Related papers: On the Foundations of Dynamic Games and Probabilit…

In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…

Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on "conditioning on…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the…

Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret,…

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a…

Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5--32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical…

Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…

Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…

Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data…

Under certain circumstances such as lack of information or bounded rationality, human players can take decisions on which strategy to choose in a game on the basis of simple opinions. These opinions can be modified after each round by…

Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing…

We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…

Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…

We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…

Evolutionarily stable strategy (ESS) is the defining concept of evolutionary game theory. It has a fairly unanimously accepted definition for the case of symmetric games which are played in a homogeneous population where all individuals are…

This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…

A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…

Games offer a compelling paradigm for developing general reasoning capabilities in language models, as they naturally demand strategic planning, probabilistic inference, and adaptive decision-making. However, existing self-play approaches…