Related papers: Selection problems in Large Deviations in Games un…

As large language models (LLMs) advance in linguistic competence, their reasoning abilities are gaining increasing attention. In humans, reasoning often performs well in domain specific settings, particularly in normative rather than purely…

A multitude of classifiers can be trained on the same data to achieve similar performances during test time, while having learned significantly different classification patterns. This phenomenon, which we call prediction discrepancies, is…

This work investigates continuous time stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are…

In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of…

We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…

An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of her neighbors. Such games have been used to model issues including the formation of…

Aligning large language models (LLMs) with diverse human preferences is critical for ensuring fairness and informed outcomes when deploying these models for decision-making. In this paper, we seek to uncover fundamental statistical limits…

Motivated by the study of asymptotic behaviour of the bandit problems, we obtain several strategy-driven limit theorems including the law of large numbers, the large deviation principle, and the central limit theorem. Different from the…

The deployment of large language models (LLMs) in diverse applications requires a thorough understanding of their decision-making strategies and behavioral patterns. As a supplement to a recent study on the behavioral Turing test, this…

In this paper, we investigate the phenomena of "selection biases" in Large Language Models (LLMs), focusing on problems where models are tasked with choosing the optimal option from an ordered sequence. We delve into biases related to…

As large language models (LLMs) transition from chat interfaces to integral components of stochastic pipelines and systems approaching general intelligence, the ability to faithfully sample from specified probability distributions has…

In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show…

We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity,…

LLM (large language model) practitioners commonly notice that outputs can vary for the same inputs under settings expected to be deterministic. Yet the questions of how pervasive this is, and with what impact on results, have not to our…

We explore a class of stochastic multiplayer games where each player in the game aims to optimize its objective under uncertainty and adheres to some expectation constraints. The study employs an offline learning paradigm, leveraging a…

Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…

We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to…

Whether in agentic workflows, social studies, or chat settings, large language models (LLMs) are increasingly being asked to replace humans in choosing which goals to pursue, rather than completing predefined tasks. However, the assumption…