Search results for "Approachability"
showing 7 items of 7 documents
Distributed $n$-player approachability and consensus in coalitional games
2015
We study a distributed allocation process where, at each time, every player: i) proposes a new bid based on the average utilities produced up to that time, ii) adjusts such allocations based on the inputs received from its neighbors, and iii) generates and allocates new utilities. The average allocations evolve according to a doubly (over time and space) averaging algorithm. We study conditions under which the average allocations reach consensus to any point within a predefined target set even in the presence of adversarial disturbances. Motivations arise in the context of coalitional games with transferable utilities (TU) where the target set is any set of allocations that makes the grand …
Consensus in opinion dynamics as a repeated game
2018
Abstract We study an n -agent averaging process with dynamics subject to controls and adversarial disturbances. The model arises in multi-population opinion dynamics with macroscopic and microscopic intertwined dynamics. The averaging process describes the influence from neighbouring populations, whereas the input term indicates how the distribution of opinions in the population changes as a result of dynamical evolutions at a microscopic level (individuals’ changing opinions). The input term is obtained as the vector payoff of a two player repeated game. We study conditions under which the agents achieve robust consensus to some predefined target set. Such conditions build upon the approac…
Distributed <inline-formula> <tex-math notation="TeX">$n$</tex-math></inline-formula>-Player Approachability and Consensus in…
2015
We study a distributed allocation process where, at each time, every player: i) proposes a new bid based on the average utilities produced up to that time, ii) adjusts such allocations based on the inputs received from its neighbors, and iii) generates and allocates new utilities. The average allocations evolve according to a doubly (over time and space) averaging algorithm. We study conditions under which the average allocations reach consensus to any point within a predefined target set even in the presence of adversarial disturbances. Motivations arise in the context of coalitional games with transferable utilities (TU) where the target set is any set of allocations that makes the grand …
Approachability in Population Games
2014
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 population of individuals with given distribution on actions. First, convergence conditions are revisited based on the common prior on the population distribution, and we define the notion of \emph{1st-moment approachability}. Second, we develop a model of two coupled partial differential equations (PDEs) in the spirit of mean-field game theory: one describing the best-response of every player given the population distribution (this is a \emph{Hamilton-Jacobi-Bell…
Adaptation, coordination, and local interactions via distributed approachability
2017
This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent\ud systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework\ud of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability\ud theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for\ud the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local\ud information and interaction structure. The game model turns i…
Distributed n-player approachability via time and space average consensus
2012
Abstract In this paper we consider repeated coalitional games with transferable utilities (TU) over networks. Namely, we consider a set of n players that have to distribute among themselves a vector of rewards (one for each player). In our network version there is no coordinator allocating the rewards, but the agents have to agree on a common time-averaged vector by updating the local estimates of the reward vector. The common time-averaged reward vector has to approach a suitable constraint set, called core of the game, that guarantees that no agents benefit from quitting the grand coalition. We propose a doubly (over time and space) averaging distributed algorithm. At every iteration, eac…
Population Games with Vector Payoff and Approachability
2016
This paper studies population games with vector payoffs. It provides a new perspective on approachability based on mean-field game theory. The model involves a Hamilton-Jacobi-Bellman equation which describes the best-response of every player given the population distribution and an advection equation, capturing the macroscopic evolution of average payoffs if every player plays its best response.