As Large Language Models (LLMs) increasingly operate as autonomous decision-makers in interactive and multi-agent systems and human societies, understanding their strategic behaviour has profound implications for safety, coordination, and the design of AI-driven social and economic infrastructures. Assessing such behaviour requires methods that capture not only what LLMs output, but the underlying intentions that guide their decisions. In this work, we extend the FAIRGAME framework to systematically evaluate LLM behaviour in repeated social dilemmas through two complementary advances: a payoff-scaled Prisoners Dilemma isolating sensitivity to incentive magnitude, and an integrated multi-agent Public Goods Game with dynamic payoffs and multi-agent histories. These environments reveal consistent behavioural signatures across models and languages, including incentive-sensitive cooperation, cross-linguistic divergence and end-game alignment toward defection. To interpret these patterns, we train traditional supervised classification models on canonical repeated-game strategies and apply them to FAIRGAME trajectories, showing that LLMs exhibit systematic, model- and language-dependent behavioural intentions, with linguistic framing at times exerting effects as strong as architectural differences. Together, these findings provide a unified methodological foundation for auditing LLMs as strategic agents and reveal systematic cooperation biases with direct implications for AI governance, collective decision-making, and the design of safe multi-agent systems.

In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games -- one in continuous and one in discrete time with the aim of characterizing the long-run behavior of the induced sequence of play. In stark contrast to deterministic, full-information models of learning (or models with a vanishing learning rate), we show that the resulting dynamics do not converge in general. In lieu of this, we ask instead which actions are played more often in the long run, and by how much. We show that, in strongly monotone games, the dynamics of regularized learning may wander away from equilibrium infinitely often, but they always return to its vicinity in finite time (which we estimate), and their long-run distribution is sharply concentrated around a neighborhood thereof. We quantify the degree of this concentration, and we show that these favorable properties may all break down if the underlying game is not strongly monotone -- underscoring in this way the limits of regularized learning in the presence of persistent randomness and uncertainty.

In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain invariant to small -- but otherwise arbitrary -- perturbations to the game's payoff structure, and we provide a crisp geometric characterization thereof. Subsequently, we turn to the question of dynamic robustness, and we examine which equilibria may arise as stable limit points of the dynamics of "follow the regularized leader" (FTRL) in the presence of randomness and uncertainty. Despite their very distinct origins, we establish a structural correspondence between these two notions of robustness: strategic robustness implies dynamic robustness, and, conversely, the requirement of strategic robustness cannot be relaxed if dynamic robustness is to be maintained. Finally, we examine the rate of convergence to robust equilibria as a function of the underlying regularizer, and we show that entropically regularized learning converges at a geometric rate in games with affinely constrained action spaces.

Large language models (LLMs) are increasingly being deployed as autonomous agents on behalf of institutions and individuals in economic, political, and social settings that involve negotiation. Yet this trend carries significant risks if their strategic behavior is not well understood. In this work, we revisit the NegotiationArena framework and run controlled simulation experiments on a diverse set of frontier LLMs across three multi turn bargaining games: Buyer Seller, Multi turn Ultimatum, and Resource Exchange. We ask whether improved general reasoning capabilities lead to rational, unbiased, and convergent negotiation strategies. Our results challenge this assumption. We find that models diverge into distinct, model specific strategic equilibria rather than converging to a unified optimal behavior. Moreover, strong numerical and semantic anchoring effects persist: initial offers are highly predictive of final agreements, and models consistently generate biased proposals by collapsing diverse internal valuations into rigid, generic price points. More concerningly, we observe dominance patterns in which some models systematically achieve higher payoffs than their counterparts. These findings underscore an urgent need to develop mechanisms to mitigate these issues before deploying such systems in real-world scenarios.

We study methods to enhance privacy in blockchain transactions from an economic angle. We consider mechanisms for privacy-aware users whose utility depends not only on the outcome of the mechanism but also negatively on the exposure of their economic preferences. Specifically, we study two auction-theoretic settings with privacy-aware users. First, we analyze an order flow auction, where a user auctions off to specialized agents, called searchers, the right to execute her transaction while maintaining a degree of privacy. We examine how the degree of privacy affects the revenue of the auction and, broadly, the net utility of the privacy-aware user. In this new setting, we describe the optimal auction, which is a sealed-bid auction. Subsequently, we analyze a variant of a Dutch auction in which the user gradually decreases the price and the degree of privacy until the transaction is sold. We compare the revenue of this auction to that of the optimal one as a function of the number of communication rounds. Then, we introduce a two-sided market - a privacy marketplace - with multiple users selling their transactions under their privacy preferences to multiple searchers. We propose a posted-price mechanism for the two-sided market that guarantees constant approximation of the optimal social welfare while maintaining incentive compatibility (from both sides of the market) and budget balance. This work builds on the emerging line of research that attempts to improve the performance of economic mechanisms by appending cryptographic primitives to them.

We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among $n$ teams in a league. Such a mechanism should satisfy the natural properties of monotonicity and Condorcet consistency. Moreover, from the league's perspective, the winner-determination tournament rule should be strategyproof, meaning that no team can do better by losing a game on purpose. Past work considered settings in which each team is fully selfish, caring only about its own probability of winning, and settings in which each team is fully selfless, caring only about the total winning probability of itself and the team to which it deliberately loses. More recently, researchers considered a mixture of these two settings with a parameter $\lambda$. Intermediate selfishness $\lambda$ means that a team will not lose on purpose unless its pair gains at least $\lambda s$ winning probability, where $s$ is the individual team's sacrifice from its own winning probability. All of the dozens of previously known tournament rules require $\lambda = \Omega(n)$ to be strategyproof, and it has been an open problem to find such a rule with the smallest $\lambda$. In this work, we make significant progress by designing a tournament rule that is strategyproof with $\lambda = 11$. Along the way, we propose a new notion of multiplicative pairwise non-manipulability that ensures that two teams cannot manipulate the outcome of a game to increase the sum of their winning probabilities by more than a multiplicative factor $\delta$ and provide a rule which is multiplicatively pairwise non-manipulable for $\delta = 3.5$.

Autodeleveraging (ADL) is a last-resort loss socialization mechanism for perpetual futures venues. It is triggered when solvency-preserving liquidations fail. Despite the dominance of perpetual futures in the crypto derivatives market, with over \60 trillion of volume in 2024, there has been no formal study of ADL. In this paper, we provide the first rigorous model of ADL. We prove that ADL mechanisms face a fundamental \emph{trilemma}: no policy can simultaneously satisfy exchange \emph{solvency}, \emph{revenue}, and \emph{fairness} to traders. This impossibility theorem implies that as participation scales, a novel form of \emph{moral hazard} grows asymptotically, rendering `zero-loss' socialization impossible. Constructively, we show that three classes of ADL mechanisms can optimally navigate this trilemma to provide fairness, robustness to price shocks, and maximal exchange revenue. We analyze these mechanisms on the Hyperliquid dataset from October 10, 2025, when ADL was used repeatedly to close \2.1 billion of positions in 12 minutes. By comparing our ADL mechanisms to the standard approaches used in practice, we demonstrate empirically that Hyperliquid's production queue overutilized ADL by approximately $8\times$ relative to our optimal policy, imposing roughly \$630 million of unnecessary haircuts on winning traders. This comparison also suggests that Binance overutilized ADL far more than Hyperliquid. Our results both theoretically and empirically demonstrate that optimized ADL mechanisms can dramatically reduce the loss of trader profits while maintaining exchange solvency.

Large Language Models' (LLMs) programming capabilities enable their participation in open-source games: a game-theoretic setting in which players submit computer programs in lieu of actions. These programs offer numerous advantages, including interpretability, inter-agent transparency, and formal verifiability; additionally, they enable program equilibria, solutions that leverage the transparency of code and are inaccessible within normal-form settings. We evaluate the capabilities of leading open- and closed-weight LLMs to predict and classify program strategies and evaluate features of the approximate program equilibria reached by LLM agents in dyadic and evolutionary settings. We identify the emergence of payoff-maximizing, cooperative, and deceptive strategies, characterize the adaptation of mechanisms within these programs over repeated open-source games, and analyze their comparative evolutionary fitness. We find that open-source games serve as a viable environment to study and steer the emergence of cooperative strategy in multi-agent dilemmas.

Multi-agent contract design has largely evaluated contracts through the lens of pure Nash equilibria (PNE). This focus, however, is not without loss: In general, the principal can strictly gain by recommending a complex, possibly correlated, distribution over actions, while preserving incentive compatibility. In this work, we extend the analysis of multi-agent contracts beyond pure Nash equilibria to encompass more general equilibrium notions, including mixed Nash equilibria as well as (coarse-)correlated equilibria (CCE). The latter, in particular, captures the limiting outcome of agents engaged in learning dynamics. Our main result shows that for submodular and, more generally, XOS rewards, such complex recommendations yield at most a constant-factor gain: there exists a contract and a PNE whose utility is within a constant factor of the best CCE achievable by any contract. This provides a black-box lifting: results established against the best PNE automatically apply with respect to the best CCE, with only a constant factor loss. For submodular rewards, we further show how to transform a contract and a PNE of that contract into a new contract such that any of its CCEs gives a constant approximation to the PNE. This yields black-box robustness: up to constant factors, guarantees established for a specific contract and PNE automatically extend to the modified contract and any of its CCEs. We thus expand prior guarantees for multi-agent contracts and lower the barrier to new ones. As an important corollary, we obtain poly-time algorithms for submodular rewards that achieve constant approximations in any CCE, against the best CCE under the best contract. Such worst-case guarantees are provably unattainable for XOS rewards. Finally, we bound the gap between different equilibrium notions for subadditive, supermodular, and general rewards.

Standard decision frameworks addresses uncertainty about facts but assumes fixed values. We extend the Jeffrey-Bolker framework to model refinements in values and prove a value-of-information theorem for axiological refinement. In multi-agent settings, we establish that mutual refinement will characteristically transform zero-sum games into positive-sum interactions and yields Pareto-improving Nash bargains. These results show that a framework of rational choice can be extended to model value refinement and its associated benefits. By unifying epistemic and axiological refinement under a single formalism, we broaden the conceptual foundations of rational choice and illuminate the normative status of ethical deliberation.

Recently, Maggiorano et al. (2025) claimed that they have developed a strongly polynomial-time combinatorial algorithm for the nucleolus in convex games that is based on the reduced game approach and submodular function minimization method. Thereby, avoiding the ellipsoid method with its negative side effects in numerical computation completely. However, we shall argue that this is a fallacy based on an incorrect application of the Davis/Maschler reduced game property (RGP). Ignoring the fact that despite the pre-nucleolus, other solutions like the core, pre-kernel, and semi-reactive pre-bargaining set possess this property as well. This causes a severe selection issue, leading to the failure to compute the nucleolus of convex games using the reduced games approach. In order to assess this finding in its context, the ellipsoid method of Faigle et al. (2001) and the Fenchel-Moreau conjugation-based approach from convex analysis of Meinhardt (2013) to compute a pre-kernel element were resumed. In the latter case, it was exploited that for TU games with a single-valued pre-kernel, both solution concepts coincide. Implying that one has computed the pre-nucleolus if one has found the sole pre-kernel element of the game. Though it is a specialized and highly optimized algorithm for the pre-kernel, it assures runtime complexity of O(n^3) for computing the pre-nucleolus whenever the pre-kernel is a single point, which indicates a polynomial-time algorithm for this class of games.

Motivated by online platforms such as job markets, we study an agent choosing from a list of candidates, each with a hidden quality that determines match value. The agent observes only a noisy ranking of the candidates plus a binary signal that indicates whether each candidate is "free" or "busy." Being busy is positively correlated with higher quality, but can also reduce value due to decreased availability. We study the agent's optimal selection problem in the presence of ranking noise and free-busy signals and ask how the accuracy of the ranking tool impacts outcomes. In a setting with one high-valued candidate and an arbitrary number of low-valued candidates, we show that increased accuracy of the ranking tool can result in reduced social welfare. This can occur for two reasons: agents may be more likely to make offers to busy candidates, and (paradoxically) may be more likely to select lower-ranked candidates when rankings are more indicative of quality. We further discuss conditions under which these results extend to more general settings.

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an individual's peer network and comparisons. We propose a theoretical model of perceived fairness networks, in which each individual's sense of discrimination depends on the local topology of interactions. We show that even if a decision rule satisfies standard criteria of fairness, perceived discrimination can persist or even increase in the presence of homophily or assortative mixing. We propose a formalism for the concept of fairness perception, linking network structure, local observation, and social perception. Analytical and simulation results highlight how network topology affects the divergence between objective fairness and perceived fairness, with implications for algorithmic governance and applications in finance and collaborative insurance.

Ethereum's upcoming Glamsterdam upgrade introduces EIP-7732 enshrined Proposer--Builder Separation (ePBS), which improves the block production pipeline by addressing trust and scalability challenges. Yet it also creates a new liveness risk: builders gain a short-dated ``free'' option to prevent the execution payload they committed to from becoming canonical, without incurring an additional penalty. Exercising this option renders an empty block for the slot in question, thereby degrading network liveness. We present the first systematic study of the free option problem. Our theoretical results predict that option value and exercise probability grow with market volatility, the length of the option window, and the share of block value derived from external signals such as external market prices. The availability of a free option will lead to mispricing and LP losses. The problem would be exacerbated if Ethereum further scales and attracts more liquidity. Empirical estimates of values and exercise probabilities on historical blocks largely confirm our theoretical predictions. While the option is rarely profitable to exercise on average (0.82\% of blocks assuming an 8-second option time window), it becomes significant in volatile periods, reaching up to 6\% of blocks on high-volatility days -- precisely when users most require timely execution. Moreover, builders whose block value relies heavily on CEX-DEX arbitrage are more likely to exercise the option. We demonstrate that mitigation strategies -- shortening the option window or penalizing exercised options -- effectively reduce liveness risk.

We study the trade-off between envy and inefficiency in repeated resource allocation settings with stochastic replenishments, motivated by real-world systems such as food banks and medical supply chains. Specifically, we consider a model in which a decision-maker faced with stochastic demand and resource donations must trade off between an equitable and efficient allocation of resources over an infinite horizon. The decision-maker has access to storage with fixed capacity $M$, and incurs efficiency losses when storage is empty (stockouts) or full (overflows). We provide a nearly tight (up to constant factors) characterization of achievable envy-inefficiency pairs. Namely, we introduce a class of Bang-Bang control policies whose inefficiency exhibits a sharp phase transition, dropping from $\Theta(1/M)$ when $\Delta = 0$ to $e^{-\Omega(\Delta M)}$ when $\Delta > 0$, where $\Delta$ is used to denote the target envy of the policy. We complement this with matching lower bounds, demonstrating that the trade-off is driven by supply, as opposed to demand uncertainty. Our results demonstrate that envy-inefficiency trade-offs not only persist in settings with dynamic replenishment, but are shaped by the decision-maker's available capacity, and are therefore qualitatively different compared to previously studied settings with fixed supply.

Strategic classification addresses a learning problem where a decision-maker implements a classifier over agents who may manipulate their features in order to receive favorable predictions. In the standard model of online strategic classification, in each round, the decision-maker implements and publicly reveals a classifier, after which agents perfectly best respond based on this knowledge. However, in practice, whether to disclose the classifier is often debated -- some decision-makers believe that hiding the classifier can prevent misclassification errors caused by manipulation. In this paper, we formally examine how limiting the agents' access to the current classifier affects the decision-maker's performance. Specifically, we consider an extended online strategic classification setting where agents lack direct knowledge about the current classifier and instead manipulate based on a weighted average of historically implemented classifiers. Our main result shows that in this setting, the decision-maker incurs $(1-\gamma)^{-1}$ or $k_{\text{in}}$ times more mistakes compared to the full-knowledge setting, where $k_{\text{in}}$ is the maximum in-degree of the manipulation graph (representing how many distinct feature vectors can be manipulated to appear as a single one), and $\gamma$ is the discount factor indicating agents' memory of past classifiers. Our results demonstrate how withholding access to the classifier can backfire and degrade the decision-maker's performance in online strategic classification.