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We consider time-homogeneous uniformly nondegenerate stochastic differential games in domains and propose constructing $\varepsilon$-optimal strategies and policies by using adjoint Markov strategies and adjoint Markov policies which are…
Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning…
In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…
The paper deals with the order statistics and empirical mathematical expectation (which is also called the estimate of mathematical expectation in the literature) in the case of infinitely increasing random variables. The Kolmogorov concept…
In this paper we propose game theoretic Medium Access Control (MAC) strategies for data dissemination scenarios. In particular, we use energy-based utility functions that inherently imply power-awareness, while we consider network coding…
The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a…
We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a…
In this paper, we study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
Agents often have individual goals which depend on a group's actions. If agents trust a forecast of collective action and adapt strategically, such prediction can influence outcomes non-trivially, resulting in a form of performative…
We examine the Markovian properties of coalition bargaining games, in particular, the case where past rejected proposals cannot be repeated. We propose a Markovian embedding with filtrations to render the sates Markovian and thus, fit into…
Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty -- e-processes for testing and confidence sequences for estimation -- that remain valid at all stopping times, accommodating continuous monitoring…
Markov kernels play a decisive role in probability and mathematical statistics theories, and are an extension of the concepts of sigma-field and statistic. Concepts such as independence, sufficiency, completeness, ancillarity or conditional…
We give a game-theoretic proof of the celebrated Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair coin tossing. Our proof, based on Bayesian strategy, is explicit as many other game-theoretic proofs of the laws in…
We present an alternative proof of a theorem by Courcelle, Makowski and Rotics which states that problems expressible in MSO are solvable in linear time for graphs of bounded rankwidth. Our proof uses a game-theoretic approach and has the…
We consider a model of language development, known as the naming game, in which agents invent, share and then select descriptive words for a single object, in such a way as to promote local consensus. When formulated on a finite and…
The framework of uncoupled online learning in multiplayer games has made significant progress in recent years. In particular, the development of time-varying games has considerably expanded its modeling capabilities. However, current regret…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
We propose a new model, independent linear Markov game, for multi-agent reinforcement learning with a large state space and a large number of agents. This is a class of Markov games with independent linear function approximation, where each…
We provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. We first establish a generic result that links true common beliefs (and, respectively, common knowledge) of players' rationality defined by…