Game theory and power control in ultrawideband networks

This paper describes a theoretical framework for the design and analysis of power control algorithms for high-throughput wireless networks using ultrawideband (UWB) technologies. The tools of game theory are shown to be expedient for deriving scalable, energy-efficient, distributed power control schemes to be applied to a population of battery-operated user terminals in a rich multipath environment. In particular, the power control issue is modeled as a dynamic noncooperative game in which each user chooses its transmit power so as to maximize its own utility, which is defined as the ratio of throughput to transmit power. Although distributed (noncooperative) control is known to be suboptimal with respect to the optimal centralized (cooperative) solution, it is shown via large-system analysis that the game-theoretic distributed algorithm based on Nash equilibrium exhibits negligible performance degradation with respect to the centralized socially optimal configuration. The framework described here is general enough to also encompass the analysis of code division multiple access (CDMA) systems and to show that UWB slightly outperforms CDMA in terms of achieved utility at the Nash equilibrium.     

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time,we find that when Nasli equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ.When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.     

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time,we find that when Nash equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ.When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.     

Joint utility-based uplink power and rate allocation in wireless networks: A non-cooperative game theoretic framework

In this paper a novel utility-based game theoretic framework is proposed to address the problem of joint transmission power and rate allocation in the uplink of a cellular wireless network. Initially, each user is associated with a generic utility function, capable of properly expressing and representing mobile user’s degree of satisfaction, in relation to the allocated system’s resources for heterogeneous services with various transmission rates. Then, a Joint Utility-based uplink Power and Rate Allocation (JUPRA) game is formulated, where each user aims selfishly at maximizing his utility-based performance under the imposed physical limitations, and its unique Nash equilibrium is determined with respect to both variables, i.e. uplink transmission power and rate. The JUPRA game’s convergence to its unique Nash equilibrium is proven and a distributed, iterative and low complexity algorithm for computing JUPRA game’s equilibrium is introduced. The performance of the proposed approach is evaluated in detail and its superiority compared to various state of the art approaches is illustrated, while the contribution of each component of the proposed framework in its performance is quantified and analyzed.     

Price-based interference control for two-tier femtocell networks

This paper presents a novel price-based interference control scheme for two-tier femtocell networks, aiming to limit the interference from femtocell users to macrocell base station (MBS). Assuming that the MBS protects itself by pricing the interference power from the femtocell users, the femtocell users set their transmission powers by competitively selecting the interference power fractions under the constraint of the total tolerable interference. The problem of femtocell users’ competitive interference occupation process is cast into a non-cooperative interference power purchase game, and the existence and uniqueness of the Nash equilibrium is proved. Then, a distributed interference power fraction iterative algorithm is developed to find the Nash equilibrium of the game, and the convergence analyses in both synchronous and asynchronous cases are presented. The distributed implementations are also shown. Simulation results show the convergence of the interference power fraction iterative algorithm and the effectiveness of the proposed interference control scheme.     

Statistical physics approach to graphical games: local and global interactions

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.     

Quantum Prisoners’ Dilemma in Fluctuating Massless Scalar Field

Quantum systems are easily affected by external environment. In this paper, we investigate the influences of external massless scalar field to quantum Prisoners’ Dilemma (QPD) game. We firstly derive the master equation that describes the system evolution with initial maximally entangled state. Then, we discuss the effects of a fluctuating massless scalar field on the game’s properties such as payoff, Nash equilibrium, and symmetry. We find that for different game strategies, vacuum fluctuation has different effects on payoff. Nash equilibrium is broken but the symmetry of the game is not violated.     

Evolutionarily stable strategies in quantum games

Evolutionarily stable strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population engaged in symmetric bimatrix game of prisoner's dilemma. Secondly we show that in an asymmetric quantum game between two players an ESS pair can be made to appear or disappear by resorting to entangled or unentangled initial states used to play the game even when the strategy pair remains a Nash equilibrium in both forms of the game.     

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under theinfluence of amplitude damping, depolarizing, and dephasing channels. It isshown that under the effect of decoherence, there is a Nash equilibrium ofthe game in case of depolarizing channel for Alice's quantum strategy.Whereas in case of dephasing noise, the game is not influenced by thequantum channel. For amplitude damping channel, Bob's payoffs are foundsymmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strategy remains always dominant against any choice of Alice's strategy.     

Binary power allocation for cognitive radio networks with centralized and distributed user selection strategies

Motivated by the desire for efficient spectral utilization, we present a novel algorithm based on binary power allocation for sum rate maximization in Cognitive Radio Networks (CRN). At the core lies the idea of combining multi-user diversity gains with spectral sharing techniques and consequently maximizing the secondary user sum rate while maintaining a guaranteed quality of service (QoS) to the primary system. We consider a cognitive radio network consisting of multiple secondary transmitters and receivers communicating simultaneously in the presence of the primary system. Our analysis treats both uplink and downlink scenarios. We first present a distributed power allocation algorithm that attempts to maximize the throughput of the CRN. The algorithm is simple to implement, since a secondary user can decide to either transmit data or stay silent over the channel coherence time depending on a specified threshold, without affecting the primary users’ QoS. We then address the problem of user selection strategy in the context of CRN. Both centralized and distributed solutions are presented. Simulation results carried out based on a realistic network setting show promising results.     

一种基于势博弈的无线传感器网络拓扑控制算法

在实际的应用中,无线传感器网络常常由大量电池资源有限的传感器节点组成.如何降低网络功耗,最大化网络生存时间,是传感器网络拓扑控制技术的重要研究目标.随着传感节点的运行,节点的能量分布可能越来越不均衡,需要在考虑该因素的情况下,动态地调整节点的网络负载以均衡节点的能耗,达到延长网络生存时间的目的.该文引入博弈理论和势博弈的概念,综合考虑节点的剩余能量和节点发射功率等因素,设计了一种基于势博弈的拓扑控制模型,并证明了该模型纳什均衡的存在性.通过构造兼顾节点连通性和能耗均衡性的收益函数,以确保降低节点功耗的同时维持网络的连通性.通过提高邻居节点的平均剩余能量值以实现将剩余能量多的节点选择作为自身的邻居节点,提高节点能耗的均衡性.在此基础上,提出了一种分布式的能耗均衡拓扑控制算法.理论分析证明了该算法能保持网络的连通性.与现有基于博弈理论的DIA算法和MLPT算法相比,本算法形成的拓扑负载较重、剩余能量较小的瓶颈节点数量较少,节点剩余能量的方差较小,网络生存时间更长.     

Stability of Mixed Nash Equilibria in Symmetric Quantum Games

In bimatrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permitpure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initialquantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixedsymmetric Nash equilibrium.     

基于博弈论的认知无线电网络跨层资源分配

针对多跳认知无线电网络的多层资源分配问题,提出了协作去耦合方法和跨层联合方法,协作去耦合方法首先单独完成路径选择任务,随后进行信道与功率的博弈分配;跨层联合方法则通过博弈直接对路径、信道、功率三层资源进行同时分配,两种方法都综合考虑网络层、介质访问控制层、物理层的启发原则,引入了节点被干扰度信息和节点主动干扰度信息来辅助路径选择,设计了基于功率允许宽度信息的Boltzmann探索来完成信道与功率选择,设计了长链路和瓶颈链路替换消除机制以进一步提高网络性能,从促进收敛角度,选择序贯博弈并设计了具体的博弈过程,此外还分析了博弈的纳什均衡,讨论了两种算法的复杂度,仿真结果表明,协作去耦合方法和跨层联合方法在成功流数量、流可达速率、发射功耗性能指标上均优于简单去耦合的链路博弈、流博弈方法。     

Quantum Games under Decoherence

Quantum systems are easily influenced by ambient environments. Decoherence is generated by system interaction with external environment. In this paper, we analyse the effects of decoherence on quantum games with Eisert-Wilkens-Lewenstein (EWL) (Eisert et al., Phys. Rev. Lett. 83(15), 3077 1999) and Marinatto-Weber (MW) (Marinatto and Weber, Phys. Lett. A 272, 291 2000) schemes. Firstly, referring to the analytical approach that was introduced by Eisert et al. (Phys. Rev. Lett. 83(15), 3077 1999), we analyse the effects of decoherence on quantum Chicken game by considering different traditional noisy channels. We investigate the Nash equilibria and changes of payoff in specific two-parameter strategy set for maximally entangled initial states. We find that the Nash equilibria are different in different noisy channels. Since Unruh effect produces a decoherence-like effect and can be perceived as a quantum noise channel (Omkar et al., arXiv:1408.1477v1), with the same two parameter strategy set, we investigate the influences of decoherence generated by the Unruh effect on three-player quantum Prisoners’ Dilemma, the non-zero sum symmetric multiplayer quantum game both for unentangled and entangled initial states. We discuss the effect of the acceleration of noninertial frames on the the game’s properties such as payoffs, symmetry, Nash equilibrium, Pareto optimal, dominant strategy, etc. Finally, we study the decoherent influences of correlated noise and Unruh effect on quantum Stackelberg duopoly for entangled and unentangled initial states with the depolarizing channel. Our investigations show that under the influence of correlated depolarizing channel and acceleration in noninertial frame, some critical points exist for an unentangled initial state at which firms get equal payoffs and the game becomes a follower advantage game. It is shown that the game is always a leader advantage game for a maximally entangled initial state and there appear some points at which the payoffs become zero.     

The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein–Podolsky–Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.     

The rock–paper–scissors game

Rock–Paper–Scissors (RPS), a game of cyclic dominance, is not merely a popular children’s game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no background in game theory, this paper introduces the concepts of Nash equilibrium and evolutionarily stable strategy, and reviews some recent theoretical and empirical efforts on the non-equilibrium properties of the iterated RPS, including collective cycling, conditional response patterns and microscopic mechanisms that facilitate cooperation. We also introduce several dynamical processes to illustrate the applications of RPS as a simplified model of species competition in ecological systems and price cycling in economic markets.     

Resource allocation for LTE-based cognitive radio network with queue stability and interference constraints

We consider the problem of interference management and resource allocation in a cognitive radio network (CRNs) where the licensed spectrum holders (primary users) share their spare capacity with the non-licensed spectrum holders (secondary users). Under such shared spectrum usage the transmissions of the secondary users should have a minimal impact on the quality of service (QoS) and the operating conditions of the primary users. Therefore, it is important to distinguish the two types of users, and formulate the problem of resource allocation considering hard restrictions on the user-perceived QoS (such as packet end-to-end delay and loss) and physical-layer channel characteristics (such as noise and interference) of the primary users. To achieve this goal, we propose to assign the bandwidth and transmission power to minimize the total buffer occupancy in the system subject to capacity constraints, queue stability constraints, and interference requirements of the primary users. We apply this approach for resource allocation in a CRN built upon a Third Generation Partnership Project (3GPP) long-term evolution (LTE) standard platform. Performance of the algorithm is evaluated using simulations in OPNET environment. The algorithm shows consistent performance improvement when compared with other relevant resource allocation techniques.     

Constructing quantum games from symmetric non-factorizable joint probabilities

We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and quantum games without recourse to the formalism of quantum mechanics.     

Tripartite Dynamic Zero-Sum Quantum Games

The Nash equilibrium plays a crucial role in game theory. Most of results are based on classical resources. Our goal in this paper is to explore multipartite zero-sum game with quantum settings. We find that in two different settings there is no strategy for a tripartite classical game being fair. Interestingly, this is resolved by providing dynamic zero-sum quantum games using single quantum state. Moreover, the gains of some players may be changed dynamically in terms of the committed state. Both quantum games are robust against the preparation noise and measurement errors.     

Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents

We introduce an analytical model to study the evolution towards equilibrium in spatialgames, with ‘memory-aware’ agents, i.e., agents that accumulate their payoff over time. Inparticular, we focus our attention on the spatial Prisoner’s Dilemma, as it constitutes anemblematic example of a game whose Nash equilibrium is defection. Previous investigationsshowed that, under opportune conditions, it is possible to reach, in the evolutionaryPrisoner’s Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms likemotion may lead a population to become cooperative. In the proposed model, we map agentsto particles of a gas so that, on varying the system temperature, they randomly move. Indoing so, we are able to identify a relation between the temperature and the finalequilibrium of the population, explaining how it is possible to break the classical Nashequilibrium in the spatial Prisoner’s Dilemma when considering agents able to increasetheir payoff over time. Moreover, we introduce a formalism to study order-disorder phasetransitions in these dynamics. As result, we highlight that the proposed model allows toexplain analytically how a population, whose interactions are based on the Prisoner’sDilemma, can reach an equilibrium far from the expected one; opening also the way todefine a direct link between evolutionary game theory and statistical physics.