Cournot oligopoly interval games

In this paper we consider cooperative Cournot oligopoly games. Following Chander and Tulkens (1997) we assume that firms react to a deviating coalition by choosing individual best reply strategies. Lardon (2009) shows that if the inverse demand function is not differentiable, it is not always possible to define a Cournot oligopoly TU(Transferable Utility)-game. In this paper, we prove that we can always specify a Cournot oligopoly interval game. Furthermore, we deal with the problem of the non-emptiness of two induced cores: the interval gamma-core and the standard gamma-core. To this end, we use a decision theory criterion, the Hurwicz criterion (Hurwicz 1951), that consists in combining, for any coalition, the worst and the better worths that it can obtain in its worth interval. The first result states that the interval gamma-core is non-empty if and only if the oligopoly TU-game associated with the better worth of every coalition in its worth interval admits a non-empty gamma-core. However, we show that even for a very simple oligopoly situation, this condition fails to be satisfied. The second result states that the standard gamma-core is non-empty if and only if the oligopoly TU- game associated with the worst worth of every coalition in its worth interval admits a nonempty gamma-core. Moreover, we give some properties on every individual profit function and every cost function under which this condition always holds, what substantially extends the gamma-core existence results in Lardon (2009).Cournot oligopoly interval game; Interval gamma-core; Standard gamma-core; Hurwicz criterion;

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy

Channel Selection for Network-assisted D2D Communication via No-Regret Bandit Learning with Calibrated Forecasting

We consider the distributed channel selection problem in the context of device-to-device (D2D) communication as an underlay to a cellular network. Underlaid D2D users communicate directly by utilizing the cellular spectrum but their decisions are not governed by any centralized controller. Selfish D2D users that compete for access to the resources construct a distributed system, where the transmission performance depends on channel availability and quality. This information, however, is difficult to acquire. Moreover, the adverse effects of D2D users on cellular transmissions should be minimized. In order to overcome these limitations, we propose a network-assisted distributed channel selection approach in which D2D users are only allowed to use vacant cellular channels. This scenario is modeled as a multi-player multi-armed bandit game with side information, for which a distributed algorithmic solution is proposed. The solution is a combination of no-regret learning and calibrated forecasting, and can be applied to a broad class of multi-player stochastic learning problems, in addition to the formulated channel selection problem. Analytically, it is established that this approach not only yields vanishing regret (in comparison to the global optimal solution), but also guarantees that the empirical joint frequencies of the game converge to the set of correlated equilibria.Comment: 31 pages (one column), 9 figure

Exploring resource/performance trade-offs for streaming applications on embedded multiprocessors

Embedded system design is challenged by the gap between the ever-increasing customer demands and the limited resource budgets. The tough competition demands ever-shortening time-to-market and product lifecycles. To solve or, at least to alleviate, the aforementioned issues, designers and manufacturers need model-based quantitative analysis techniques for early design-space exploration to study trade-offs of different implementation candidates. Moreover, modern embedded applications, especially the streaming applications addressed in this thesis, face more and more dynamic input contents, and the platforms that they are running on are more flexible and allow runtime configuration. Quantitative analysis techniques for embedded system design have to be able to handle such dynamic adaptable systems. This thesis has the following contributions: - A resource-aware extension to the Synchronous Dataflow (SDF) model of computation. - Trade-off analysis techniques, both in the time-domain and in the iterationdomain (i.e., on an SDF iteration basis), with support for resource sharing. - Bottleneck-driven design-space exploration techniques for resource-aware SDF. - A game-theoretic approach to controller synthesis, guaranteeing performance under dynamic input. As a first contribution, we propose a new model, as an extension of static synchronous dataflow graphs (SDF) that allows the explicit modeling of resources with consistency checking. The model is called resource-aware SDF (RASDF). The extension enables us to investigate resource sharing and to explore different scheduling options (ways to allocate the resources to the different tasks) using state-space exploration techniques. Consistent SDF and RASDF graphs have the property that an execution occurs in so-called iterations. An iteration typically corresponds to the processing of a meaningful piece of data, and it returns the graph to its initial state. On multiprocessor platforms, iterations may be executed in a pipelined fashion, which makes performance analysis challenging. As the second contribution, this thesis develops trade-off analysis techniques for RASDF, both in the time-domain and in the iteration-domain (i.e., on an SDF iteration basis), to dimension resources on platforms. The time-domain analysis allows interleaving of different iterations, but the size of the explored state space grows quickly. The iteration-based technique trades the potential of interleaving of iterations for a compact size of the iteration state space. An efficient bottleneck-driven designspace exploration technique for streaming applications, the third main contribution in this thesis, is derived from analysis of the critical cycle of the state space, to reveal bottleneck resources that are limiting the throughput. All techniques are based on state-based exploration. They enable system designers to tailor their platform to the required applications, based on their own specific performance requirements. Pruning techniques for efficient exploration of the state space have been developed. Pareto dominance in terms of performance and resource usage is used for exact pruning, and approximation techniques are used for heuristic pruning. Finally, the thesis investigates dynamic scheduling techniques to respond to dynamic changes in input streams. The fourth contribution in this thesis is a game-theoretic approach to tackle controller synthesis to select the appropriate schedules in response to dynamic inputs from the environment. The approach transforms the explored iteration state space of a scenario- and resource-aware SDF (SARA SDF) graph to a bipartite game graph, and maps the controller synthesis problem to the problem of finding a winning positional strategy in a classical mean payoff game. A winning strategy of the game can be used to synthesize the controller of schedules for the system that is guaranteed to satisfy the throughput requirement given by the designer

Game theoretic models for resource sharing in wireless networks

Wireless communications have been recently characterized by rapid proliferation of wireless networks, impressive growth of standard and technologies, evolution of the end-user terminals, and increasing demand in the wireless spectrum. New, more flexible schemes for the management of the available resources, from both the user and the network side, are necessary in order to improve the efficiency in the usage of the available resources.This work aims at shedding light on the performance modeling of radio resource sharing/allocation situations. Since, in general, the quality of service perceived by a system (e.g., user, network) strictly depends on the behavior of the other entities, and the involved interactions are mainly competitive, this work introduces a framework based on non–cooperative game theoretic tools. Furthermore, non–cooperative game theory is suitable in distributed networks, where control and management are inherently decentralized.First, we consider the case in which many users have to make decisions on which wireless access point to connect to. In this scenario, the quality perceived by the users mainly depends on the number of other users choosing the very same accessing opportunity. In this context, we also consider two–stage games where network make decisions on how to use the available resources, and users react to this selecting the network that maximizes their satisfaction. Then, we refer to the problem of spectrum sharing, where users directly compete for portions of the available spectrum. Finally, we provide a more complex model where the users utility function is based on the Shannon rate. The aim of this second part is to provide a better representation of the satisfaction perceived by the users, i.e., in terms of achievable throughput. Due to the complexity of the game model, we first provide a complete analytical analysis of the two–user case. Then, we extend the model to the N–user case. We mainly analyze this game through simulations. Finally, inspired by the results obtained numerically, we introduce stochastic geometry in the analysis of spectrum games in order to predict the performance of the game in large networks.Ph.D., Electrical Engineering -- Drexel University, 201