Game Theory Papers

ALT 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.

ALT Automated mechanism design has enabled the learning of complex auction mechanisms using neural networks. However, designing non-truthful auctions remains challenging because bidders' equilibrium strategies depend on the auction mechanism and thus evolve as the mechanism is optimized. In this work, we formulate auction design as a Stackelberg game with multiple strategic followers and develop a fully first-order algorithm for revenue optimization in non-truthful auctions. We establish non-asymptotic guarantees for hypergradient approximation and show that, under standard smoothness and strong-monotonicity assumptions, our method reaches an O(ε)-stationary point using Õ(ε⁻²) first-order oracle calls. Experiments on symmetric and asymmetric single-item auctions, as well as multi-item auctions, show that our method converges faster than second- and zeroth-order baselines and scales better as the number of bidders increases. Our method also discovers auctions that achieve revenue close to t

ALT We study routing games in which competing mediators recommend routes to fixed nonatomic populations. Each mediator chooses a randomized flow allocation to minimize its population's expected travel cost, subject to users having no conditional expected gain above a tolerance ε from disregarding their recommendations. We define a fragmented obedient equilibrium (FOE) by combining user obedience with mediator optimality, and establish existence under a lower-hemicontinuity assumption on the obedient policy correspondences. Under affine edge latencies and independent mediator sampling, we derive an exact reformulation in first and second flow moments that preserves best responses and equilibrium profiles. Every feasible moment pair admits a finitely supported realizing policy. When the network has at most four routes, each mediator's best-response problem is an exact semidefinite program. A numerical illustration on the Braess network shows that relaxing obedience can reduce FOE costs, whil

ALT 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 reg

ALT We study a pricing game in markets with budget-constrained buyers, where each seller offers a single good at a price she sets, and each buyer chooses a utility-maximizing bundle subject to her budget. We consider both the rivalrous setting, such as markets for physical goods, and the non-rivalrous setting, such as markets for datasets. Pure Nash equilibria often fail to exist in this game. However, Nash equilibrium assumes that the other sellers keep their prices fixed when one seller deviates, whereas in practice, sellers harmed by a price change may respond, for example, by matching the new price. We propose a new equilibrium notion called Response-Aware Rational Equilibrium (RARE). At a RARE, every deviation by a seller can be deterred by a response from the other sellers, in which no responder earns less than she did right after the deviation. Every Nash equilibrium is a RARE. Assuming that buyers' purchases (among their optimal choices) change continuously with prices, we show tha

ALT 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 ⊆ BSCCE ⊆ BCCE. Our ma

ALT Time-series forecasters are ranked almost entirely by accuracy metrics, but a forecast's decision value, its effect on the downstream decision, need not track accuracy and is rarely measured. This problem compounds as large language model (LLM) agents increasingly consume forecasters as tools, mediating them through stochastic, opaque policies. We present Vendster, an evaluation arena measuring how a forecaster's bias and prediction-interval width change the outcome of a buyer–vendor discount negotiation between two LLM agents. In the reference instance Vendster-M5, sampling base demand patterns from the M5 dataset, we evaluate two frontier-closed LLM families (Claude Opus 4.6 and GPT-5.6 Sol) and two open ones (DeepSeek-V3.2 and Qwen3-235B-A22B). Model-generated forecasts raise sales target attainment by up to +17 percentage points (p<0.001), yet standard forecast evaluation metrics such as relWQL and MASE do not predict negotiation outcomes at a statistically significant level. To is

ALT Model distillation has become a major concern in the rapidly growing generative AI discourse. In its simplest form, distillation is the phenomenon where smaller firms can use data distilled from transcripts of conversations with powerful proprietary closed-weight models to train their own models, thus achieving reasonably high model quality but at much lower costs. Besides the legitimate safety and security concerns associated with distillation, another major issue is how it can also distort marketplace outcomes. This motivates us to initiate an exploration of the problem from an economic theory lens. We consider a setting with two players: an incumbent and a distilling competitor and characterize how the incumbent's model characteristics drive the incentives around how much the competitor should distill. We also consider the impact of distillation on key market outcomes like user-side surplus and the incumbent's utility. Our key contribution, however, is to study interventions for pre

ALT We study experimental results of best response dynamics (BRD) in randomly generated weighted action networked multiagent optimization problems where agent utility is the agent's marginal contribution to the system objective. We compare those results to the Price of Anarchy (PoA) established in the literature for marginal contribution and to the expected value of randomly choosing from the available equilibria. PoA is used as a metric to describe the performance of various solutions to multiagent optimization problems, but the utility of this metric may be overrated if such worst-case instances are rare in practice. Our study provides evidence to support this doubt, showing that simple best response mechanics tend to out perform the PoA prediction and a uniform random equilibrium selection, even when agents are unable to observe all other agents' actions. In the process of seeking a more ideal metric, we discover that BRD appears to perform better than average. That is, when multiple eq

ALT We describe the agent we submitted to the GLEE Competition, which plays bargaining, negotiation, and persuasion games against a shared pool of human and AI opponents. The agent is built around three central components: a classical game-theoretic solver to compute numeric moves, an online Bayesian layer to estimate opponent archetypes, and a language model to write accompanying messages. We utilize Rubinstein bargaining for bargaining, Faratin concession for negotiation, and Kamenica–Gentzkow disclosure for persuasion, and adapt those models to live opponents using two separate layers: a Bayesian estimate of the opponent's hidden discount factor, reservation value, or signaling reliability, and a Thompson sampling bandit over five moral-foundation framings coupled with an evidence-intuition spectrum to establish message register. Most of the development effort went into the recurring problem that theoretically optimal policies perform poorly in certain live settings; we report associate

ALT Token systems support repeated service exchange without monetary transfers, but their viability depends on the stability of token balances. We study token systems with compatibility constraints among agents. A requester is randomly sampled in each period, and only a few randomly sampled agents are available to provide service. We establish a necessary and sufficient condition for stability and show that the minimum-token rule, which selects the available provider with the lowest token balance, achieves the optimal stability region. We then apply this stability criterion to a random token system generated from stochastic block models with uniformly sampled requesters. We tightly characterize the stability regime by identifying two obstructions to stability: insufficient service opportunities for a group of communities or for an individual agent.

ALT We consider T repeated second-price auctions across n pacing bidders with i.i.d. item arrivals, and show that it is computationally impossible for all bidders to achieve no-regret simultaneously while satisfying their respective budget or return-on-investment constraints. Therefore, in the prominent internet auction systems where buyers simultaneously deploy pacing algorithms or automated bidding agents, we cannot hope to achieve joint no-regret guarantees in general. We establish a deterministic relationship that high variance in online bidding systems implies high regret. By showing that one can extract a pacing equilibrium from a low-variance system, we prove PPAD-hardness of attaining joint no-regret. For several widely used bidding algorithms, we also show evidence from dynamical systems and numerical simulations that they can indeed display high-variance behavior through cycling, even on simple market instances.

ALT Miner extractable value (MEV) poses a persistent challenge for blockchain ecosystems. It arises from the fact that a block builder can exploit its unilateral control over transaction inclusion and ordering to extract profit, potentially at users' expense. Recent work has explored consensus-aided mechanism design to mitigate MEV. This approach combines generic consensus-layer guarantees with application-layer mechanisms that use these guarantees to address application-specific MEV problems. Prior work exemplifies this approach for automated market makers (AMMs). When the consensus layer offers fair sequencing, which orders transactions according to their arrival times, their proposed mechanism achieves incentive compatibility (IC) and weak local efficiency (wLE). Informally, IC rules out profitable strategic deviations by users and builders. Meanwhile, wLE ensures that after execution, any order willing to trade at the initial price cannot benefit from further trade with the pool at the

ALT 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 resilienc

ALT Recent work has shown that, in zero-sum games, an optimizer can extract Ω(√T) strategic surplus—cumulative payoff above the minimax benchmark—against noiseless no-regret learners with a constant step size. However, in practice, learners often act on perturbed payoff scores and use decaying learning rates ηₜ. Since existing extraction mechanisms rely on exact scores, a natural question is whether noise shields the learner from exploitation and eliminates surplus altogether. We address this question for the widely used class of Follow-the-Regularized-Leader (FTRL) algorithms. Under standard regularity conditions, we establish three results, none of which assumes independence of the noise. First, under summability conditions, passive play of a strategy fixed independently of the horizon earns at most constant surplus. Second, we design a new mechanism that exploits the learner's noise-dependent response: a clairvoyant optimizer who knows the update rule and the limiting mean response secu

ALT We study facility location in multidimensional normed spaces with the objective of minimizing social cost, the sum of agents' distances to their nearest facility. A deterministic mechanism selects k facility locations based on the reports of n agents and is strategyproof (SP) if no agent can reduce her distance by misreporting her location. We establish optimal approximation ratios and impossibility results. For a single facility in the Euclidean plane, we prove that the optimal approximation ratios among deterministic SP mechanisms are exactly those obtained by Goel and Hann-Caruthers [SCW 2023] for the coordinate-wise median (CM): √(2(n²+1))/n+1 for odd n≥3 and √2 for even n≥4. We remove the anonymity assumption from their optimality result. However, CM is not always optimal in non-Euclidean spaces: we give an SP mechanism that minimizes social cost exactly in ℓ∞ᵈ, whereas CM has a tight uniform approximation ratio of 2 already in the plane. We then consider two facilities in ℓₚ spac

ALT The inefficiency of decentralized resource allocation is classically measured by the Price of Anarchy (PoA) and the Price of Stability (PoS). The most widely studied and foundational class of these models are atomic and non-atomic congestion games, for which a robust theory quantifying the inefficiency of equilibria is well-established. To mitigate the effects of selfish behavior, we employ Coordination Mechanisms, which modify resource costs to incentivize socially improved equilibria. However, standard Coordination Mechanisms assume unknown, adversarial demand, restricting positive results mainly to specialized networks such as parallel links. We address this limitation by studying learning-augmented coordination mechanisms, where the mechanism is endowed with a potentially inaccurate prediction of the demand. We study general atomic and non-atomic congestion games with polynomial latency functions of degree d. Our main positive result is a learning-augmented coordination mechanism t

ALT Replicator dynamics, the central model of evolutionary game theory, describe populations evolving under selection and agents learning by trial and error. They also admit a third use: continuous-time Bayesian inference, in which an agent planning against an opponent accumulates evidence for each candidate strategy. Here we show that this use divides all two-player games into two classes. With the standard expected-utility payoff, the dynamics can be expressed as Bayesian updating only in games (with any number of actions) where no player has a dominant strategy. The logarithmic payoff of Ay and Erb admits the Bayesian representation in every game. Coordination, anti-coordination, and cyclic games share qualitative dynamics under both payoff definitions, with equilibria displaced and selection thresholds shifted. In contrast, the flows of every game with a dominant strategy are reversed between the payoff definitions, with the strictly dominant strategy eliminated under logarithmic payof

ALT We study how learning algorithm design shapes equilibrium selection in infinite-horizon discounted Markov games with finite states and actions. Each episode, players choose smooth best responses to beliefs about opponents' policies, test them using noisy observations, and resample rejected beliefs or explore at rates determined by increasing transformations of their discounted values. We show that stochastically stable states induce approximate stationary Nash equilibria maximizing the minimum transformed discounted value across players, with transformations governing which players selection favors. In repeated games with bounded recall of noisy public signals, longer recall weakly increases the selected minimum transformed value. In repeated Cournot games, every stochastically stable state induces an approximate public perfect equilibrium whose minimum discounted profit across firms exceeds the Cournot-Nash benchmark. Collusion is therefore inevitable under these conditions and learni

ALT We study the computational complexity of clairvoyant strategy optimization against a known online learner in finite-horizon repeated games. In general-sum games with bounded payoffs, unless P=NP, no polynomial-time optimizer can achieve a reward within cT of the reward of the optimal pure-action sequence for an absolute constant c>0, even when allowed to output explicitly represented mixed strategies at every round. Our hardness result strengthens prior work along two complementary axes: it extends to a broader class of learning dynamics, including widely used mean-based algorithms, answering an open question of Assos, Dagan, and Rajaraman (2025) for learners beyond multiplicative weights; and it permits mixed outputs while retaining the weaker pure-sequence benchmark. Thus, neither mixed strategies nor algorithmic specificity removes the computational obstruction in general-sum games. In sharp contrast, zero-sum games exhibit the reverse phenomenon: deterministic pure actions suffice