Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games, and algorithmic game theory.
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In multi-agent tasks, the central challenge lies in the dynamic adaptation of strategies. However, directly conditioning on opponents' strategies is intractable in the prevalent deep reinforcement learning paradigm due to a fundamental ``representational bottleneck'': neural policies are opaque, high-dimensional parameter vectors that are incomprehensible to other agents. In this work, we propose a paradigm shift that bridges this gap by representing policies as human-interpretable source code and utilizing Large Language Models (LLMs) as approximate interpreters. This programmatic representation allows us to operationalize the game-theoretic concept of \textit{Program Equilibrium}. We reformulate the learning problem by utilizing LLMs to perform optimization directly in the space of programmatic policies. The LLM functions as a point-wise best-response operator that iteratively synthesizes and refines the ego agent's policy code to respond to the opponent's strategy. We formalize this process as \textit{Programmatic Iterated Best Response (PIBR)}, an algorithm where the policy code is optimized by textual gradients, using structured feedback derived from game utility and runtime unit tests. We demonstrate that this approach effectively solves several standard coordination matrix games and a cooperative Level-Based Foraging environment.
With the rapid advancement of generative AI (GenAI), mechanism design adapted to its unique characteristics poses new theoretical and practical challenges. Unlike traditional goods, content from one domain can enhance the training and performance of GenAI models in other domains. For example, OpenAI's video generation model Sora (Liu et al., 2024b) relies heavily on image data to improve video generation quality. In this work, we study nonlinear procurement mechanism design under data transferability, where online platforms employ both human creators and GenAI to satisfy cross-domain content demand. We propose optimal mechanisms that maximize either platform revenue or social welfare and identify the specific properties of GenAI that make such high-dimensional design problems tractable. Our analysis further reveals which domains face stronger competitive pressure and which tend to experience overproduction. Moreover, the growing role of data intermediaries, including labeling companies such as Scale AI and creator organizations such as The Wall Street Journal, introduces a third layer into the traditional platform-creator structure. We show that this three-layer market can result in a lose-lose outcome, reducing both platform revenue and social welfare, as large pre-signed contracts distort creators' incentives and lead to inefficiencies in the data market. These findings suggest a need for government regulation of the GenAI data ecosystem, and our theoretical insights are further supported by numerical simulations.
In Bayesian single-item auctions, a monotone bidding strategy--one that prescribes a higher bid for a higher value type--can be equivalently represented as a partition of the quantile space into consecutive intervals corresponding to increasing bids. Kumar et al. (2024) prove that agile online gradient descent (OGD), when used to update a monotone bidding strategy through its quantile representation, is strategically robust in repeated first-price auctions: when all bidders employ agile OGD in this way, the auctioneer's average revenue per round is at most the revenue of Myerson's optimal auction, regardless of how she adjusts the reserve price over time. In this work, we show that this strategic robustness guarantee is not unique to agile OGD or to the first-price auction: any no-regret learning algorithm, when fed gradient feedback with respect to the quantile representation, is strategically robust, even if the auction format changes every round, provided the format satisfies allocation monotonicity and voluntary participation. In particular, the multiplicative weights update (MWU) algorithm simultaneously achieves the optimal regret guarantee and the best-known strategic robustness guarantee. At a technical level, our results are established via a simple relation that bridges Myerson's auction theory and standard no-regret learning theory. This showcases the potential of translating standard regret guarantees into strategic robustness guarantees for specific games, without explicitly minimizing any form of swap regret.
In this paper, we settle the problem of learning optimal linear contracts from data in the offline setting, where agent types are drawn from an unknown distribution and the principal's goal is to design a contract that maximizes her expected utility. Specifically, our analysis shows that the simple Empirical Utility Maximization (EUM) algorithm yields an $\varepsilon$-approximation of the optimal linear contract with probability at least $1-δ$, using just $O(\ln(1/δ) / \varepsilon^2)$ samples. This result improves upon previously known bounds and matches a lower bound from Duetting et al. [2025] up to constant factors, thereby proving its optimality. Our analysis uses a chaining argument, where the key insight is to leverage a simple structural property of linear contracts: their expected reward is non-decreasing. This property, which holds even though the utility function itself is non-monotone and discontinuous, enables the construction of fine-grained nets required for the chaining argument, which in turn yields the optimal sample complexity. Furthermore, our proof establishes the stronger guarantee of uniform convergence: the empirical utility of every linear contract is a $\varepsilon$-approximation of its true expectation with probability at least $1-δ$, using the same optimal $O(\ln(1/δ) / \varepsilon^2)$ sample complexity.
Collective Investment Algorithms (CoinAlgs) are increasingly popular systems that deploy shared trading strategies for investor communities. Their goal is to democratize sophisticated -- often AI-based -- investing tools. We identify and demonstrate a fundamental profitability-fairness tradeoff in CoinAlgs that we call the CoinAlg Bind: CoinAlgs cannot ensure economic fairness without losing profit to arbitrage. We present a formal model of CoinAlgs, with definitions of privacy (incomplete algorithm disclosure) and economic fairness (value extraction by an adversarial insider). We prove two complementary results that together demonstrate the CoinAlg Bind. First, privacy in a CoinAlg is a precondition for insider attacks on economic fairness. Conversely, in a game-theoretic model, lack of privacy, i.e., transparency, enables arbitrageurs to erode the profitability of a CoinAlg. Using data from Uniswap, a decentralized exchange, we empirically study both sides of the CoinAlg Bind. We quantify the impact of arbitrage against transparent CoinAlgs. We show the risks posed by a private CoinAlg: Even low-bandwidth covert-channel information leakage enables unfair value extraction.
2601.00329We study coalition structure generation (CSG) when coalition values are not given but must be learned from episodic observations. We model each episode as a sparse linear regression problem, where the realised payoff \(Y_t\) is a noisy linear combination of a small number of coalition contributions. This yields a probabilistic CSG framework in which the planner first estimates a sparse value function from \(T\) episodes, then runs a CSG solver on the inferred coalition set. We analyse two estimation schemes. The first, Bayesian Greedy Coalition Pursuit (BGCP), is a greedy procedure that mimics orthogonal matching pursuit. Under a coherence condition and a minimum signal assumption, BGCP recovers the true set of profitable coalitions with high probability once \(T \gtrsim K \log m\), and hence yields welfare-optimal structures. The second scheme uses an \(\ell_1\)-penalised estimator; under a restricted eigenvalue condition, we derive \(\ell_1\) and prediction error bounds and translate them into welfare gap guarantees. We compare both methods to probabilistic baselines and identify regimes where sparse probabilistic CSG is superior, as well as dense regimes where classical least-squares approaches are competitive.
We introduce the concept of multilevel fair allocation of resources with tree-structured hierarchical relations among agents. While at each level it is possible to consider the problem locally as an allocation of an agent to its children, the multilevel allocation can be seen as a trace capturing the fact that the process is iterated until the leaves of the tree. In principle, each intermediary node may have its own local allocation mechanism. The main challenge is then to design algorithms which can retain good fairness and efficiency properties. In this paper we propose two original algorithms under the assumption that leaves of the tree have matroid-rank utility functions and the utility of any internal node is the sum of the utilities of its children. The first one is a generic polynomial-time sequential algorithm that comes with theoretical guarantees in terms of efficiency and fairness. It operates in a top-down fashion -- as commonly observed in real-world applications -- and is compatible with various local algorithms. The second one extends the recently proposed General Yankee Swap to the multilevel setting. This extension comes with efficiency guarantees only, but we show that it preserves excellent fairness properties in practice.
We formulate two-party policy competition as a two-player non-cooperative game, generalizing Lin et al.'s work (2021). Each party selects a real-valued policy vector as its strategy from a compact subset of Euclidean space, and a voter's utility for a policy is given by the inner product with their preference vector. To capture the uncertainty in the competition, we assume that a policy's winning probability increases monotonically with its total utility across all voters, and we formalize this via an affine isotonic function. A player's payoff is defined as the expected utility received by its supporters. In this work, we first test and validate the isotonicity hypothesis through voting simulations. Next, we prove the existence of a pure-strategy Nash equilibrium (PSNE) in both one- and multi-dimensional settings. Although we construct a counterexample demonstrating the game's non-monotonicity, our experiments show that a decentralized gradient-based algorithm typically converges rapidly to an approximate PSNE. Finally, we present a grid-based search algorithm that finds an $ε$-approximate PSNE of the game in time polynomial in the input size and $1/ε$.
We study a sequential mechanism design problem in which a principal seeks to elicit truthful reports from multiple rational agents while starting with no prior knowledge of agents' beliefs. We introduce Distributionally Robust Adaptive Mechanism (DRAM), a general framework combining insights from both mechanism design and online learning to jointly address truthfulness and cost-optimality. Throughout the sequential game, the mechanism estimates agents' beliefs and iteratively updates a distributionally robust linear program with shrinking ambiguity sets to reduce payments while preserving truthfulness. Our mechanism guarantees truthful reporting with high probability while achieving $\tilde{O}(\sqrt{T})$ cumulative regret, and we establish a matching lower bound showing that no truthful adaptive mechanism can asymptotically do better. The framework generalizes to plug-in estimators, supporting structured priors and delayed feedback. To our knowledge, this is the first adaptive mechanism under general settings that maintains truthfulness and achieves optimal regret when incentive constraints are unknown and must be learned.
2512.21657We study the classical coalition structure generation (CSG) problem and compare the anytime behavior of three algorithmic paradigms: dynamic programming (DP), MILP branch-and-bound, and sparse relaxations based on greedy or $l_1$-type methods. Under a simple random "sparse synergy" model for coalition values, we prove that sparse relaxations recover coalition structures whose welfare is arbitrarily close to optimal in polynomial time with high probability. In contrast, broad classes of DP and MILP algorithms require exponential time before attaining comparable solution quality. This establishes a rigorous probabilistic anytime separation in favor of sparse relaxations, even though exact methods remain ultimately optimal.
In multi-agent tasks, the central challenge lies in the dynamic adaptation of strategies. However, directly conditioning on opponents' strategies is intractable in the prevalent deep reinforcement learning paradigm due to a fundamental ``representational bottleneck'': neural policies are opaque, high-dimensional parameter vectors that are incomprehensible to other agents. In this work, we propose a paradigm shift that bridges this gap by representing policies as human-interpretable source code and utilizing Large Language Models (LLMs) as approximate interpreters. This programmatic representation allows us to operationalize the game-theoretic concept of \textit{Program Equilibrium}. We reformulate the learning problem by utilizing LLMs to perform optimization directly in the space of programmatic policies. The LLM functions as a point-wise best-response operator that iteratively synthesizes and refines the ego agent's policy code to respond to the opponent's strategy. We formalize this process as \textit{Programmatic Iterated Best Response (PIBR)}, an algorithm where the policy code is optimized by textual gradients, using structured feedback derived from game utility and runtime unit tests. We demonstrate that this approach effectively solves several standard coordination matrix games and a cooperative Level-Based Foraging environment.
Online fantasy cricket has emerged as large-scale competitive systems in which participants construct virtual teams and compete based on real-world player performances. This massive growth has been accompanied by important questions about whether outcomes are primarily driven by skill or chance. We develop a statistical framework to assess the role of skill in determining success on these platforms. We construct and analyze a range of deterministic and stochastic team selection strategies, based on recent form, historical statistics, statistical optimization, and multi-criteria decision making. Strategy performance is evaluated based on points, ranks, and payoff under two contest structures Mega and 4x or Nothing. An extensive comparison between different strategies is made to find an optimal set of strategies. To capture adaptive behavior, we further introduce a dynamic tournament model in which agent populations evolve through a softmax reweighting mechanism proportional to positive payoff realizations. We demonstrate our work by running extensive numerical experiments on the IPL 2024 dataset. The results provide quantitative evidence in favor of the skill element present in online fantasy cricket platforms.
Autonomous multi-agent systems are fundamentally fragile: they struggle to solve the Hayekian Information problem (eliciting dispersed private knowledge) and the Hurwiczian Incentive problem (aligning local actions with global objectives), making coordination computationally intractable. I introduce Mechanism-Based Intelligence (MBI), a paradigm that reconceptualizes intelligence as emergent from the coordination of multiple "brains", rather than a single one. At its core, the Differentiable Price Mechanism (DPM) computes the exact loss gradient $$ \mathbf{G}_i = - \frac{\partial \mathcal{L}}{\partial \mathbf{x}_i} $$ as a dynamic, VCG-equivalent incentive signal, guaranteeing Dominant Strategy Incentive Compatibility (DSIC) and convergence to the global optimum. A Bayesian extension ensures incentive compatibility under asymmetric information (BIC). The framework scales linearly ($\mathcal{O}(N)$) with the number of agents, bypassing the combinatorial complexity of Dec-POMDPs and is empirically 50x faster than Model-Free Reinforcement Learning. By structurally aligning agent self-interest with collective objectives, it provides a provably efficient, auditable and generalizable approach to coordinated, trustworthy and scalable multi-agent intelligence grounded in economic principles.
2512.16895Core stability is a natural and well-studied notion for group fairness in multi-winner voting, where the task is to select a committee from a pool of candidates. We study the setting where voters either approve or disapprove of each candidate; here, it remains a major open problem whether a core-stable committee always exists. In this work, we develop an approach based on mixed-integer linear programming for deciding whether and when core-stable committees are guaranteed to exist. In contrast to SAT-based approaches popular in computational social choice, our method can produce proofs for a specific number of candidates independent of the number of voters. In addition to these computational gains, our program lends itself to a novel duality-based reformulation of the core stability problem, from which we obtain new existence results in special cases. Further, we use our framework to reveal previously unknown relationships between core stability and other desirable properties, such as notions of priceability.
2512.16570Online Resource Allocation addresses the problem of efficiently allocating limited resources to buyers with incomplete knowledge of future requests. In our setting, buyers arrive sequentially demanding a set of items, each with a value drawn from a known distribution. We study environments where buyers' valuations exhibit complementarities. In such settings, standard item-pricing mechanisms fail to leverage item multiplicities, while existing static bundle-pricing mechanisms rely on problem-specific arguments that do not generalize. We develop a unified technique for online resource allocation with complementarities for three domains: (i) single-minded combinatorial auctions with maximum bundle size $d$, (ii) general single-minded combinatorial auctions, and (iii) a graph-based routing model in which buyers request to route a unit of flow from a source node $s$ to a target node $t$ in a capacitated graph. Our approach yields static and anonymous bundle-pricing mechanisms whose performance improves exponentially with item capacities. For the $d$-single-minded setting with minimum item capacity $B$, we obtain an $O(d^{1/B})$-competitive mechanism, recovering the known $O(d)$ bound for unit capacities ($B=1$) and achieving exponentially better guarantees as capacities grow. For general single-minded combinatorial auctions and the graph-routing model, we obtain $O(m^{1/(B+1)})$-competitive mechanisms, where $m$ is the number of items. We complement these results with information-theoretic lower bounds. We show that no online algorithm can achieve a competitive ratio better than $Ω((m/\ln m)^{1/(B+2)})$ in the general single-minded setting and $Ω((d/\ln d)^{1/(B+1)})$ in the $d$-single-minded setting. In doing so, we reveal a deep connection to the extremal combinatorics problem of determining the maximum number of qualitatively independent partitions of a ground set.
2512.16514A central challenge in blockchain tokenomics is aligning short-term performance incentives with long-term decentralization goals. We propose a framework for algorithmic monetary policies that navigates this tradeoff in repeated participation games. Agents, characterized by type (capability) and stake, choose to participate or abstain at each round; the policy (probabilistically) selects high-type agents for task execution (maximizing throughput) while distributing rewards to sustain decentralization. We analyze equilibria under two agent behaviors: myopic (short-term utility maximization) and foresighted (multi-round planning). For myopic agents, performance-centric policies risk centralization, but foresight enables stable decentralization with some volatility to the token value. We further discuss virtual stake--a hybrid of type and stake--as an alternative approach. We show that the initial virtual stake distribution critically impacts long-term outcomes, suggesting that policies must indirectly manage decentralization.
Recently, joint advertising has gained significant attention as an effective approach to enhancing the efficiency and revenue of advertising slot allocation. Unlike traditional advertising, which allocates advertising slots exclusively to a single advertiser, joint advertising displays advertisements from brands and stores that have established a joint selling relationship within the same advertising slot. However, existing approaches often struggle to accommodate both joint and traditional advertising frameworks, thereby limiting the revenue potential and generalizability of joint advertising. Furthermore, these methods are constrained by two critical limitations: they generally neglect the influence of global externalities, and they fail to address the bidding variability stemming from multi-party advertiser participation. Collectively, these limitations present substantial challenges to the design of joint auction mechanisms. To address these challenges, we propose a Joint Auction Framework incorporating Externalities and Adaptation, and leverage the automated mechanism design (AMD) method through our proposed JEANet to compute joint auction mechanisms that satisfy the conditions of individual rationality (IR) and approximate dominant strategy incentive compatibility (DSIC). As the first AMD method to integrate global externalities into joint auctions, JEANet dynamically adapts to the bidding characteristics of multi-party advertiser and enables unified auctions that integrate both joint and traditional advertising. Extensive experimental results demonstrate that JEANet outperforms state-of-the-art baselines in multi-slot joint auctions.
Top-tier academic conferences are failing under the strain of two irreconcilable roles: (1) rapid dissemination of all sound research and (2) scarce credentialing for prestige and career advancement. This conflict has created a reviewer roulette and anonymous tribunal model - a zero-cost attack system - characterized by high-stakes subjectivity, turf wars, and the arbitrary rejection of sound research (the equivalence class problem). We propose the Impact Market (IM), a novel three-phase system that decouples publication from prestige. Phase 1 (Publication): All sound and rigorous papers are accepted via a PC review, solving the "equivalence class" problem. Phase 2 (Investment): An immediate, scarce prestige signal is created via a futures market. Senior community members invest tokens into published papers, creating a transparent, crowdsourced Net Invested Score (NIS). Phase 3 (Calibration): A 3-year lookback mechanism validates these investments against a manipulation-resistant Multi-Vector Impact Score (MVIS). This MVIS adjusts each investor's future influence (their Investor Rating), imposing a quantifiable cost on bad actors and rewarding accurate speculation. The IM model replaces a hidden, zero-cost attack system with a transparent, accountable, and data-driven market that aligns immediate credentialing with long-term, validated impact. Agent-based simulations demonstrate that while a passive market matches current protocols in low-skill environments, introducing investor agency and conviction betting increases the retrieval of high-impact papers from 28% to over 85% under identical conditions, confirming that incentivized self-selection is the mechanism required to scale peer review.
Being able to find small Petri nets with the same behaviour as formal specifications of concurrent systems benefits both effective verification and practical implementation of such systems. This paper considers specifications given in the form of compositionally defined safe nets. The paper discusses a novel concept of distributed place which implements the behaviour of an individual net place. It is shown that if distributed places cover a safe Petri net, then it is possible to delete some places without changing the behaviour. Crucially, the reduction is both static and local, making it computationally feasible in practice. The resulting reduction technique is then applied to an algebra of safe Petri nets (boxes) derived compositionally from process (box) expressions. Though the original derivation can yield exponentially large boxes, prior research demonstrated that if a box expression does not involve cyclic behaviours, the exponential number of places can be reduced down to polynomial (quadratic). In this paper, using distributed places, it is show that similar optimisation can also be achieved in the case of process expressions with iteration.
2512.13244We consider a scheduling problem of strategic agents representing jobs of different weights. Each agent has to decide on one of a finite set of identical machines to get their job processed. In contrast to the common and exclusive focus on makespan minimization, we want the outcome to be fair under strategic considerations of the agents. Two natural properties are credibility, which ensures that the assignment is a Nash equilibrium and equality, requiring that agents with equal-weight jobs are assigned to machines of equal load. We combine these two with a hierarchy of fairness properties based on envy-freeness together with several relaxations based on the idea that envy seems more justified towards agents with a higher weight. We present a complete complexity landscape for satisfiability and decision versions of these properties, alone or in combination, and study them as structural constraints under makespan optimization. For our positive results, we develop a unified algorithmic approach, where we achieve different properties by fine-tuning key subroutines.
2512.12910We introduce, to our knowledge, the first direct second-order method for computing Nash equilibria in two-player zero-sum games. To do so, we construct a Douglas-Rachford-style splitting formulation, which we then solve with a semi-smooth Newton (SSN) method. We show that our algorithm enjoys local superlinear convergence. In order to augment the fast local behavior of our SSN method with global efficiency guarantees, we develop a hybrid method that combines our SSN method with the state-of-the-art first-order method for game solving, Predictive Regret Matching$^+$ (PRM$^+$). Our hybrid algorithm leverages the global progress provided by PRM$^+$, while achieving a local superlinear convergence rate once it switches to SSN near a Nash equilibrium. Numerical experiments on matrix games demonstrate order-of-magnitude speedups over PRM$^+$ for high-precision solutions.
Generative Artificial Intelligence (GenAI) enables digital representatives to make decisions on behalf of team members in collaborative tasks, but faces challenges in accurately representing preferences. While supplying GenAI with detailed personal information improves representation fidelity, feasibility constraints make complete information access impractical. We bridge this gap by developing a game-theoretic framework that models strategic information revelation to GenAI in collective decision-making. The technical challenges lie in characterizing members' equilibrium behaviors under interdependent strategies and quantifying the imperfect preference learning outcomes by digital representatives. Our contribution includes closed-form equilibrium characterizations that reveal how members strategically balance team decision preference against communication costs. Our analysis yields an interesting finding: Conflicting preferences between team members drive competitive information revelation, with members revealing more information than those with aligned preferences. While digital representatives produce aggregate preference losses no smaller than direct participation, individual members may paradoxically achieve decisions more closely aligned with their preferences when using digital representatives, particularly when manual participation costs are high or when GenAI systems are sufficiently advanced.