101,148 research outputs found
Strategic thinking under social influence: Scalability, stability and robustness of allocations
No full textThis paper studies the strategic behavior of a large number of game designers and studies the scalability, stability and robustness of their allocations in a large number of homogeneous coalitional games with transferable utilities (TU). For each TU game, the characteristic function is a continuous-time stochastic process. In each game, a game designer allocates revenues based on the extra reward that a coalition has received up to the current time and the extra reward that the same coalition has received in the other games. The approach is based on the theory of mean-field games with heterogeneous groups in a multi-population regime
Mixed Integer Optimal Compensation: Decomposition and Mean-Field Approximations
No full textMixed integer optimal compensation deals with
optimizing integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature
of controls might be a cause of intractability for instances of
larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem
into n independent scalar problems of lot sizing form. Each
scalar problem is then reformulated as a shortest path one and
solved through linear programming over a receding horizon.
This last reformulation step mirrors a standard procedure
in mixed integer programming. We apply the decomposition
method to a mean-field coupled multi-agent system problem,
where each agent seeks to compensate a combination of the
exogenous signal and the local state average. We discuss a
large population mean-field type of approximation as well as
the application of predictive control method
Robust Mean Field Games
No full textRecently there has been renewed interest in large-scale games in
several research disciplines, with diverse application domains as in the smart
grid, cloud computing, nancial markets, biochemical reaction networks, transportation
science and molecular biology. Prior works have provided rich mathematical
foundations and equilibrium concepts but relatively little in terms of
robustness in the presence of uncertainties. In this paper, we study mean-eld
games with uncertainty in both states and payos. We consider a population
of players with individual states driven by a standard Brownian motion and
a disturbance term. The contribution is three-fold: First, we establish a mean
eld system for such robust games. Second, we apply the methodology to production
of an exhaustible resource. Third, we show that the dimension of the
mean eld system can be signicantly reduced by considering a functional of
the first moment of the mean field process
Numerical approximation for a visibility based pursuit-evasion game
No full textThis work addresses a vision-based target tracking problem between a mobile observer and a target in the presence of a circular obstacle. The task of keeping the target in the observer's field-of-view is modeled as a pursuit-evasion game by assuming that the target is adversarial in nature. Due to the presence of obstacles, this is formulated as a game with state constraints. The objective of the observer is to maintain a line-of-sight with the target at all times. The objective of the target is to break the line-of-sight in finite amount of time. First, we establish that the value of the game exists in this setting. Then we reduce the dimension of the problem by formulating the game in relative coordinates, and present a discretization in time and space for the reduced game. Based on this discretization, we use a fully discrete semi-Lagrangian scheme to compute the Kružkov transform of the value function numerically, and show that the scheme converges for our problem. Finally, we compute the optimal control action of the players from the Kružkov transform of the value function, and demonstrate the performance of the numerical scheme by numerous simulations. © 2014 IEEE
Opinion Dynamics in Social Networks through Mean-Field Games
No full textEmulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input and a vector-valued exogenous disturbance. The controlled input of each network is to align its state to the mean distribution of other networks’ states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean field game for the cases of both polytopic and L2 bounds on controls and disturbances. A second contribution is the establishment of a robust mean-field equilibrium, that is, a solution including the worst-case value function, the state feedback best-responses for the controlled inputs and worst-case disturbances, and a density evolution. This solution is characterized by the property that no player can benefit from a unilateral deviation even in the presence of the disturbance. As a third contribution, microscopic and macroscopic analyses are carried out to show convergence properties of the population distribution using stochastic stability theory
Large networks of dynamic agents: Consensus under adversarial disturbances
No full textThis paper studies interactions among homogeneous social groups within the framework of large population games. Each group is represented by a network and the behavior described by a two-player repeated game. The contribution is three-fold. Beyond the idea of providing a novel two-level model with repeated games at a lower level and population games at a higher level, we also establish a mean field equilibrium and study state feedback best-response strategies as well as worst-case adversarial disturbances in that context. © 2012 IEEE
Letter, [Author unclear] to Paulina T. Merritt
No full textHandwritten letter to Paulina Merritt from an unknown author, October 1, 1876.
Robust linear quadratic mean-field games in crowd-seeking social Networks
No full textWe consider a social network where opinions evolve following a stochastic averaging process under the influence of adversarial disturbances. We provide a robust mean-field game model in the spirit of H∞-optimal control, establish existence of a mean-field equilibrium, and analyze its stochastic stability. ©2013 IEEE
Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems
No full textMixed integer optimal compensation deals with optimization problems with integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of an exogenous signal and the local state average. We discuss a large population mean-field type of approximation and extend our study to opinion dynamics in social networks as a special case of interest
Handwritten biographical information on Paulina T. McClung Merritt
No full textA handwritten biography of Paulina T. McClung Merritt by an unknown author, 1892.
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