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The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…

We propose networked policy gradient play for solving Markov potential games with continuous and/or discrete state-action pairs. During the game, agents use parametrized and differentiable policies that depend on the current state and the…

Routing games are amongst the most studied classes of games. Their two most well-known properties are that learning dynamics converge to equilibria and that all equilibria are approximately optimal. In this work, we perform a stress test…

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the…

Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…

This paper investigates the long-term behavior of an interacting particle system of interest in the hot topic of evolutionary game theory. Each site of the $d$-dimensional integer lattice is occupied by a player who is characterized by one…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics.…

The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and…

This paper studies partially observable two-person zero-sum semi-Markov games under a probability criterion, in which the system state may not be completely observed. It focuses on the probability that the accumulated rewards of player 1…

In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well…

Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…

We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an…

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…

Decentralized multiple access channels where each transmitter wants to selfishly maximize his transmission energy-efficiency are considered. Transmitters are assumed to choose freely their power control policy and interact (through…

Learning the influence graph G of a high-dimensional Markov process is central to many application domains, including social networks, neuroscience, and financial risk analysis. However, in many of these applications, future states of the…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

The single- and multi- processor cup games can be used to model natural problems in areas such as processor scheduling, deamortization, and buffer management. At the beginning of the single-processor cup game, $n$ cups are initially empty.…

Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…