compare the payoffs attainable by an informed and uninformed expert, providing a benchmark for the value of information. Finally, we consider a decision-maker who uses a mean-based learning strategy and show that the expert can guarantee at least the calibration benchmark and sometimes strictly more.
The Limits of Price Discrimination When the Market Is Unknown
Irfan Tekdir
AI 速览：在仅知可能价值集合、不知具体价值分布的情况下，刻画市场与市场分割所能产生的消费者剩余与生产者剩余组合。
Bergemann, Brooks, and Morris (2015) characterize the consumer and producer surplus pairs that segmentation can produce when the distribution of values is known. I fix only the set of possible values and characterize the pairs that some market and some segmentation can produce. They form a convex polygon. Its outer edge is the largest efficient surplus a market can have when its uniform-price profit is capped, net of that profit, and truncated equal-revenue markets attain it. At the values no segmentation is needed; strictly between two values, reaching the frontier requires splitting a market into two extremal markets. With a continuum of values up to $\bar{v}$, consumer surplus is at most $π\ln(\bar{v}/π)$ when producer surplus (the seller's profit) is $π$, this bound is reached without segmentation, and no market gives consumers more than $\bar{v}/e$.
Classical theory predicts that irrational traders lose money to rational traders and are eventually driven out of the market. Yet noise trading, herding, and heuristic trading persist even in highly developed markets. We model a financial market as an ecology of two trading-behavior types, relatively rational (R) and boundedly rational (N), whose composition evolves under replicator dynamics according to relative performance. Each type's fitness depends on the share of the other type and on frictions. When the interaction is complementary, that is, rational traders profit from the mispricing created by boundedly rational traders while the latter benefit from the liquidity and price correction supplied by the former, and when the difference in frictions is moderate, a unique interior composition exists and is globally asymptotically stable: bounded rationality persists endogenously. When the interaction is antagonistic, the same point becomes a tipping threshold between two one-type regimes. Comparative statics show that lowering the costs of disciplined trading, as algorithmic and AI-based trading does, shifts the composition toward rational trading continuously but does not eliminate bounded rationality unless the cost advantage exceeds an explicit threshold.
In a duopoly with captive and contested consumers, I characterize every pair of consumer and producer surplus that can arise under some market composition and some public segmentation, and construct a market that produces each pair. The set is lens-shaped. At any level of industry profit, consumers do worst when captive and contested consumers are perfectly separated and best in an unsegmented market in which the two firms have equally many captives. A market with unequal captive bases and some contested consumers cannot reach this upper frontier under any segmentation. Between Bertrand competition and monopoly, the frontier itself lies strictly below what consumers would get if everyone paid a single deterministic price yielding the same profit. Firms must randomize, and with downward-sloping demand the resulting price dispersion lowers consumer surplus.
Janik Bürgermeister, Julius Durmann, Martin Bichler, Mete Şeref Ahunbay, Bary Pradelski, Marco Scarsini
We study equilibrium learning in discretized Bayesian games, focusing on first-price auctions as a testbed for gradient-based learning dynamics under private information. While the symmetric independent private values model admits a unique Bayesian correlated equilibrium (BCE) in the continuous limit, standard convergence guarantees for gradient-based learners do not apply: classical no-regret theory predicts convergence only to Bayesian coarse correlated equilibria (BCCE), which can remain large and far from the competitive equilibrium even under fine discretizations. To bridge this gap, we introduce the notion of Bayesian semicoarse correlated equilibrium (BSCCE), an equilibrium concept that refines BCCE by restricting deviations to probability-preserving transformations consistent with projected gradient dynamics. We provide a linear programming characterization of BSCCE with polynomially many variables and constraints and establish the inclusion hierarchy $BCE \subseteq BSCCE \subseteq BCCE$. Our main finding is that the BSCCE set contracts in many cases as the discretization of the Bayesian game is refined. Even with priors for which BCCE fails to concentrate, the diameter of the BSCCE polytope shrinks toward zero, indicating convergence to the unique continuous-game Bayes-Nash equilibrium. These results provide a principled explanation for the observed robustness of gradient-based learning in discretized Bayesian games, showing that these dynamics select a smaller equilibrium set than standard no-regret theory predicts.
A perfectly divisible cake is to be divided among a group of agents. Each agent is entitled to a share between zero and one, and these entitlements are compatible in that they sum to one. The mediator does not know the preferences of the agents, but can query the agents to make cuts and appraise slices in order to learn. For each entitlement profile, we provide a lower bound on the number of queries that the mediator requires to construct an allocation that respects the entitlements regardless of preferences. If one of the entitlements is irrational, then the mediator requires an arbitrarily large number of queries.
Machine learning recommendations are often evaluated one model at a time, despite deployment across interconnected decision makers. For continuous NPK fertilizer prescriptions, correlated errors can aggregate across farms and generate systemic costs. A model of shared and farm-specific recommendation errors links expected social loss to model adoption shares; the Herfindahl-Hirschman Index characterizes concentration effects when common model errors are independent and predictive risks are equal. A covariance-generalized formulation captures the dependence between model families. A two-model threshold characterizes when privately optimal monoculture is socially dominated, and a convex portfolio rule limits average private predictive regret. Nine model families across five Moroccan cereal systems provide a benchmark-based calibration. Under illustrative parameters and a 10% regret cap, accuracy-constrained diversification lowers modeled social loss in all five systems by 10.89-41.53% (mean 19.41%). Uniform allocation reduces modeled loss in this setting, but breaches the regret cap in every crop. Correlation sensitivity shows that highly dependent model errors attenuate the benefits of diversification. These counterfactual outcomes are not estimates of agronomic or monetary welfare; the framework identifies adoption architecture and error dependence as ecosystem-level evaluation variables.
Karen Frilya Celine, Warut Suksompong, Nicholas Teh
When allocating indivisible goods, the maximum Nash welfare rule is known to be the unique welfarist rule satisfying envy-freeness up to one good. We strengthen this characterization by showing that envy-freeness up to one good can be replaced by substantially weaker fairness requirements: envy-freeness up to $k$ goods or proportionality up to $k$ goods, for any fixed $k$. Our characterization holds even for profiles with identical goods.
When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are log-linear functions of observations and admit a signal-counting interpretation of accuracy. Networks where agents observe multiple neighbors but not their common predecessors confound information, and even a small amount of confounding can lead to much lower accuracy. In a class of networks where agents move in generations and observe the previous generations, we quantify the information loss with an aggregative efficiency index. Aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Later generations contribute little additional information, even when generations are arbitrarily large and agents observe arbitrarily far into the past.
The adaptive clinching auction of Dobzinski, Lavi, and Nisan (FOCS'08) is a cornerstone of mechanism design with budget-constrained bidders, and it has since inspired a broad range of extensions to substantially richer market settings. Adaptive clinching enjoys compelling guarantees: it is Pareto optimal, and truthful bidding is a dominant strategy whenever budgets cannot be overreported. In many real-world environments, however, identities are cheap to create, making resilience to Sybil attacks an additional requirement. Whether the guarantees of adaptive clinching survive when a bidder can split its budget across fake identities has remained open. We introduce a generalized framework for adaptive clinching and prove that it satisfies Sybil-robust incentive compatibility: a bidder cannot benefit from splitting into any finite number of identities with arbitrary value reports, provided their aggregate reported budget does not exceed the bidder's enforceable true budget. Sybil resilience thus joins the list of ideal properties of adaptive clinching. Our work is motivated by practical problems in decentralized finance, where automated market makers (AMMs) are among the most widely used applications. We design a new AMM mechanism that extends classical adaptive clinching in two ways: it supports a two-sided market and protects against two-sided strategies, and it allows the supply function to depend on the auction state. Its one-sided special case is captured by our generalized adaptive clinching framework, and our proof techniques show that the full two-sided mechanism simultaneously satisfies Sybil-robust incentive compatibility and a relaxed notion of Pareto optimality. We argue that these guarantees are essentially the best possible via impossibility results. More broadly, our work reveals new connections between classical algorithmic game theory and modern decentralized blockchains.
Strategic replicators combine evaluated choice and reproductive transmission. An agent chooses among alternatives; the consequences of those choices influence continuation or reproduction; and successors receive organization that shapes later choices. Artificial intelligence makes this combination salient when agents have authority to create, configure, or retire software instances. This paper organizes the general logic around three principles: situated choice, reproductive transmission, and institution-mediated coupling. The principles are constitutive rather than predictions of growth or improvement. A common representation distinguishes carriers, inherited records, decision owners, and the mechanisms that allocate consequences. Actual parent-descendant attribution yields a selection-transmission identity. Separate compatibility results characterize when utility-maximizing choices also maximize a reproductive criterion. Gode and Sunder's zero-intelligence traders reveal the role of institutions: enforced properties can hold across different decision procedures, while aggregate efficiency alone determines neither individual gains nor descent. A worked market-rent-entry model connects institutional profits to actual offspring, with its occurrence-level ancestry bridge checked in Lean. A direct-deployment example then shows evaluated preferences undergoing selection without presupposing that every chooser values reproduction. Formal appendices develop games with endogenous players, deployment-induced tipping, endogenous electorates, and the production of institutions, with models, proofs, and examples. The paper and its supporting formal artifacts are a prototype kernel with a generative function: an instrument for constructing models of strategic replication. The results are formal; their application to deployed populations and their empirical implications remain to be tested.
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly conservative play. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability and behaving potentially arbitrarily with the remaining probability. We prove that a safe equilibrium exists in all strategic-form games (for all possible values of the rationality parameters), and prove that its computation is PPAD-hard. We present exact algorithms for computing a safe equilibrium in both 2 and $n$-player games, as well as scalable approximation algorithms.
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash equilibrium refinement concepts have been proposed and studied for sequential imperfect-information games, the most prominent being trembling-hand perfect equilibrium, quasi-perfect equilibrium, proper equilibrium, and recently one-sided quasi-perfect equilibrium. These concepts are robust to certain arbitrarily small mistakes, and are guaranteed to always exist; however, we argue that none of these is the correct concept for developing strong agents in sequential games of imperfect information. We define a new equilibrium refinement concept for extensive-form games called observable perfect equilibrium in which the solution is robust over trembles in publicly-observable action probabilities (not necessarily over all action probabilities that may not be observable by opposing players). Observable perfect equilibrium correctly captures the assumption that the opponent is playing as rationally as possible given mistakes that have been observed (while previous solution concepts do not). We prove that observable perfect equilibrium is always guaranteed to exist, and demonstrate that it selects a unique equilibrium in a simplified no-limit poker game where the prior extensive-form refinements retain a continuum of equilibria. We expect observable perfect equilibrium to be a useful equilibrium refinement concept for modeling many important imperfect-information games of interest in artificial intelligence.
The celebrated Myerson--Satterthwaite theorem shows that in bilateral trade, no mechanism can be simultaneously fully efficient, Bayesian incentive compatible (BIC), and budget balanced (BB). This naturally raises the question of how closely the gains from trade (GFT) achievable by a BIC and BB mechanism can approximate the first-best (fully efficient) benchmark. The optimal BIC and BB mechanism is typically complex and highly distribution-dependent, making it difficult to characterize directly. Consequently, much of the literature analyzes simpler mechanisms such as the Random-Offerer (RO) mechanism and establishes constant-factor guarantees relative to the first-best GFT. An important open question concerns the worst-case performance of the RO mechanism relative to first-best (FB) efficiency. While it was originally hypothesized that the approximation ratio $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}}$ is bounded by $2$, recent work provided counterexamples to this conjecture: Cai et al. proved that the ratio can be strictly larger than $2$, and Babaioff et al. exhibited an explicit example with ratio approximately $2.02$. In this work, we employ AlphaEvolve, an AI-guided evolutionary search framework, to explore the space of value distributions. We identify a new worst-case instance that yields an improved lower bound of $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}} \ge \textbf{2.0749}$. This establishes a new lower bound on the worst-case performance of the Random-Offerer mechanism, demonstrating a wider efficiency gap than previously known.