Search results for "Mathematica"
showing 10 items of 7971 documents
Game-Theoretic Learning and Allocations in Robust Dynamic Coalitional Games
2019
The problem of allocation in coalitional games with noisy observations and dynamic environments is considered. The evolution of the excess is modeled by a stochastic differential inclusion involvin...
A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma
2016
We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the syst…
Online Pricing via Stackelberg and Incentive Games in a Micro-Grid
2019
This paper deals with the analysis and design of online pricing mechanisms in micro-grids. Two cases are studied in which the market layer is modeled as an open-loop and closed-loop dynamical system respectively. In the case of open-loop market dynamics, the price is generated as equilibrium price of a Stackelberg game with an incentive strategy. In such Stackelberg game, the leader is the energy supplier, the follower is the consumer, and the leader plays an incentive strategy. In the case of closed-loop market dynamics, the price is obtained as a function of the power supplied and the demand. A stability analysis is provided for both cases, which sheds light on the transient and steady-st…
Crowd-Averse Cyber-Physical Systems: The Paradigm of Robust Mean-Field Games
2016
For a networked controlled system, we illustrate the paradigm of robust mean-field games. This is a modeling framework at the interface of differential game theory, mathematical physics, and $H_{\infty}$ - optimal control that tries to capture the mutual influence between a crowd and its individuals. First, we establish a mean-field system for such games including the effects of adversarial disturbances. Second, we identify the optimal response of the individuals for a given population behavior. Third, we provide an analysis of equilibria and their stability.
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…
On coincidence of feedback and global Stackelberg equilibria in a class of differential games
2021
This paper shows for a class of differential games that the global Stackelberg equilibrium (GSE) coincides with the feedback Stackelberg equilibrium (FSE), although the GSE assumes that the leader/regulator an- nounces at the initial time the regulatory instrument rule she will follow for the rest of the game, while in the FSE, the regulator at any time chooses the optimal level of the regulatory instrument rate. This coincidence is based on the fact that the FSE is calculated using dynamic programming what implies that although the regulator chooses the regulatory instrument rate level that maximizes social welfare, the first-order condition for the maximization of the right-hand side of t…
Explicit solutions of Riccati equations appearing in differential games
1990
Abstract In this paper an explicit closed form solution of Riccati differential matrix equations appearing in games theory is given.
Collusion constrained equilibrium
2018
We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This allows groups to put positive probability on alternatives that are suboptimal for the group in certain razor's edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained e…
Worst Case Analysis of Non-local Games
2013
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input x i to the i th player who then responds by sending an answer a i to the referee. The players win if the answers a i satisfy a condition that may depend on the inputs x i .
On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games
2002
In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, conditions for obtaining the coincidence between the Stackelberg and Nash equilibria are defined in terms of the instantaneous pay-off function and the state equation of the game. Secondly, it is showed that for a class of differential games with state-interdependence both equilibria are identical independently of the player being the leader of the game. A survey of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting i…