Related papers: On the Foundations of Dynamic Games and Probabilit…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
This paper employs the Friedkin-Johnsen (FJ) model to describe the dynamics of opinion evolution within a social network. Under the FJ framework, the society is divided into two subgroups that include stubborn agents and regular agents. The…
Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In practical applications, though, agents often have only partial observability of their environment. Furthermore, agents…
This paper provides an analysis of different formal representations of beliefs in epistemic game theory. The aim is to attempt a synthesis of different structures of beliefs in the presence of indeterminate probabilities. Special attention…
Over the past decade, random forest models have become widely used as a robust method for high-dimensional data regression tasks. In part, the popularity of these models arises from the fact that they require little hyperparameter tuning…
We present an algorithm for learning decision trees using stochastic gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, our method operates in the incremental learning…
In many practical uses of reinforcement learning (RL) the set of actions available at a given state is a random variable, with realizations governed by an exogenous stochastic process. Somewhat surprisingly, the foundations for such…
We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order "coefficient"…
Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative…
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit…
We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow…
We apply Game Theory to a mathematical representation of two competing teams of agents connected within a complex network, where the ability of each side to manoeuvre their resource and degrade that of the other depends on their ability to…
Building upon developments in theoretical and applied machine learning, as well as the efforts of various scholars including Guimera and Sales-Pardo (2011), Ruger et al. (2004), and Martin et al. (2004), we construct a model designed to…