Large Language Models Playing Mixed Strategy Nash Equilibrium Games

Generative artificial intelligence (Generative AI), and in particular Large Language Models (LLMs) have gained significant popularity among researchers and industrial communities, paving the way for integrating LLMs in different domains, such as robotics, telecom, and healthcare. In this paper, we study the intersection of game theory and generative artificial intelligence, focusing on the capabilities of LLMs to find the Nash equilibrium in games with a mixed strategy Nash equilibrium and no pure strategy Nash equilibrium (that we denote mixed strategy Nash equilibrium games). The study reveals a significant enhancement in the performance of LLMs when they are equipped with the possibility to run code and are provided with a specific prompt to incentivize them to do so. However, our research also highlights the limitations of LLMs when the randomization strategy of the game is not easy to deduce. It is evident that while LLMs exhibit remarkable proficiency in well-known standard games, their performance dwindles when faced with slight modifications of the same games. This paper aims to contribute to the growing body of knowledge on the intersection of game theory and generative artificial intelligence while providing valuable insights into LLMs strengths and weaknesses. It also underscores the need for further research to overcome the limitations of LLMs, particularly in dealing with even slightly more complex scenarios, to harness their full potential.

Experimental Comparison of Ensemble Methods and Time-to-Event Analysis Models Through Integrated Brier Score and Concordance Index

Time-to-event analysis is a branch of statistics that has increased in popularity during the last decades due to its many application fields, such as predictive maintenance, customer churn prediction and population lifetime estimation. In this paper, we review and compare the performance of several prediction models for time-to-event analysis. These consist of semi-parametric and parametric statistical models, in addition to machine learning approaches. Our study is carried out on three datasets and evaluated in two different scores (the integrated Brier score and concordance index). Moreover, we show how ensemble methods, which surprisingly have not yet been much studied in time-to-event analysis, can improve the prediction accuracy and enhance the robustness of the prediction performance. We conclude the analysis with a simulation experiment in which we evaluate the factors influencing the performance ranking of the methods using both scores.

Experimental Comparison of Semi-parametric, Parametric, and Machine Learning Models for Time-to-Event Analysis Through the Concordance Index

In this paper, we make an experimental comparison of semi-parametric (Cox proportional hazards model, Aalen's additive regression model), parametric (Weibull AFT model), and machine learning models (Random Survival Forest, Gradient Boosting with Cox Proportional Hazards Loss, DeepSurv) through the concordance index on two different datasets (PBC and GBCSG2). We present two comparisons: one with the default hyper-parameters of these models and one with the best hyper-parameters found by randomized search.

Colonel Blotto and Hide-and-Seek Games as Path Planning Problems with Side Observations

Resource allocation games such as the famous Colonel Blotto (CB) and Hide-and-Seek (HS) games are often used to model a large variety of practical problems, but only in their one-shot versions. Indeed, due to their extremely large strategy space, it remains an open question how one can efficiently learn in these games. In this work, we show that the online CB and HS games can be cast as path planning problems with side-observations (SOPPP): at each stage, a learner chooses a path on a directed acyclic graph and suffers the sum of losses that are adversarially assigned to the corresponding edges; and she then receives semi-bandit feedback with side-observations (i.e., she observes the losses on the chosen edges plus some others). Then, we propose a novel algorithm, EXP3-OE, the first-of-its-kind with guaranteed efficient running time for SOPPP without requiring any auxiliary oracle. We provide an expected-regret bound of EXP3-OE in SOPPP matching the order of the best benchmark in the literature. Moreover, we introduce additional assumptions on the observability model under which we can further improve the regret bounds of EXP3-OE. We illustrate the benefit of using EXP3-OE in SOPPP by applying it to the online CB and HS games.