Static Non-cooperative Game Research Articles

Non-cooperative game algorithms for computation offloading in mobile edge computing environments

Mobile Edge Computing (MEC) has become a promising technology for 5G networks. Computation offloading is an essential issue of MEC, which enables mobile User Equipment (UE) to enjoy rich wireless resources and huge computing power anywhere. This paper considers the Quality-of-Experience (QoE) of UEs in 5G MEC systems and presents a dynamic non-cooperative game (QCOG-DG) algorithm and a static non-cooperative game (QCOG-SG) algorithm for computation offloading of MEC applications. We establish an MEC computation offloading model by considering the QoE requirements of UEs, and discuss the communication overheads, computation cost, and energy consumption models to minimize the energy consumption and time delay of each UE. Considering that there are multiple UEs who want to offload their computation tasks to a resource-constrained MEC server, and each UE is selfish and competitive, we formulate the problem of computation offloading decision as a non-cooperative game model. We prove the existence of a Nash Equilibrium (NE) solution for the proposed game model. In addition, we propose an algorithm that jointly optimizes energy consumption and time delay under QoE preferences to achieve optimal offloading benefits for each UE. Moreover, we respectively propose a dynamic non-cooperative game (QCOG-DG) algorithm and a static non-cooperative game (QCOG-SG) algorithm to efficiently find the NE solution. Extensive simulation experiments are conducted to verify the effectiveness of the proposed MEC computation offloading model and the QCOG-DG and QCOG-SG algorithms. Simulation results show that the proposed QCOG-DG algorithm can efficiently find the NE solutions in the MEC scenarios with UEs of different sizes.

Utility Optimization for Multi-User Task Offloading in Mobile Ad Hoc Cloud: A Stochastic Game Approach

Offloading tasks to the mobile ad hoc cloud (MAHC) can improve the utility of mobile devices in scenarios without infrastructure. However, when multiple resource demanders (RDs) offload tasks to multiple resource providers (RPs) in the MAHC with task random generation, how to optimize the utility of RDs and the service quality of the MAHC is an issue worth researching. To this end, we investigate this issue from the stochastic game perspective. Firstly, we combine the obtained time, energy, and monetary revenue as the utility of each RD and construct the utility improvement of each RD as a static non-cooperative game. Secondly, according to the randomness of RD’s task generation, we transform the single-shot non-cooperative game into a stochastic game in an infinite time horizon to obtain the long-term utility. Thirdly, to reduce the computational complexity for achieving Nash equilibrium, we propose an action reduction alternate backward iteration algorithm according to the games characteristics and prove its convergence. Finally, we compare the utility obtained from the static game with the stochastic game, the numerical results indicating that the utility of each RD can be effectively improved by utilizing the stochastic game.

Fast convergence to Nash equilibria without steady-state oscillation

The problem of fast convergence to Nash equilibrium without steady state oscillation in static non-cooperative games with N players is considered in this paper. In this regard, players can generate their actions to achieve Nash equilibrium only by measuring their own payoff values, which means that the players do not need any information about the details of payoff function or other players’ actions. Additionally, in contrast to the most classical extremum seeking algorithms, this algorithm can converge to Nash equilibria without steady state oscillation and faster, because the amplitude of excitation sinusoidal signal in the conventional extremum seeking is adjusted to converge to zero, so the deleterious effects of steady state oscillation will be eliminated. Moreover, since each player can possess a dynamic, the actions are filtered before applying to the payoff function, which can make this algorithm appealing to many applications such as mobile sensor networks. In addition, the details of convergence to Nash equilibria are provided. Finally, we illustrate the application of this algorithm to solve the formation control problem of non-holonomic unicycles, and evasion of jammer attacks on unmanned autonomous vehicles (UAVs), which clearly shows the effectiveness and superiority of this algorithm through simulation results.

Matching and chatting: An experimental study of the impact of network communication on school-matching mechanisms

While, in theory, the school matching problem is a static non-cooperative one-shot game, in reality the “matching game” is played by parents who choose their strategies after consulting or chatting with other parents in their social networks. In this paper we compare the performance of the Boston and the Gale–Shapley mechanisms in the presence of chatting through social networks. Our results indicate that allowing subjects to chat has an important impact on the likelihood that subjects change their strategies and also on the welfare and stability of the outcomes determined by the mechanism.

An Ordinal Game Theory Approach to the Analysis and Selection of Partners in Public–Private Partnership Projects

Nowadays, public---private partnership projects have become a standard for delivering public services in both developed and developing countries. In this paper, we are concerned with the analysis of private sector proposals and the selection of the private sector partner to whom to award the contract. To the best of our knowledge, this problem has not been addressed within a game theory framework. To fill this gap, we model this decision problem as a static non-cooperative game of complete information and propose a new ordinal game theory algorithm for finding an optimal generalized Nash equilibrium. The proposed algorithm determines a single ranking of proposals or bidders that takes account of multiple performance criteria and reflects both the public sector and the private sector perspectives, and can handle any number of private sector players and any number of contractual terms. An illustrative scenario is provided to guide the reader through the workings of the proposed ordinal game theory algorithm. The proposed ordinal game theory-based analysis framework can be used by the private sector to analyse any set of potential proposals most likely to be submitted by bidders and to assist with the choice of bidding strategies, and by the public sector player to analyse any set of potential proposals most likely to be submitted under any set of contractual terms and to assist with the choice of a realistic set of contractual terms and their performance measures.

Applications of Repeated Games in Wireless Networks: A Survey

A repeated game is an effective tool to model interactions and conflicts for players aiming to achieve their objectives in a long-term basis. Contrary to static noncooperative games that model interactions among players in only one period, in repeated games, interactions of players repeat for multiple periods. Thus, the players become aware of other players' past behaviors and their future benefits, so as to adapt their strategies accordingly. In wireless networks, conflicts among wireless nodes can lead to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. In this paper, we survey applications of repeated games in different wireless networks. The main goal is to demonstrate the use of repeated games in encouraging wireless nodes into cooperations, thereby improving network performances and avoiding network disruption due to selfish behaviors. Furthermore, various problems in wireless networks and variations of repeated game models together with the corresponding solutions are discussed in this survey. Finally, we outline some open issues and future research directions.

Repeated Intersession Network Coding Games: Efficiency and Min-Max Bargaining Solution

Recent results have shown that selfish users do not have an incentive to participate in intersession network coding in a static noncooperative game setting. Because of this, the worst-case network efficiency (i.e., the price-of-anarchy) can be as low as 20%. In this paper, we show that if the same game is played repeatedly, then the price-of-anarchy can be improved to 36%. We design a grim-trigger strategy that encourages users to cooperate and participate in the intersession network coding. A key challenge is to determine a common cooperative coding rate that the users should mutually agree on. We resolve the conflict of interest among the users through a bargaining process and obtain tight upper bounds for the price-of-anarchy that are valid for any possible bargaining scheme. Moreover, we propose a simple and efficient min-max bargaining solution that can achieve these upper bounds, as confirmed through simulation studies. The coexistence of multiple selfish network coding sessions as well as the coexistence of selfish network coding and routing sessions are also investigated. Our results represent a first step toward designing practical intersession network coding schemes that achieve reasonable performance for selfish users.

Disturbance and Delay Robustness Guarantees of Gradient Systems Based on Static Noncooperative Games With an Application to Feedback Control for PEV Charging Load Allocation

This paper investigates robustness of gradient-type dynamical systems derived from static noncooperative games with a large number of players. The control objective is to drive state variables to the vicinities of Nash equilibria in the presence of disturbance and time-delay. The framework of integral input-to-state stability for large-scale systems is employed for verifying such global robustness. Several robustness criteria are presented, and Lyapunov-Krasovskii functionals are constructed. The developed theory is applied to the plug-in electric vehicle charging problem of allocating the charging load to the overnight demand valley to reduce the impact on the electric grid. Securing robustness of the dynamic load allocation is important, since eliminating uncertainties in demand predictions would become harder due to energy storage integration coupled with various energy-aware technologies. Introducing feedback, this paper guarantees stability and achieves robustness of the allocation dynamics subject to communication delay when demand predictions are not accurate. The usefulness of the proposed decentralized scheme is illustrated by numerical simulations.

Selfish users in energy constrained ALOHA systems with power capture

We consider a slotted ALOHA setting where backlogged, energy-constrained users selfishly select the probability with which they transmit packets. Packets are successfully received, even in case of collision, if the signal to interference plus noise ratio at the access point exceeds some threshold (power capture). The user problem of finding appropriate transmission probabilities is formulated as a static non-cooperative game and the performance limits for stationary and mobile scenarios are determined. The equilibrium analyses show that for stationary scenarios, users with high pathgains share the channel fairly while others never transmit. In the mobile case users utilize a binary strategy where they try to monopolize the channel when their pathgain exceeds some threshold that depends on system parameters (number of users, transmission costs, etc.). Otherwise they shut their transmitters off. Compared to traditional nondiscriminatory distributed multiaccess protocols the operating points achieved by selfish users generally increase sum-utility although this comes at the expense of larger user performance variations.

Multiradio Channel Allocation in Multihop Wireless Networks

Channel allocation was extensively investigated in the framework of cellular networks, but it was rarely studied in the wireless ad hoc networks, especially in the multihop networks. In this paper, we study the competitive multiradio multichannel allocation problem in multihop wireless networks in detail. We first analyze that the static noncooperative game and Nash equilibrium (NE) channel allocation scheme are not suitable for the multihop wireless networks. Thus, we model the channel allocation problem as a hybrid game involving both cooperative game and noncooperative game. Within a communication session, it is cooperative; and among sessions, it is noncooperative. We propose the min-max coalition-proof Nash equilibrium (MMCPNE) channel allocation scheme in the game, which aims to maximize the achieved data rates of communication sessions. We analyze the existence of MMCPNE and prove the necessary conditions for MMCPNE. Furthermore, we propose several algorithms that enable the selfish players to converge to MMCPNE. Simulation results show that MMCPNE outperforms NE and coalition-proof Nash equilibrium (CPNE) schemes in terms of the achieved data rates of multihop sessions and the throughput of whole networks due to cooperation gain.

Asynchronous Iterative Water-Filling for Gaussian Frequency-Selective Interference Channels

This paper considers the maximization of information rates for the Gaussian frequency-selective interference channel, subject to power and spectral mask constraints on each link. To derive decentralized solutions that do not require any cooperation among the users, the optimization problem is formulated as a static noncooperative game of complete information. To achieve the so-called Nash equilibria of the game, we propose a new distributed algorithm called asynchronous iterative water-filling algorithm. In this algorithm, the users update their power spectral density (PSD) in a completely distributed and asynchronous way: some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference. The proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water-filling algorithms, e.g., sequential and simultaneous versions. The main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the (unique) Nash equilibrium of the game.

Non-cooperative games with a continuum of players whose payoffs depend on summary statistics

We consider static non-cooperative games with a continuum of small players whose payoffs depend on their own actions and finitely many summary statistics of the aggregate strategy profile. We prove the existence of an equilibrium in pure strategies without any convexity restrictions on payoffs or the common action space. We show that this result applies to a broad class of monopolistic competition models.

Posterior odds comparison of a symmetric low-price, sealed-bid auction within the common-value and the independent-private-values paradigms

I attempt to decide, using the posterior odds ratio, whether the symmetric common-value paradigm or the symmetric independent-private-values paradigm is a more probable explanation of the low-price, sealed-bid auctions conducted by the Indian Oil Corporation to purchase crude-oil from the international market. The estimation approach is structural parametric. The auctions are modelled as static non-cooperative games of incomplete information with risk neutral bidders. I conclude that the symmetric independent-private-values paradigm is more probable. Copyright © 1999 John Wiley & Sons, Ltd.

Evolutionary Game Theory

This text introduces current evolutionary game theory -- where ideas from evolutionary biology and rationalistic economics meet -- emphasizing the links between static and dynamic approaches and noncooperative game theory. Much of the text is devoted to the key concepts of evolutionary stability and replicator dynamics. The former highlights the role of mutations and the latter the mechanisms of selection. Moreover, set-valued static and dynamic stability concepts, as well as processes of social evolution, are discussed. Separate background chapters are devoted to noncooperative game theory and the theory of ordinary differential equations. There are examples throughout as well as individual chapter summaries. Because evolutionary game theory is a fast-moving field that is itself branching out and rapidly evolving, Jorgen Weibull has judiciously focused on clarifying and explaining core elements of the theory in an up-to-date, comprehensive, and self-contained treatment. The result is a text for second-year graduate students in economic theory, other social sciences, and evolutionary biology. The book goes beyond filling the gap between texts by Maynard-Smith and Hofbauer and Sigmund that are currently being used in the field. Evolutionary Game Theory will also serve as an introduction for those embarking on research in this area as well as a reference for those already familiar with the field. Weibull provides an overview of the developments that have taken place in this branch of game theory, discusses the mathematical tools needed to understand the area, describes both the motivation and intuition for the concepts involved, and explains why and how it is relevant to economics.