相关论文: Selection problems in Large Deviations in Games un…

In many biological systems, natural selection acts simultaneously on multiple levels of organization. This scenario typically presents an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to…

We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…

Large language models have recently demonstrated remarkable abilities to self-correct their responses through iterative refinement, often referred to as self-consistency or self-reflection. However, the dynamics of this self-correction…

Social choice has become a foundational component of modern machine learning systems. From auctions and resource allocation to the alignment of large generative models, machine learning pipelines increasingly aggregate heterogeneous…

We investigate the choice patterns of Large Language Models (LLMs) in the context of Decisions from Experience tasks that involve repeated choice and learning from feedback, and compare their behavior to human participants. We find that on…

We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy ("cooperation" and "defection") games in populations comprising cooperation facilitators. The latter are individuals that…

We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…

We consider (random) strategic interactions in a large population consisting of a variety of players. A rational player chooses actions that maximize certain utility functions, while a behavioral player chooses actions based on preferences…

We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The…

This paper investigates the voting behaviors of Large Language Models (LLMs), specifically GPT-4 and LLaMA-2, their biases, and how they align with human voting patterns. Our methodology involved using a dataset from a human voting…

Equilibrium in Economics has been seldom addressed in a situation where some variables are discrete. This work introduces a problem related to lot-sizing with several players, and analyses some strategies which are likely to be found in…

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…

The prisoner's dilemma (PD) game is a simple model for understanding cooperative patterns in complex systems consisting of selfish individuals. Here, we study a PD game problem in scale-free networks containing hierarchically organized…

The conformity effect describes the tendency of individuals to align their responses with the majority. Studying this bias in large language models (LLMs) is crucial, as LLMs are increasingly used in various information-seeking and…

Human decision behaviour is quite diverse. In many games humans on average do not achieve maximal payoff and the behaviour of individual players remains inhomogeneous even after playing many rounds. For instance, in repeated prisoner…

We study the performance of machine learning binary classification techniques in terms of error probabilities. The statistical test is based on the Data-Driven Decision Function (D3F), learned in the training phase, i.e., what is…

We consider optimal control of a stochastic network,where service is controlled to prevent buffer overflow. We use a risk-sensitive escape time criterion, which in comparison to the ordinary escape time criteria heavily penalizes exits…

The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an $\alpha $-stable process. It is proved that extremal solutions are selected and the respective…

Playing games has a long history of describing intricate interactions in simplified forms. In this paper we explore if large language models (LLMs) can play games, investigating their capabilities for randomisation and strategic adaptation…

We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. Using the simple symmetric exclusion process as a prototypical example, we investigate the convergence of…