Lyapunov stochastic stability and control of robust dynamic coalitional games with transferable utilities

This paper considers a dynamic game with transferable utilities (TU), where the characteristic function is a continuous-time bounded mean ergodic process. A central planner interacts continuously over time with the players by choosing the instantaneous allocations subject to budget constraints. Before the game starts, the central planner knows the nature of the process (bounded mean ergodic), the bounded set from which the coalitions' values are sampled, and the long run average coalitions' values. On the other hand, he has no knowledge of the underlying probability function generating the coalitions' values. Our goal is to find allocation rules that use a measure of the extra reward that a coalition has received up to the current time by re-distributing the budget among the players. The objective is two-fold: i) guaranteeing convergence of the average allocations to the core (or a specific point in the core) of the average game, ii) driving the coalitions' excesses to an a priori given cone. The resulting allocation rules are robust as they guarantee the aforementioned convergence properties despite the uncertain and time-varying nature of the coaltions' values. We highlight three main contributions. First, we design an allocation rule based on full observation of the extra reward so that the average allocation approaches a specific point in the core of the average game, while the coalitions' excesses converge to an a priori given direction. Second, we design a new allocation rule based on partial observation on the extra reward so that the average allocation converges to the core of the average game, while the coalitions' excesses converge to an a priori given cone. And third, we establish connections to approachability theory and attainability theory

Strategic thinking under social influence: Scalability, stability and robustness of allocations

This 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

Game-theoretic learning and allocations in robust dynamic coalitional games

The problem of allocation in coalitional games with noisy observations and dynamic4 environments is considered. The evolution of the excess is modelled by a stochastic differential5 inclusion involving both deterministic and stochastic uncertainties. The main contribution is a6 set of linear matrix inequality conditions which guarantee that the distance of any solution of the7 stochastic differential inclusions from a predefined target set is second-moment bounded. As a direct8 consequence of the above result we derive stronger conditions still in the form of linear matrix9 inequalities to hold in the entire state space, which guarantee second-moment boundedness. Another10 consequence of the main result are conditions for convergence almost surely to the target set, when the11 Brownian motion vanishes in proximity of the set. As further result we prove convergence conditions12 to the target set of any solution to the stochastic differential equation if the stochastic disturbance13 has bounded support. We illustrate the results on a simulated intelligent mobility scenario involving14 a transport network

Opinion dynamics in coalitional games with transferable utilities

© 2014 IEEE. This paper studies opinion dynamics in a large number of homogeneous coalitional games with transferable utilities (TU), where the characteristic function is a continuous-time stochastic process. For each game, which we can see as a 'small world', the players share opinions on how to allocate revenues based on the mean-field interactions with the other small worlds. As a result of such mean-field interactions among small worlds, in each game, a central planner 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 paper also studies the convergence and stability of opinions on allocations via stochastic stability theory

Dynamic Cooperative and Non-cooperative Games under Stochastic Uncertainty: Optimal Strategies, Stability and Control

In this thesis, we have studied different models of cooperative and non-cooperative games in a dynamic framework. In cooperative games, we have studied the benefit of coalition formation in different problems, such as coordinated maintenance, coordinated replenishment, wind power production, and linear production games. Through these chapters, we have designed allocation rules to distribute the total income of the coalitions among its members in a fair and stable way, thereby encouraging cooperation between the players. In the chapters related to non-cooperative games, we have investigated dynamic games with various characteristics, including stochasticity, discreteness, and with both complete and incomplete information. The primary focus of these chapters is to determine whether or not an equilibrium exists, namely, if there exist strategies in which all the players are making their best decisions and do not benefit from changing the strategy. In this thesis, we have tackled the problems we set out to solve by using different disciplines. We have applied not only concepts from game theory but also from control theory, optimization, probability, and data learning, among others. By combining these disciplines, we enable decision-makers in the games to learn from their environment and make smarter decisions