How can we design a market of human-generated content for use in training AI models that both enables technological progress and preserves individual incentives for high-quality content creation? Existing approaches take polar positions: a "free-for-all" model based on fair use and a "strong intellectual property rights" model. We show that both fail: Free-for-all does not compensate creators, and -- by modeling as a static Stackelberg game -- strong intellectual property rights also underpower creative incentives. We find this especially true for more innovative creators, a phenomenon we term the "originality penalty." Extending this insight to a dynamic model, we find another market failure undermining AI model performance, even for an initially good model: Such a model induces greater reliance by humans on AI-assisted creation, resulting in homogenized content feeding back into training, which degrades the model performance -- a "curse of precision." We further propose a market design with a data intermediary internalizing cross-creator externalities and subsidizing innovative contributions, thereby restoring efficiency.

We consider the strategic facility location problem in $\ell_q(\mathbb R^d)$ spaces where the social cost is defined by an arbitrary $p$-norm of the individual costs. While the optimal approximation ratios for deterministic strategyproof mechanisms are well established in the $d = 1$ setting, the guarantees for multi-dimensional spaces under an arbitrary $p$-norm are less understood. In this work, we analyze the well-studied, strategyproof coordinate-wise median (CM) mechanism and provide approximation guarantees for these generalized social costs. For $d = 2$, we establish tight approximation ratios for all $p, q \geq 1$. In particular, we show that the CM mechanism is a $2^{1 - 1/ \max(p, q)}$-approximation, resolving a conjecture of Goel and Hann-Caruthers (Social Choice and Welfare, 2023). Furthermore, for $d\geq 3$, we give upper bounds on the approximation ratio of the CM mechanism for arbitrary $p$-norm social costs, generalizing the recent result of Gravin and Jia (STOC, 2025) for the utilitarian social cost. Remarkably, we show that this approximation ratio never exceeds 3, regardless of the dimension.

We study a shared infrastructure deployed by an Infrastructure Provider (InP) and used by multiple firms that generate revenues through resource usage. We focus on a challenging setting where: (i) infrastructure deployment requires substantial upfront investment, which the InP must recover via payments by firms that depend on their uncertain future revenues; (ii) firms' resource usage is jointly influenced by exogenous factors, infrastructure pricing, operational costs, and resource congestion; and (iii) firms exhibit heterogeneous risk aversion. This setting is typical in emerging technologies, e.g., Mobile Edge Computing (MEC). We formalize this setting as a novel Stackelberg game with risk-aware take-or-pay contracting and firm-side operational and congestion costs, in which the InP acts as the leader and jointly optimizes capacity dimensioning and access pricing, while firms act as followers that share the infrastructure and commit upfront to future resource usage under uncertain revenues. Followers' heterogeneous risk aversion is modeled through Conditional Value-at-Risk (CVaR). We prove the existence of a Stackelberg equilibrium (SE), in which the followers' decisions constitute a generalized Nash equilibrium, and develop a polynomial-time algorithm that computes an approximate SE with a bounded optimality gap. We also derive a lower bound on the followers' Probability of Profit (PoP). Monte Carlo simulations for a MEC case study show that higher followers' risk aversion reduces infrastructure capacity, pricing, and leader profit, while increasing followers' PoP.

Our work revolves around Fictitious Play, one of the first iterative methods that is known to converge to a Nash equilibrium in zero-sum games. In recent years, there has been a revived interest, due to applications in various machine learning problems, which has motivated a line of work on its convergence properties and on proposing new variants of the initial algorithm. Our paper is along this direction and introduces one new variant, which we refer to as Almost Greedy Fictitious Play. The proposed algorithm greedily attempts to find the optimal stepsize at each iteration but its search space is constrained and includes almost all the line between the cumulative mixed strategy and the current best response. Our main result is that the method achieves an instance dependent convergence rate of $\mathcal{O}(1/T)$ with respect to the duality gap. This matches the rate of Continuous Fictitious Play, and offers an alternative to discretization. We complement our theoretical findings with experiments that demonstrate the effectiveness of the method.

Electoral control is the study of whether an attacker, by structural changes on an election such as adding/deleting/partitioning voters or candidates, can affect the winner in some desired way. Forty-four such attack types are often considered standard, and recently there has been work showing that sometimes the attack types -- though seemingly distinct -- in fact "collapse," that is, for every input, either the attacker can achieve their goal under both of the control types or under neither of the control types. The papers doing this, however, while often exploiting axiomatic results that ensured collapses, found all the separations by human or computer-generated counterexamples. This left open the issue of whether even the separation direction can be driven by axiomatic results that allow large groups of separations to be almost automatically obtained. Our paper provides many such results, and we apply them to seven important voting systems, finding sixty-four new collapses and 1901 new separations. We not only give axiomatic sufficient conditions and one complete characterization result, but also identify some control-problem pairs that universally separate -- in other words, they separate under every voting rule.

Semantic communications enable AI-native wireless systems by mapping raw data into compressed task-oriented latent representations. However, independently trained agents often rely on heterogeneous latent spaces and background knowledge, leading to semantic mismatch that degrades mutual understanding and downstream task execution, especially in interferencelimited multi-user wireless networks. This paper investigates distributed latent-space alignment in multi-user semantic MIMO interference networks with cognitive radio constraints. We consider primary users and semantic-aware secondary users sharing the same wireless resources, where secondary agents must simultaneously mitigate interference and align heterogeneous semantic representations. To address this problem, we formulate semantic alignment as a non-cooperative game and derive a closed-form solution for the joint optimization of linear semantic MIMO transceivers under power and interference constraints. Exploiting the structure of the problem, we recast the original matrix valued optimization into a lower-dimensional power-allocation game, leading to an iterative semantic water-filling algorithm. We establish sufficient conditions for existence, uniqueness, and global convergence to a Nash equilibrium, explicitly relating semantic alignment properties and physical-channel interactions. Numerical results assess the performance of the proposed framework, revealing key trade-offs among semantic compression, task performance, and hierarchical spectrum access.

The Price of Anarchy (PoA) is a popular measure of the costs of decentralization in terms of efficiency losses. Almost all PoA analyses operate within a framework assuming both Cardinal Full-Comparability (CFC) and smoothness, in which case any derived bounds conveniently extend beyond pure Nash to coarse correlated equilibria and no-regret learning outcomes. However, interpersonal utility comparability is an additional assumption that generally has to be justified. Without it, cardinal utilities (e.g. defined under classical von Neumann--Morgenstern framework) are unique only up to agent-specific affine transformations, rendering both the utilitarian PoA and the classical smoothness conditions representation-dependent. In this paper, we operate under a more general Cardinal Non-Comparability (CNC) framework, under which the weighted Nash welfare is a canonical admissible aggregator. We introduce multiplicative smoothness, a product-form condition matched to the multiplicative structure of Nash welfare, and obtain PoA bounds that are CNC-invariant and extend to coarse correlated equilibria. We demonstrate applicability of our framework on single-choice welfare games, deriving the bounds through simple proof relying on multiplicative retention envelope and geometric closure. The interpretation of this bound in terms of the true cost of decentralization depends crucially on interpersonal comparability of utilities.

Classical Game Theory underpins much of AI and multiagent research, but hybrid Human AI systems require a framework in which execution authority can alternate within a digital environment. We introduce NeoGame Theory, an extension of classical Game Theory for hybrid Human AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen-Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency convergence equilibrium, providing the foundation for later extensions and computational validation.

Real-world multi-agent systems, from traffic coordination to resource allocation, are often modeled as general-sum games where individual incentives conflict with collective welfare. In these settings, the central challenge is not merely finding an equilibrium, but selecting socially desirable outcomes among many suboptimal Nash equilibria. Standard deep multi-agent reinforcement learning (MARL) methods struggle with this problem, as value-decomposition approaches are constrained by monotonicity assumptions and policy-gradient methods often converge to stable but socially inefficient equilibria. To address this limitation, we propose $\Phi$-Actor-Critic ($\Phi$-AC), a framework that leverages swap regret minimization to steer learning toward high-welfare correlated equilibria (CE). To make counterfactual regret estimation tractable in deep MARL, $\Phi$-AC employs a centralized attention critic that predicts vector-valued regrets in a single forward pass, avoiding computationally expensive counterfactual simulations. We further introduce a Lagrangian-based equilibrium selection mechanism that optimizes social welfare while enforcing stability through regret constraints. Experiments on matrix games, Multi-Agent Particle Environments (MPE), and the Melting Pot Harvest scenario demonstrate that $\Phi$-AC learns efficient and stable coordination strategies across diverse mixed-motive settings while maintaining high collective return and competitive fairness.

Conscious access in the human brain is often described as the outcome of a competition among candidate representations, but this competition is usually left at the level of mechanism or metaphor rather than analyzed as a strategic allocation problem. We introduce an access contest in which internal modules compete for a scarce broadcast slot by choosing a costly amplification effort. Access is allocated by a smooth probabilistic rule, allowing the model to interpolate between diffuse selection and winner-take-all competition. We establish pure-strategy equilibrium existence under standard convexity and bounded-benefit assumptions, and give sufficient conditions for uniqueness using diagonal strict concavity. We then analyze capture in the two-module case, and for quadratic costs, we derive a sharp threshold in the competition intensity above which capture occurs. For strongly convex costs, we prove an if-and-only-if capture criterion in terms of the cost-adjusted amplification advantage of the lower-value module. Under the same curvature-dominance condition that guarantees uniqueness, we show that the unique pure Nash equilibrium of the general \(M\)-module access contest can be approximated efficiently by projected pseudo-gradient dynamics, with logarithmic dependence on the desired accuracy. Finally, we prove an impossibility theorem for single-slot access mechanisms. Exact winner-take-all efficiency is incompatible with robustness to small score perturbations. Thus, smooth probabilistic access rules are not merely analytically convenient, but structurally motivated. These results provide a game-theoretic foundation for studying competition for conscious access, connecting equilibrium analysis, capture, computation, and mechanism-level limitations under a common formal model.

This thesis studies the convergence of finite-population stochastic evolutionary dynamics to their deterministic mean-field limit in continuous-time finite state space games. We first develop refined ergodic theorems for Markov chains with a single positive-recurrent class, guaranteeing the existence of a unique invariant distribution and almost-sure convergence of time averages. Next, we prove that the mean-field model, described by a system of Lipschitz-continuous ordinary differential equations, admits a unique solution that depends continuously on its initial condition and that constitutes the almost-sure limit for the empirical distributions with fixed policy. Furthermore, we show that every Mixed Stationary Nash Equilibrium of the mean-field game is approximated by a Nash equilibrium of the corresponding $N$-player game within an error $\epsilon$ for sufficiently large $N$. We finally demonstrate, by Kurtz's theorem, that the empirical state-policy distribution converges in probability to the mean-field trajectory. Numerical simulations conducted in MATLAB confirm the theoretical $\mathcal{O}(N^{-1/2})$ convergence rate in both models across a range of population sizes.

We study local pure coordination games on finite social networks, continuing the framework of Hutchcroft, Rospuskova, and Tamuz. They showed that low inefficiency in local coordination forces the underlying graph to be amenable, with a square-root loss in the amenability parameter. We improve this loss in the binary unbiased setting. Using Shapley values of a mutual-information game associated with the players' local outputs, we prove that if the average disagreement is at most $\varepsilon$, then the graph is $(O(\varepsilon\log(1/\varepsilon)),r)$-amenable. This gives a sharper quantitative converse between local coordination and graph amenability.

Given rationals $\alpha$ and $\beta$, the sure-almost-sure problem for a threshold Boolean objective $\varphi$ in a Markov decision process (MDP) asks if one can simultaneously ensure that all outcomes of the MDP have $\varphi$-value at least $\alpha$ (i.e. sure $\alpha$ satisfaction) and with probability $1$ the outcome has $\varphi$-value at least $\beta$ (i.e. almost-sure $\beta$ satisfaction). The sure-limit-sure problem asks if for all $\varepsilon > 0$ one can simultaneously ensure that all outcomes have $\varphi$-value at least $\alpha$ and with probability at least $1 - \varepsilon$ the outcome has $\varphi$-value at least $\beta$. Moreover, if simultaneous satisfaction of objectives is possible, then one would also like to construct a strategy (for sure-almost-sure) or a family of strategies (for sure-limit-sure) that achieves this. In this paper, we solve the sure-almost-sure and sure-limit-sure problems for window mean-payoff objectives. The window mean-payoff objective strengthens the standard mean-payoff objective by requiring that eventually, from every point in the infinite run, the average payoff becomes greater than a given threshold within a finite window length. We study two variants of window mean payoff: in the fixed variant, the window length $\ell$ is given, while in the bounded variant, the length is not given but is required to be bounded throughout the run. We show that the sure-almost-sure problem and the sure-limit-sure problem are both in P for the fixed variant (if $\ell$ is given in unary) and are both in NP $\cap$ coNP for the bounded variant, matching the computational complexity of sure satisfaction and almost-sure satisfaction when considered separately for these objectives. We also give bounds for the memory requirement of winning strategies for all considered problems.

Many strategic decision-making problems, such as environment design for warehouse robots, can be naturally formulated as bi-level reinforcement learning (RL), where a leader agent optimizes its objective while a follower solves a Markov decision process (MDP) conditioned on the leader's decisions. In many situations, a fundamental challenge arises when the leader cannot intervene in the follower's optimization process; it can only observe the optimization outcome. We address this decentralized setting by deriving the hypergradient of the leader's objective, i.e., the gradient of the leader's strategy that accounts for changes in the follower's optimal policy. Unlike prior hypergradient-based methods that require extensive data for repeated state visits or rely on gradient estimators whose complexity can increase substantially with the high-dimensional leader's decision space, we leverage the Boltzmann covariance trick to derive an alternative hypergradient formulation. This enables efficient hypergradient estimation solely from interaction samples, even when the leader's decision space is high-dimensional. Additionally, to our knowledge, this is the first method that enables hypergradient-based optimization for 2-player Markov games in decentralized settings. Experiments highlight the impact of hypergradient updates and demonstrate our method's effectiveness in both discrete and continuous state tasks.

The Prisoner's Dilemma, zero-sum games, LQR team problems, and differential games have shaped game theory in controls for decades, but the field's most pressing adversarial challenges demand a richer framework, and its name is Colonel Blotto. Strategic adversarial constraints represent a fundamental consideration in control systems, from cybersecurity defense to infrastructure protection. Colonel Blotto games, despite their direct relevance to such applications, remain underutilized in the controls community relative to other game-theoretic approaches. This article aims to close that gap for the controls community. Indeed, theoretical advances within the last two decades have spurred a resurgence of interest and enabled their applications across several domains. In this article, we introduce the Colonel Blotto framework, survey key analytical and computational results, and demonstrate how problems spanning cybersecurity, network defense, and multi-agent systems fit naturally within this structure. Three research directions are examined in depth: interdependent contest objectives that capture networked vulnerabilities, alternate winning rules that model partial rewards and structural asymmetries, and multi-agent competitive environments involving coalition formation and strategic concessions. Taken together, these directions reveal a framework that is both practically deployable and rich enough to capture the strategic complexity inherent in adversarial resource allocation.

Informal and privatized transit services, such as minibuses and shared auto-rickshaws, are integral to daily travel in large urban metropolises, providing affordable commutes where formal public transport is inadequate and other options are unaffordable. A defining feature of these systems is their decentralized organization, with drivers providing service in response to rider demand and earning opportunities. While this structure helps fill critical mobility gaps, it can also generate inefficient service patterns when profit-driven driver route choices do not align with system-wide mobility goals. We develop an analytically tractable game-theoretic framework to study incentives underlying informal and privatized transit systems with a fixed menu of routes, quantify efficiency losses from decentralized driver route choice, and design incentive mechanisms to mitigate these inefficiencies. Here, profit-maximizing informal operators (drivers) decide where to provide service and cost-minimizing commuters (riders) decide whether to use these services. Within this framework, we establish tight price of anarchy bounds showing that decentralized, profit-maximizing driver behavior can lead to bounded yet substantial losses in cumulative driver profit and rider demand served and that these losses can be mitigated through targeted interventions: budget-balanced cross-subsidization, which uses route-specific tolls/subsidies to shape driver payoffs, and fare optimization, which changes rider demand and driver margins through centrally regulated route-level fares. Finally, numerical experiments based on a real-world informal transit system in Nalasopara, India, reinforce these findings.

We study a stylized social learning dynamics where self-interested agents collectively follow a simple multi-armed bandit protocol. Each agent controls an ``episode": a short sequence of consecutive decisions. Motivating applications include users repeatedly interacting with an AI, or repeatedly shopping at a marketplace. While agents are incentivized to explore within their respective episodes, we show that the aggregate exploration fails: e.g., its Bayesian regret grows linearly over time. In fact, such failure is a (very) typical case, not just a worst-case scenario. This conclusion persists even if an agent's per-episode utility is some fixed function of the per-round outcomes: e.g., $\min$ or $\max$, not just the sum. Thus, externally driven exploration is needed even when some amount of exploration happens organically.

We study a screening problem in which an agent privately knows which actions or technologies are feasible and can disclose only a subset to a principal. Once disclosed, feasible options are verifiable and their payoff consequences are publicly known, so private information concerns feasibility rather than payoffs, misreporting restricts the principal's choices directly rather than distorting her beliefs. Assuming feasible sets are ordered by inclusion, we establish a simple characterization of the optimal mechanism, where the principal either behaves as if there is no asymmetric information or locally provides no reward for better proposals. We derive comparative statics and illustrate the framework in applications to managing persuasion, action elicitation, and production-technology elicitation.

This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter indexes a planner's attitude towards inequality. This link offers insights into structural properties of matchings and trade-offs between objectives, showing how stability can lead to welfare inequalities, even among similar agents. Our model captures supply-demand imbalances in contexts like spatial markets, school choice, and ride-sharing. We also show that large markets with idiosyncratic preferences can be well approximated by aligned preferences, expanding the applicability of our results.