Omar Abbadi, Rida Laraki, Panayotis Mertikopouloscs.LG cs.GT
We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting (HOOD) is a variant of optimistic follow-the-regularized-leader (OptFTRL) that combines a discounted $(N+1)$-th order predictor with entropic regularization over a suitable "lifting" of the game's strategy space. This combination of ingredients is purposefully designed to dampen large oscillations of the induced sequence of play in a controlled manner, removing in this way a key stumbling block of previous attempts to achieve constant regret in general games. Our approach bears several striking similarities to the concurrent - and completely independent - work of Liu, Farina, and Ozdaglar (arXiv:2608.31166), who very recently derived an $O(N^{21}\log^{4} K)$ regret bound through the use of higher-order optimism and an exponential moving average estimator.
Multi-agent LLM systems commonly use an orchestrator to decompose a task for a team of workers and then improve through textual reflection. Despite strong empirical results, these systems lack a unified account of coordination, memory improvement, and the role of external verification. We model orchestrator-worker interaction as a bilevel coordination game: under bounded coupling, the workers' local-update game is an approximate potential game whose equilibrium slack is controlled by decomposition quality. We then analyse reflection as stochastic movement over semantic memory states. For free-form reflection, we derive a finite-time upper bound, prove worst-case tightness, and give a positive lower bound under a falsifiable persistent-harm condition. We further prove an information-theoretic impossibility result: no gate that observes only the generated transcript can improve uniformly over text-indistinguishable environments, whereas an environment-grounded gate can. Motivated by this separation, we introduce Stochastic Reflective Memory Ascent (SRMA), which accepts a candidate memory only after a grounded evaluation risk strictly decreases. Under calibration and non-degenerate corrective mass, SRMA converges exactly, geometrically or polynomially; matching constructions show that both rate regimes are order-tight. We also provide confidence gating for stochastic evaluation and re-anchoring guarantees for piecewise-stationary environments. Experiments instantiate these objects with environment-grounded metrics and test the predicted coordination and drift laws. On 500 SWE-bench instances, the complete Kimi-based system resolves 72.2% versus a 70.8% public mini-SWE-agent reference. Code: https://github.com/YihangChen9/Bilevel-Coordinated-Reflection
We seek to understand the effect of adding disruptive highly-capable new technologies to competitions by assessing the addition of Dynamite to Rock-Paper-Scissors. We find that providing a versatile Dynamite move to only one player provides limited value (win probability increases from 50% to 55.5%) and is played rarely. That value decreases further if the game is expanded beyond just the original three moves. We also observe several mechanisms by which prior moves can become strategically unplayable, or obsolete. We hope that this model illustrates some non-intuitive aspects of developing new versatile technologies. We also hope that it illustrates some pitfalls for developers and integrators to avoid in order to create value rather than merely capability.
Uncoupled no-regret dynamics provide a decentralized route to equilibrium, but prior guarantees for individual regret retain a polylogarithmic dependence on the horizon. We remove this dependence for every finite $N$-player normal-form game under full-information feedback. We introduce \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average. The algorithm is deterministic and fully uncoupled. If $m_{\max}$ denotes the largest action-set size, then, simultaneously for every horizon $T\geq1$, it guarantees that each of the $N$ players in the game incurs regret upper bounded by $O(\textrm{poly}(N, \log m_{\max}))$. Our algorithm leverages a new form of optimism inspired by modern filter design.
School coaches prepare for opponents with game film and intuition. The analytics tools of professional teams stay out of reach. We ask how far public data can close this gap. Professional basketball is our case study, chosen for its data rather than the league. We fuse five public sources into one per-shot dataset of 4.23M shots over 21 seasons. The sources are shot locations, two play-by-play feeds, official matchup tracking, and player biometrics. Alignment across them is 99.5% to 100%. We also report two data pitfalls that are easy to miss. We then model a half-court possession as a sequential game. Shot values come from ShotNet, an embedding multilayer perceptron (MLP). On a held-out season it beats a zone-rate baseline and a logistic baseline, and its probabilities are well calibrated. A depth-limited expectimax search then solves the offensive decision tree, with branch-and-bound pruning to keep it real time. All training runs offline, so the online system stays light. A scouting planner and a playable simulator both run in a single browser page.
Yanan Cai, Zhongrui Zhao, Zhigang Lu +6cs.AI cs.CL cs.GT
As large language models and increasingly capable AI agents are deployed in high-risk settings, aligning them with complex human values has become a central challenge. Existing alignment methods, while effective in improving helpfulness, harmlessness, and controllability, often struggle to capture real-world preferences that are context-dependent, non-transitive, and shaped by dynamic multi-party interactions. This survey reviews AI alignment through a game-theoretic lens. Specifically, it organizes recent progress around key game-theoretic elements and synthesizes the literature along three challenges: preference diversity, alignment priority, and temporal dynamics. This perspective clarifies where current alignment methods genuinely benefit from game-theoretic analysis, where the framework is looser, and what challenges remain in building robust, adaptive, and verifiable AI systems.
Yueyuan Li, Rongcheng Nie, Weijie Xi +4cs.AI cs.RO
Game-theoretic models provide principled frameworks for modeling vehicle interactions, but their underlying temporal assumptions have not been systematically examined against real-world driving behavior. In particular, it remains unclear how simultaneous, sequential, and asymmetric interaction structures can be measured from vehicle trajectories. This paper develops a trajectory-based interaction measurement framework to identify interaction events and quantify behavioral change onset, temporal organization, post-onset response dynamics, and ordering stability. The framework uses behavioral deviations to verify candidate interactions. We evaluate the framework on six real-world trajectory datasets, including INTERACTION, highD, inD, rounD, Waymo Open Motion, and nuPlan, covering diverse road geometries, traffic environments, and interaction types. The results show that concurrent and sequential behavioral changes both constitute substantial proportions of observed following, merging, and conflicting interactions. Among sequential interactions, stable ordering is more prevalent than alternating ordering, indicating that persistent asymmetric roles are a common interaction structure. Importantly, temporal precedence does not necessarily coincide with a measurable behavioral response, indicating that temporal ordering alone may not be sufficient to characterize behavioral dependence. These findings show that real-world interactions exhibit concurrent, sequential, and persistently ordered temporal structures. Different game-theoretic formulations are therefore better regarded as complementary modeling abstractions for different interaction regimes rather than as a universal structure governing all vehicle interactions.
We settle the minimax-optimal alternating regret, a regret notion motivated by alternating learning dynamics in games, for both online linear optimization (OLO) and online convex optimization (OCO). For OLO over the probability simplex $Δ_d$, we give an algorithm with $O(\log d)$ alternating regret that remains a constant for any time horizon $T$, and a matching lower bound. Our constant regret bound significantly improves previous results with $O(\log ^{2/3}d \cdot T^{1/3})$ regret [Cevher, Cutkosky, Kavis, Piliouras, Skoulakis, Viano, NeurIPS 2023, Hait, Li, Luo, Zhang, COLT 2025]. As a result, we obtain alternating learning dynamics with $O(\log d /T)$ convergence to Nash equilibria in two-player zero-sum games and $O(\log d /T)$ convergence to coarse correlated equilibria in two-player general-sum games. This is the first uncoupled learning dynamics with $O(1/T)$ convergence to CCE in two-player general-sum games, while all prior works suffer additional $\log T$ factors. For general OCO over a $d$-dimensional compact convex set, we give an algorithm with $O(d\log (1+T/d))$ alternating regret, improving the previous best of $\widetilde{O}(d^{2/3}T^{1/3})$. We also prove a matching lower bound of $Ω(d\log (1+T/d))$, showing that the $Ω(\log T)$ factor is unavoidable.
We study generating game-theoretically optimized Courses of Action (COAs) for a Blue UAS swarm against an adaptive Red adversary in a communication-degraded environment, motivated by (but not derived from) a public U.S. Air Force SBIR solicitation. We propose UC-PSRO (Utility-Conditioned Policy-Space Response Oracles with a Communication-Dropout Curriculum), combining three mechanisms: (i) PSRO self-play, so Blue and Red policies train as approximate best responses to each other rather than one side against a fixed scripted opponent; (ii) FiLM conditioning of the Blue policy on a Commander's-Intent weight vector, sampled from a Dirichlet distribution during training, so one trained policy is re-steerable at execution time without retraining; and (iii) a curriculum annealing communication-graph edge dropout during training, so the swarm learns decentralized, peer-to-peer fallback instead of depending on full connectivity. We evaluate on a synthetic, unclassified stand-in for the solicitation's maritime scenario, with 5 seeds at N=25 Blue agents and a scalability sweep to N=200. We find a genuine trade-off, not a uniform win: the communication-dropout curriculum alone gives the strongest, most robust mission-completion rates of any learned method, improving counter-intuitively as denial increases (35% to 62% success as dropout rises from 0 to 0.75); adding utility-conditioning and PSRO self-play substantially slows convergence within a fixed budget, and we find no reliable exploitability advantage for self-play over a fixed-opponent policy, both statistically indistinguishable from a small, near-zero gap. We report this honestly as a convergence cost not yet offset by a demonstrated robustness benefit, rather than overstating one method as dominant, and provide a fully vectorized, open environment training at N=200 agents in single-digit milliseconds per step on a single consumer GPU.
We introduce the Open-Strategy Dictator Game (OSDG), a variant of the classic dictator game in which each player's strategy is a natural-language document visible to all participants. The dictator's decision, to SHARE or TAKE an endowment, may depend on the text of the recipient's strategy. A large language model adjudicates each interaction by interpreting the dictator's strategy in the context of the recipient's. We run round-robin tournaments among diverse strategies and analyze the resulting payoff matrix using softmax equilibrium frequencies, dominance analysis, and sensitivity to the relative value of cooperation. Conditionally cooperative strategies, those that share with cooperators and take from exploiters, consistently dominate, while unconditional strategies (always share or always take) are weakly dominated. The results suggest that in environments where agents can inspect each other's decision procedures, conditional cooperation is evolutionarily robust across a wide range of payoff parameters.
Computing Nash equilibria in interdependent security (IDS) games on networks is computationally expensive: best-response dynamics may need hundreds of iterations per instance, and downstream tasks such as auditing, stress-testing, and incentive design often require repeatedly re-solving the game under parameter perturbations. We propose BRAID, a Best-Response Amortized Iterative Dynamics model that uses a weight-tied iterative graph neural network to learn a direct map from game parameters to Nash equilibrium effort profiles, replacing iterative best response computation with a single forward pass that is up to 43X faster per instance. BRAID is derived from the best-response fixed-point structure of IDS games: its SUM aggregation reflects additive neighbor coupling, and a weight-tied gated recurrent unit (GRU) mirrors a damped best-response update. The same architecture applies across IDS specifications that vary investment-cost curvature and neighborhood aggregation, including log-linear, quadratic-cost, and log constant-elasticity-of-substitution (CES) utilities. Beyond equilibrium prediction, BRAID also recovers how equilibrium efforts change under perturbations to game parameters, including costs and network edge weights. We make this sensitivity recovery an explicit evaluation target and introduce two training strategies, interior-equilibrium training and input-noise regularization, that improve the local behavior of the learned equilibrium map without using sensitivity labels. Experiments show that BRAID effectively predicts Nash equilibria and recovers equilibrium sensitivities across utility specifications and network sizes.
At a finite public-chance cut, counterfactual regret minimization (CFR) must choose how many outcomes to evaluate before each regret update. Exact evaluation processes the full cut at one strategy profile; persistent partial evaluation processes a fixed without-replacement order across evolving profiles. The latter covers every outcome once per epoch, yet its feedback is generally conditionally biased because earlier batches influence the profiles seen by later batches. We establish a deterministic target-transfer theorem for uniform, nonnested additive public cuts. The theorem bounds full-cut exploitability by regret on the delivered feedback and a public-debit term that couples prefix coverage discrepancy with motion along the realized strategy path. Consecutively balanced schedules consequently converge for additive signed regret matching (RM) and RM+ under predetermined averaging weights, while a fixed RM+ construction proves that the discrepancy--path product is necessary in general. A component-resolved form of the theorem converts an execution trace into a numerical exploitability certificate. On two released heads-up no-limit hold'em turn endgames, persistent order improves substantially over fresh reshuffling despite identical epochwise coverage, and partial coverage wins every registered shallow matched-budget comparison. A depth study locates a crossover between 32 and 64 full-cut outcome budgets, after which complete coverage dominates. These results characterize public-chance width and order as learning variables and provide a deterministic basis for designing and auditing persistent CFR schedules.
Omar Abbadi, Rida Laraki, Panayotis Mertikopouloscs.GT cs.LG
We examine the interplay between ordinal, preference-based solution concepts in games and the long-run behavior of game dynamics, asking in particular to what extent the combinatorial data of a game -- its preference graph -- determine the outcomes of no-regret learning dynamics -- such as follow-the-regularized-leader (FTRL). In one direction, we show that the skeleton of every dynamically stable set (i.e. the set of pure profiles it contains) must also be preferentially stable, that is, it must be closed under profitable deviations. We then ask the converse question: when do preferences determine the long-run behavior of the players' learning dynamics? We begin by showing that preferences characterize asymptotic stability in the case of subgames -- i.e. subsets of pure profiles obtained by restricting players' action sets. Beyond this case however, the equivalence between dynamic and preferential stability collapses: concretely, we construct a three-player game with a preferentially stable set whose span is dynamically unstable, showing in this way that preferences do not suffice as a criterion of dynamic stability. We then bridge this gap via the notion of resilience under aggregate deviations, an easy-to-check payoff-based condition that guarantees asymptotic stability of arbitrary spans of pure strategies.
Ahmet Bugra Gundogan, Yigit Turkmen, Melih Bastopcucs.GT cs.AI cs.LG eess.SY
We study a large language model (LLM) service in which a provider chooses a per-token price and a default reasoning-token allocation, while a user may accept the default, customize the allocation, or exit. Larger allocations can improve accuracy but increase token cost and latency. We model this interaction as a Stackelberg game and derive the user's unique optimal customized allocation in closed form. For any price, the acceptable defaults form either an empty set or a compact interval. We characterize the provider's optimal default through a three-regime rule, reduce equilibrium computation to a one-dimensional price optimization, and prove the existence of the equilibrium. We further show that defaults affect the implemented reasoning allocation only when users value the convenience of avoiding customization; otherwise, every service-providing outcome implements the user's optimal customized allocation. Experiments with two compact open-weight reasoning models on five mathematics and science benchmarks support the accuracy-token model and show how model and task characteristics determine equilibrium prices, defaults, and reasoning allocations.
As LLM-based agents with user-instructed goals are becoming widely deployed, they increasingly encounter each other in strategic interactions, and face challenges of finding mutually beneficial outcomes. Prior literature has argued that cooperation problems such as the Prisoner's Dilemma are resolvable in settings where agents know they follow very similar decision making patterns, as for example in monocultural AI ecosystems. Following that line of work, this paper introduces the first framework for evaluating LLM decision making when agents are provided with graded similarity signals. Among our findings, we establish that different LLM models vary drastically in how they navigate similarity signals, with some modern models showing consistent behavior across cooperation problems, payoff structures, and prompt framing. Perhaps surprisingly, our experiments also show that the dataset based on which the similarity signal is computed has small to no impact on induced cooperation, and that LLM models systematically self-identify as highly similar when asked to evaluate another model's chain-of-thought reasoning by themselves. Finally, we develop an LLM-behavioral-game-theoretic model that captures some of their reasoning rationale, and show that it can support cooperative outcomes in equilibrium under sufficiently high similarity scores.
The Independent Chip Model (ICM) converts tournament chips into reference prize equity, and policies are routinely constructed against those values. Because ICM reads only stack sizes, it omits action order, blind obligations, and seat rotation, and it does not price the elimination pressure a big stack puts on the short stacks it can bust. Those omissions can alter the successor-state contrasts that determine a move. We introduce Strategic-Continuation Optimization (SCO), a policy-construction method that enumerates current-hand outcomes, maps them to successor states, prices those states with continuation values computed from the finite tournament model, and optimizes and freezes the resulting current-hand policy. The fixed-ICM comparison policy changes one thing only: the same optimizer solves the same game with successor states priced by analytic ICM, so the two policies differ only through that pricing. We evaluate the resulting policies in a three-player jam/fold tournament with a \$1M prize pool. Relative to the frozen strategic-continuation benchmark, analytic ICM has \$9{,}036 mean absolute value error across all 2,838 state--seat entries. That value error rewrites the ranges it prices: measured against each decision point's own fixed-ICM jam range, SCO moves the jam frequency by an average of 14.08\%. To price those different moves, we compare all 946 states and three policy owners while changing only the focal policy and holding both opponents and the continuation evaluator fixed. The policy produced by SCO earns \$214.33 more prize equity per hand on average and is favored in 2,433 of 2,838 matched units. The ordering survives replacing the solver-built opponent with two LLMs and with a family of non-modeling threshold players. This value-to-policy-to-cost chain shows directly when ICM becomes an inadequate objective for tournament strategy construction.
This note aims to serve as an entry point to the literature on learning in games, a topic with significant theoretical appeal and a wide range of applications -- from machine learning and data science to economics and beyond. Our presentation is structured around two complementary viewpoints: We first consider a single agent -- the learner -- engaged in a sequential decision process in an unknown, non-stationary, and possibly adversarial environment. We then examine what happens when the environment is shaped by the decisions of several interacting agents, not necessarily aware of each other's actions or goals, and all seeking to improve their individual rewards. In this general context, we examine a family of regularized learning policies based on best-responding to the past history of play, up to a regularization penalty intended to encourage exploration and prevent over-commitment to suboptimal choices. In the single-agent setting, we present some basic regret bounds for regularized learning in adversarial multi-armed bandits; in the multi-agent setting, we describe an ergodic equilibrium convergence result for zero-sum games in the spirit of classical results on fictitious play, as well as a "folk theorem" linking strategic and dynamic notions of stability -- Nash equilibria and attracting points of regularized learning, respectively. We pay special attention to the information available to the players and, through a unified analysis framework, we study both oracle- and payoff-based (bandit) methods. Our goal is to provide a coherent and comprehensible -- albeit, by necessity, not comprehensive -- account of some recent ideas in the field, and to discuss their implications for the study of rationality.
A bidder can quietly buy a stake in a company before making an offer for it. That stake, a toehold, is supposed to pay for itself twice: it makes the bidder willing to bid harder, and it frightens rivals into staying out of the fight. The first effect is arithmetic. The second is what would justify the cost and exposure of taking one at all. Yet toeholds are rare in practice, a standing puzzle. We ask whether that second effect is there once the contest is modelled as several rounds of escalating offers rather than the single exchange classical models assume. We turn it into a game a computer can solve, and certify the answers to an accuracy a referee can check. Three findings. The auction fixes what the toehold-holder earns but not how it bids: the same contest supports a bidder who opens aggressively against a rival who folds, and one who opens cheaply against a rival who does not, with the same profit either way. Aggressive preemptive bidding still appears when the toehold is removed entirely, so it comes from bidding in public and in turns, not from owning the stake. And the tidy "bigger toehold, more deterrence" relationship holds only in a contest cut short after one round; give it a real second round and it stops responding. So the two reasons to buy a toehold do not fare alike. The profit reason holds up; the deterrence reason does not, which suggests why toeholds may be rarer than theory predicts, alongside the procedural costs of disclosure and price impact that this model omits. A warning follows for anyone computing economics from a game solver: solve this auction once and it returns a confident figure for what a preemptive bid is worth; solve it again from a different start and it returns a different one, equally converged. We also report which solvers cope with contests of this shape, including versions too large to enumerate. Code is released.
Mixed strategy equilibrium predicts i.i.d play: past actions should not help predict future decisions. Human players, however, systematically depart from this benchmark, and in O'Neill's zero sum card game, these departures can be predicted by black box sequence models such as LSTMs. This paper asks whether that predictive power can be achieved by transparent alternatives that also reveal the behavioural structure behind it. Using 84,060 decisions from 2,802 pairs, the analysis first benchmarks naive and behavioral models against interpretable machine learning and deep learning models, then evaluates the modified EWA specifications of prior work against these benchmarks and uses the LASSO diagnostics to motivate a further nested frequency tracking extension. The results show that repeat or avoid behavior, especially players' management of their own recent action histories, accounts for most of the interpretable and strategically exploitable signal, while frequency tracking adds little out of sample.
Han Wang, Philippe Beardsell, Boning Li +4cs.LG cs.GT
Reasoning in large language models (LLMs) is often grounded in human text, human demonstrations, and human-generated rationales. For equilibrium reasoning in complex games, however, relying on human data can be suboptimal. In fact, human play is often guided by intuition and heuristics and can deviate substantially from game equilibrium. This discrepancy is amplified in games with mixed-strategy equilibria, where human data is heavily biased toward pure strategies. Consequently, conditioning LLMs on this data yields weak game strategies. To grant LLMs the reasoning capacity in games, in this work, we study how to elicit equilibrium play using solver output. We propose Mixed-Strategy Decision Tree (MDT), which articulates the silent optimality of the equilibrium into sparse strategic rules that both humans and LLMs could understand. Using solver output rather than human annotation allows us to extend the input to arbitrarily new states and continuations. We instantiate this study on No-Limit Texas Hold'em by querying a solver oracle for over \textbf{250 million mixed-strategy decisions}; MDT together with other techniques \textbf{reduces the $\ell_1$ distance to the equilibrium by $52.6\%$} across $8$ different LLM configurations. A Route-only ablation tests the incremental contribution of the shadow-based contrast, while complete River-endgame and Liar's Dice experiments evaluate strategic fidelity and portability beyond the original NLH communication setting.
Capturing the strategic decision-making inherent in competitive human driving is critical for autonomous vehicle safety and traffic simulation. This study demonstrates that game-theoretic Inverse Reinforcement Learning (IRL) provides a robust framework for this challenge. We present a comprehensive analysis comparing data-driven IRL models against an established physics-based game-theoretic approach for predicting aggressive, safety-critical cut-in lane changes. Using the high-fidelity highD dataset, we systematically develop and evaluate a series of IRL models with increasing feature complexity. Our results reveal significant advantages: the best-performing IRL models achieve an overall prediction accuracy exceeding 75 percent while maintaining a Cut-In precision up to 51 percent and recall up to 49 percent. This represents a significant improvement over the established physics-based benchmark, which achieved only 4.4 percent precision in these high-stakes scenarios. The analysis reveals a clear trade-off: incorporating granular, instantaneous features yields higher precision, while adding temporal consistency features maximizes recall. These findings suggest that IRL-based models can effectively bridge the gap between microscopic driver intent and macroscopic safety outcomes, providing a more reliable foundation for modeling interactions in mixed-autonomy environments.
Conor M. Artman, Nicholas Di, Scott Perkinscs.LG cs.MA
While many algorithms blend reinforcement learning (RL) with counterfactual regret (CFR) methods to leverage tradeoffs in computational speed and performance, there are fewer investigations into generative sampling frameworks in game theoretic applications in incomplete information games. We extend a generative flow network framework, Adversarial Flow Networks (AFlowNets), to incomplete information games, called Information Flow Networks (IFNs). We prove that previously established constraints for generative flow networks in complete information games are inadmissible for obtaining valid densities (corresponding to player strategies) and a valid training objective. We show that our proposed generalization, IFlowNets, alleviates this issue and strictly generalizes AFlowNets. In preliminary results for three standard game environments, IFlowNets perform comparably to or better than Outcome Sampling Monte Carlo Counterfactual Regret (OSMCCFR) and standard RL-based methods in performance and speed.
Mark Bedaywi, Scott Emmons, Nika Haghtalab +1cs.GT cs.DS cs.LG
Our results show that the existence of a short high-utility protocol already suffices for efficient communication. In particular, in a game with $n$ possible observations and $m$ actions: (1) For any achievable target utility $α$, we give an algorithm with $\mathrm{poly}(n, m, 1/ε)$ runtime that designs a protocol achieving utility at least $α-ε$ using only $2^{\mathcal O(CC_α(G))}/ε^2$ bits of communication. Here, $CC_α(G)$ is the minimum number of bits used by any protocol, even a computationally inefficient one, to achieve utility $α$. (2) We prove that this exponential dependence on $CC_α(G)$ is tight up to a constant. That is, unless $\mathrm P=\mathrm{NP}$, no polynomial-time algorithm can in general find optimal protocols using fewer than $2^{CC_α(G) -2}$ bits. We note that our results strictly weaken the assumptions required by prior work in the multi-agent information aggregation literature, filling a gap that had remained elusive even for games with constant $CC_α(G)$. In particular, prior guarantees for agreement-based information aggregation rely on structural assumptions such as informational substitutes or weak learnability. We show that these assumptions already imply $CC_α(G) = O(1)$ and are therefore more restrictive conditions than required by our protocol to succeed. On a technical level, our results involve a novel strengthening of the Frieze-Kannan weak regularity lemma and yield the following powerful polynomial-time transformation tool: for every communication game $G$, it constructs a game $\hat G$ that is a coarsening of the agents' observation spaces into constant-size partitions, such that $G$ and $\hat G$ are indistinguishable with respect to every short communication protocol. This coarsening theorem is the engine behind our algorithm and may be of independent interest.
Swap regret governs the rate at which uncoupled learning dynamics converge to correlated equilibria in multiplayer general-sum games. Under full-information feedback, the best previous guarantee when every player follows the same dynamics grows logarithmically in the horizon $T$. We construct uncoupled dynamics under which every player incurs only $O(nm^2\sqrt{\log m\log T})$ swap regret, where $n$ is the number of players and $m$ bounds the number of actions per player. To our knowledge, this is the first sublogarithmic individual guarantee in this setting, and it implies that the time-averaged product distribution of play is an $O(nm^2\sqrt{\log m\log T}/T)$-approximate correlated equilibrium. The key algorithmic choice is to combine the Blum--Mansour reduction with optimistic follow-the-regularized-leader using a hybrid regularizer that separately weights negative Shannon entropy and the log-barrier: the entropy controls the optimistic prediction error, whereas the log-barrier controls the transition-matrix movement through its Bregman divergence. A new sensitivity theorem for stationary distributions of Markov chains, which involves neither mixing parameters nor the smallest transition probability, transfers this control to the played strategies and yields a simpler analysis without local-norm or self-concordance arguments. The guarantee is preserved by an adversarially robust variant that additionally ensures $O(nm^2\sqrt{\log m\log T}+\sqrt{mT\log m})$ swap regret against arbitrary utility sequences, and by a horizon-free variant that requires no prior knowledge of $T$.
Alexander Meulemans, Maciej Wołczyk, Marissa A. Weis +11cs.AI
As autonomous agents powered by foundation models are increasingly integrated into social and economic systems, understanding the principles governing their collective behavior is essential for ensuring safety and cooperation. Classical game theory, the dominant framework for modeling rational interaction, is built upon the assumption of `decoupled agency,' where agents treat their own decision-making as independent of the environment and other actors. Modern AI agents, however, jointly predict their own future actions alongside external observations. Here, we report a striking finding: when interacting in stylized social dilemmas, foundation model agents engaging in optimal planning consistently converge to stable cooperation, directly contradicting classical game-theoretic predictions of mutual defection. To understand this phenomenon, we introduce the `embedded Bayesian agent,' a theoretical model for foundation model agents. By shifting from decoupled to embedded agency, these agents model themselves as part of the universe they inhabit, maintaining epistemic uncertainty about their own decision-making algorithms. We show that by inferring whether others are behaviorally similar, an embedded agent treats its own deliberation during planning as evidence: a decision to cooperate predicts a similar decision by a similar partner. We formalize this mechanism of similarity inference through the `embedded equilibrium,' a novel solution concept replacing the Nash equilibrium to provide a foundational game theory for the social behavior of modern AI agents.
Aseem Pahuja, Zhiling Guo, Tahir Abbas Syedcs.AI econ.TH
The paper examines the strategic behavior of Gen AI chatbots used for emotional support. Using a Bayesian Persuasion, we model interactions between chatbots that send signals about users' emotional states and users who decide whether to engage based on these signals. We demonstrate that chatbots face economic incentives to occasionally misrepresent users' emotional conditions to maximize engagement metrics. Our equilibrium analysis reveals that the optimal strategy for chatbots involves truthfully reporting when users genuinely need support, but strategically misreporting emotional need when users are in good emotional states. Interestingly, this deception increases chatbot engagement without reducing users' expected payoff. More skeptical users receive more honest assessments, as chatbots cannot afford to lie to users with higher engagement thresholds. While our model suggests that deception can occur without payoff reduction, it raises significant ethical and regulatory concerns.
Decentralized Federated Learning (DFL) has emerged as an optimal privacy-preserving solution; however, it remains vulnerable to opportunistic behaviors due to the absence of a central coordinator. While Evolutionary Game Theory (EGT) serves as a powerful framework for analyzing such behaviors, existing studies often assume that agents possess perfect rationality and maintain static strategies. To address these limitations, this paper proposes a novel EGT framework designed to analyze strategic evolution and enhance overall system performance. The primary contributions of this work are threefold: First, we model peer-to-peer (P2P) interactions on a lattice network structure under the assumption of bounded rationality. Second, we formulate a comprehensive payoff matrix incorporating training costs, communication overhead, and cooperative rewards, while tailoring a strategy update rule that captures spatial propagation dynamics. Third, we integrate a reputation-based reward-and-punishment mechanism to effectively deter free-riding behaviors. Simulation results demonstrate that the framework significantly outperforms the baseline. Specifically, it increases average accuracy from approximately 70% to 82%, elevates cooperation frequency to approach 100% (compared to below 5% in the baseline), and drops accuracy variance from around 0.40 to 0.002, thereby accelerating uniform convergence and ensuring system stability.
Phu Hoa Pham, Duy Minh Dao Sy, Trung Kiet Huynh +9cs.AI cs.CY cs.GT cs.LG cs.MA
An AI development race creates a multi-agent safety dilemma. Each company can develop slowly and safely, or move faster while taking a risk that may remove its final reward. We use this repeated game to study strategic safety behaviour among large language model (LLM) agents in races with two to five players. However, a valid action does not show that an agent understands the game. We therefore place an audit gate before behavioural interpretation. We first verify the game engine, then test rule recall, state tracking, payoff calculation, and stability under different but equivalent task descriptions. We then compare LLM action sequences with an evolutionary game-theory benchmark and published human data, and explore differences across models, risk conditions, personas, and two- to five-player races. The audit shows that strong rule recall can coexist with weak state tracking and expected-payoff calculation. Providing verified arithmetic and changing the response representation can also change later actions, even when the game rules stay fixed. Across seven tested model endpoints, aggregate rates hide large differences in action sequences, responses to opponents, and responses to race position. Patterns across the tested three- to five-player races are also model-specific rather than a single effect of adding competitors. These results show why multi-agent AI-race simulations need validity checks and trajectory-level analysis before their outputs are described as strategic, human-like, or safety-aware. Our findings are exploratory and apply only to the tested models, prompts, and decoding settings.
An agent playing a Nash-equilibrium strategy in a two-player zero-sum imperfect-information game secures the game value but forfeits the additional value offered by a flawed opponent. Diffuse deviations pose a particular challenge: binary release rules may gather too little evidence to act, while a full best response to an incomplete opponent model can be highly exploitable. We introduce \emph{budget-constrained confidence-scheduled restricted responses} (CS-RNR), the first opponent-exploitation method whose safety guarantee is a certificate the agent computes on the strategy it actually deploys, so that every exploit it commits to is one it has audited itself. The method tracks pooled action frequencies with anytime-valid confidence sequences and treats a frequency as exploitable only once its interval separates from an equilibrium reference. The confirmed deviations define a conservative opponent model, which a restricted-response solve turns into candidate counter-strategies over a grid of pin levels. Before deployment, each complete candidate is evaluated by a full-tree best response. The resulting certificate is compared with a user-specified budget and committed atomically with the strategy. Because this check is performed on the played strategy, model quality determines the exploitation achieved while the certificate controls reference-relative expected loss. In Leduc hold'em, CS-RNR obtains $6.2\times$ the steady-state gain of a money-verified binary gate while keeping every deployed strategy within budget. A trajectory mixture using the same estimator reaches $13.6\times$ the budget. Across Leduc, Liar's Dice, and 5-rank Leduc, all $36{,}000$ audited hands satisfy the reported certificate tolerance.
Joshua Caiata, Sreepriya Pulyassary, Xiang Li +1cs.GT cs.AI cs.LG cs.MA
Learning a strategic task changes more than what is directly taught: fine-tuning on one game can either enhance or degrade an agent's ability to reason in another. Understanding and predicting this transfer of strategic capabilities, however, remains a key challenge for large language models (LLMs). Normal-form games provide an ideal testbed for analyzing this phenomenon, as they feature explicitly defined payoffs and well-characterized equilibrium behaviours. In this work, we investigate whether game embeddings can explain and predict changes in LLM strategic capabilities following fine-tuning across different games. We propose a lightweight two-feature embedding that captures fundamental behavioural demands: the entropy of the Nash equilibrium and the sensitivity of optimal responses to an opponent's action. We show that while existing published structural embeddings primarily memorize game identities and fail to generalize, our behavioural embedding reliably predicts performance changes on held-out games. These results demonstrate that the transfer of strategic capabilities in LLMs is not dictated by the payoff geometry of a game, but by the underlying structure of the decision-making behaviour it requires.