Constrained Cost-Coupled Stochastic Games with Independent State Processes

We consider a non-cooperative constrained stochastic games with N players with the following special structure. With each player there is an associated controlled Markov chain. The transition probabilities of the i-th Markov chain depend only on the state and actions of controller i. The information structure that we consider is such that each player knows the state of its own MDP and its own actions. It does not know the states of, and the actions taken by other players. Finally, each player wishes to minimize a time-average cost function, and has constraints over other time-avrage cost functions. Both the cost that is minimized as well as those defining the constraints depend on the state and actions of all players. We study in this paper the existence of a Nash equilirium. Examples in power control in wireless communications are given.Comment: 7 pages, submitted in september 2006 to Operations Research Letter

Foresighted Demand Side Management

We consider a smart grid with an independent system operator (ISO), and distributed aggregators who have energy storage and purchase energy from the ISO to serve its customers. All the entities in the system are foresighted: each aggregator seeks to minimize its own long-term payments for energy purchase and operational costs of energy storage by deciding how much energy to buy from the ISO, and the ISO seeks to minimize the long-term total cost of the system (e.g. energy generation costs and the aggregators' costs) by dispatching the energy production among the generators. The decision making of the entities is complicated for two reasons. First, the information is decentralized: the ISO does not know the aggregators' states (i.e. their energy consumption requests from customers and the amount of energy in their storage), and each aggregator does not know the other aggregators' states or the ISO's state (i.e. the energy generation costs and the status of the transmission lines). Second, the coupling among the aggregators is unknown to them. Specifically, each aggregator's energy purchase affects the price, and hence the payments of the other aggregators. However, none of them knows how its decision influences the price because the price is determined by the ISO based on its state. We propose a design framework in which the ISO provides each aggregator with a conjectured future price, and each aggregator distributively minimizes its own long-term cost based on its conjectured price as well as its local information. The proposed framework can achieve the social optimum despite being decentralized and involving complex coupling among the various entities

Normalized equilibrium in Tullock rent seeking game

International audienceGames with Common Coupled Constraints represent manyreal life situations. In these games, if one player fails tosatisfy its constraints common to other players, then theother players are also penalised. Therefore these games canbe viewed as being cooperative in goals related to meetingthe common constraints, and non cooperative in terms ofthe utilities. We study in this paper the Tullock rent seekinggame with additional common coupled constraints. We havesucceded in showing that the utilities satisfy the property ofdiagonal strict concavity (DSC), which can be viewed asan extention of concavity to a game setting. It not onlyguarantees the uniqueness of the Nash equilibrium but also of the normalized equilibrium