Related papers: Statistical Games
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
A matrix-based framework for Bayesian games is presented, using semi-tensor product of matrices. Static Bayesian games are considered first. Matrix expression of Bayesian games is proposed. Three kinds of conversions, which convert Bayesian…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
This paper studies two-player zero-sum stochastic Bayesian games where each player has its own dynamic state that is unknown to the other player. Using typical techniques, we provide the recursive formulas and sufficient statistics in both…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
This paper introduces and analyses some models in the framework of Mean Field Games describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games,…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
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…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
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…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…
We introduce the concepts of Bayesian lens, characterizing the bidirectional structure of exact Bayesian inference, and statistical game, formalizing the optimization objectives of approximate inference problems. We prove that Bayesian…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
This paper examines the impact of cognitive biases on financial decision-making through a static Bayesian game framework. While traditional economic theory assumes fully rational investors, real-world choices are often shaped by loss…
Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…