In this paper, a generalization of the satisfaction equilibrium (SE) for games in satisfaction form (SF) is presented. This new solution concept is referred to as the generalized satisfaction equilibrium (GSE). In games in SF, players choose their actions to satisfy an individual constraint that depends on the actions of all the others. At a GSE, players that are unsatisfied are unable to unilaterally deviate to be satisfied. The concept of GSE generalizes the SE in the sense that it allows mixed-strategy equilibria in which there exist players who are unable to satisfy their individual constraints. The pure-strategy GSE problem is closely related to the constraint satisfaction problem and finding a pure-strategy GSE is proven to be NP-hard. The existence of at least one GSE in mixed strategies is proven for the class of games in which the constraints are defined by a lower limit on the expected utility. A dynamics referred to as the satisfaction response is shown to converge to a GSE in certain classes of games. Finally, Bayesian games in SF and the corresponding Bayesian GSE are introduced. These results provide a theoretical framework for studying service-level provisioning problems in communications networks as shown by several examples.

Abstract This paper considers uplink channel access in a zone of closed‐access small‐cells that is deployed in a macrocell service area. All small‐cell user equipments (SUEs) have access to a common orthogonal set of channels, leading to intercell interference. In addition, each channel forms a separate collision domain in each cell, thus can be successfully used only by one SUE of that cell. This paper proposes two non‐cooperative Bayesian games, G1 and G2, that are played among the SUEs. G1 assumes the availability of channel state information at the transmitters, while G2 assumes the availability of only the distribution of the channel state information. Each SUE can choose to transmit over one of the channels or not to transmit. The emphasis of the paper is on the set of symmetric threshold strategies where the Nash equilibrium is fully determined by a single parameter. The existence and uniqueness of pure Bayesian–Nash symmetric equilibrium of G1 in threshold strategies and mixed Bayesian–Nash symmetric equilibrium of G2 in uniformly distributed threshold strategies are proven. Numerical results corroborate the theoretical findings and benchmark against another decentralized scheme. Copyright © 2015 John Wiley & Sons, Ltd.

We consider a point-to-point wireless link with automatic repeat request (ARQ) based packet transmission where both the transmitter and receiver nodes are energy harvesting (EHNs). Transmitter EHN has access to low-grade channel state information (CSI) as it is implicitly obtained from ARQ feedback. Furthermore, signal processing tasks such as sampling and decoding at the receiver EHN can be interrupted if there is insufficient energy in the battery that cause loss of packet and wastage of harvested energy both at the transmitter and receiver EHNs. We propose selective sampling (SS) scheme where only part of the transmitted packet is sampled and stored depending on the receiver nodes stored energy. SS information (SSI) is then fed back to the transmitter. Packet decoding is not performed until full packet is constructed. Hence, we modify the conventional ARQ messages, i.e., ACK/NAK by adding few more bits to carry additional SSI as well. Another objective is to find the optimal power allocation policy to adapt to the low-grade CSI and SSI available at the transmitter such that harvested energy can be utilized efficiently especially at the receiver. Furthermore, using a decision-theoretic framework, we propose greedy power allocation scheme to evaluate the performance of the proposed retransmission scheme. In numerical examples, we illustrate that our proposed scheme has lower average packet transmission time and packet drop probability (PDP) compared to the equal power allocation and greedy power allocation with conventional retransmission scheme.

Minimum-collisions assignment (MCA), in a wireless network, is the distribution of a finite resource set, such that the number of neighbor cells which receive common elements is minimized. In classical operator deployed networks, resources are assigned centrally. Heterogeneous networks contain user deployed cells, therefore centralized assignment is problematic. MCA includes orthogonal frequency bands, time slots, and physical cell identity (PCI) allocation. MCA is NP-complete, therefore a potential-game-theoretic model is proposed as a distributed solution. The players of the game are the cells, actions are the set of PCIs and the cost of a cell is the number of neighbor cells in collision. The price of anarchy and price of stability are derived. Moreover the paper adapts a randomized-distributed-synchronous-update algorithm, for the case, when the number of PCIs is higher than the maximum degree of the neighbor relations graph. It is proven that the algorithm converges to a optimal pure strategy Nash equilibrium in finite time and it is robust to node addition. Simulation results demonstrate that the algorithm is sub-linear in the size of the input graph, thus outperforms best response dynamics.

This paper addresses the problem of competition vs. cooperation in the downlink, between base stations (BSs), of a multiple input multiple output (MIMO) interference, heterogeneous wireless network (HetNet). This research presents a scenario where a macrocell base station (MBS) and a cochannel femtocell base station (FBS) each simultaneously serving their own user equipment (UE), has to choose to act as individual systems or to cooperate in coordinated multipoint transmission (CoMP). The paper employes both the theories of non-cooperative and cooperative games in a unified procedure to analyze the decision making process. The BSs of the competing system are assumed to operate at the maximum expected sum rate (MESR) correlated equilibrium (CE), which is compared against the value of CoMP to establish the stability of the coalition. It is proven that there exists a threshold geographical separation, dth, between the macrocell user equipment (MUE) and FBS, under which the region of coordination is non-empty. Theoretical results are verified through simulations.

This paper considers the allocation of frequency and time resources in a heterogeneous network, in a self-organizing manner. The general problem is to assign a resource set, so as to minimize the number of pairs of adjacent base stations that obtain the same resource. This can be modeled by Minimum-Collisions Coloring (MCC) on an undirected graph, where the colors are the resources, the vertices are the wireless nodes and the edges represent interference relations between nodes. The MCC decision problem is NP-complete. This paper develops a game-theoretic model for the MCC problem. The players of this game are a set of colored agents, which in practice could be software robots. The game is proven to possess multiple pure-strategy Nash Equilibria (NEs). Then a swapping mechanism is developed to improve the NE performance and the resulting coloring is shown to be pairwise-Nash stable. Further refinement is proposed by making use of an external referee. All theoretical results are corroborated through simulations.

In this paper we consider the problem of user assignment and power allocation in a small cell environment which is one of the most important problems in present wireless cellular network research. We consider a two-tier cellular network where randomly dispersed overlay femtocell base stations (FBSs) coexist with a macrocell. Our objective is to maximize the total number of users served by the FBSs while satisfying their signal to noise and interference (SINR) requirements. This problem is known to be NP-Hard and hence there is no known optimal solution to solve it in polynomial time. First we formulate the problem of maximization of allocated users under SINR constraints with constant transmit power as an integer programming problem. We provide two heuristic polynomial time algorithms. Then we propose a third algorithm for joint power and user allocation. We evaluate the complexity of the proposed algorithms and furthermore compare the results against the brute force optimal solution and a basic random user assignment through simulations. The results demonstrate the performance and the efficiency of the proposed algorithms. We see in the simulation that the best proposed heuristic for maximizing the number of assigned users is only 3% less than the optimal while reducing the power consumption below that of the optimal user assignment algorithm.

In this paper, we reconsider the resource allocation and routing problem in multi-hop Multiple-Input Multiple-Output (MIMO) Wavelet Packet Modulation (WPM) Cognitive Radio (CR) ad-hoc networks. We comply with four principles to design our resource allocation scheme with the goal to maximize the capacity of entire network. First, Primary Users (PUs) have higher priority to access to the subcarrier in private bands, while PUs and Secondary Users (SUs) have the equal opportunity in public bands. Second, the MIMO channel of each link on each subcarrier in each time slot is decomposed by Block Diagonal Geometric Mean Decomposition (BD-GMD) into multiple sub-channels with identical gains. In addition, the sub-channel gain of one link is determined by all other links sharing the same source node on the same subcarrier in the same time slot. Third, PUs have the privilege of higher signal to interference and noise ratio (SINR) threshold for the successful decoding in private bands, but PUs and SUs have the same SINR threshold in public bands. Fourth, the interference caused by one link to all other links having the same destination node should be avoided, moreover, the power of all other links is not assumed to be known but also need to be allocated at the same time. Based on our proposed resource allocation scheme, we investigate a multicast routing strategy that aims to maximize network throughput. Numerical results demonstrate that our proposed resource allocation and routing scheme can noticeably improve network throughput.

This paper addresses the problem of power allocation of the downlink in cognitive radio networks (CRNs). In a CRN the channel availability for the secondary users (SUs) is a random process determined by primary user (PU) behavior. In an overlay CRN where the PU has the priority and CRN may use only the idle channels, CRN loses the symbols that are being transmitted during that time slot when the PU takes the channel and if the error correction code cannot handle the length of symbol loss. Further, in the next time slot, the CRN has to select again a free channel to continue the communication or in the event that all channels are occupied by PUs and other SUs it enters an indefinite waiting process. Thus it is intuitive that the time averaged data rate of the CRN does not only depend on the channel characteristics (governed by Shannon's law) but also on the channels' PU activity level. CRNs, with the spectrum sensing capabilities inherent to them, have the ability to characterize those activity statistics. In this paper, we propose two schemes named ENPA (equivalent noise of PU activity) and EBPA (effective bandwidth of PU activity), which take into account the PU activity in CRN downlink power allocation. These schemes are shown to achieve higher average rates than the water-filling algorithm which is optimal for a linear filter channel.