scholarly journals A Hashing Power Allocation Game with and without Risk-free Asset

2021 ◽  
Vol 9 (3) ◽  
pp. 255-265
Author(s):  
Yukun Cheng ◽  
Donglei Du ◽  
Qiaoming Han
Keyword(s):  
Nash Equilibrium ◽  
Closed Form ◽  
Power Allocation ◽  
Pure Nash Equilibrium

Abstract Miners in various blockchain-backed cryptocurrency networks compete to maintain the validity of the underlying distributed ledgers to earn the bootstrapped cryptocurrencies. With limited hashing power, each miner needs to decide how to allocate their resource to different cryptocurrencies so as to achieve the best overall payoff. Together all the miners form a hashing power allocation game. We consider two settings of the game, depending on whether each miner can allocate their fund to a risk-free asset or not. We show that this game admits unique pure Nash equilibrium in closed-form for both settings.

scholarly journals Optimal and Robust Distributed Resource Allocation for SWIPT-Enabled Cognitive Networks

2020 ◽  
Author(s):  
Yongjun Xu ◽  
Haijian Sun ◽  
Jie Yang ◽  
Guan Gui ◽  
Song Guo
Keyword(s):  
Resource Allocation ◽  
Closed Form ◽  
Power Allocation ◽  
Energy Region ◽  
High Energy ◽  
Cognitive Networks ◽  
Feasible Region ◽  
Power Splitting ◽  
Joint Power ◽  
The Impact

Simultaneous wireless information and power transfer (SWIPT)-enabled cognitive networks (CRNs) is recognized as one of the most promising techniques to improve spectrum efficiency and prolong operation lifetime in 5G and beyond. However, existing methods focus on the centralized algorithm and the power allocation under perfect channel state information (CSI). The analytical solution and the impact of power splitting (PS) on the optimal power allocation strategy are not addressed. In addition, the influence of the PS factor on the feasible region of transit power is rarely analyzed. In this paper, we propose a joint power allocation and PS algorithm under perfect CSI and imperfect CSI, respectively, for multiuser SWIPT-enabled CRNs scenarios. The power minimization of resource allocation problem is formulated as a multivariate nonconvex optimization which is hard to obtain the closed-form solution. Hence, we propose a suboptimal algorithm to alternatively optimize the power allocation and PS coefficient under the cases of the low-harvested energy region and the high-harvested energy region, respectively. Moreover, a closed-form distributed power allocation and PS expressions are derived by the Lagrangian approach. Simulation results confirm the proposed method with good robustness and high energy efficiency.

scholarly journals A Coordinated Direct AF/DF Relay-Aided NOMA Framework for Low Outage

2021 ◽  
Author(s):  
Anand Jee ◽  
KAMAL AGRAWAL ◽  
Shankar Prakriya
Keyword(s):  
Energy Efficiency ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Outage Probability ◽  
Closed Form ◽  
Power Allocation ◽  
Multiple Access ◽  
Performance Gain ◽  
Amplify And Forward ◽  
Decode And Forward

This paper investigates the performance of a framework for low-outage downlink non-orthogonal multiple access (NOMA) signalling using a coordinated direct and relay transmission (CDRT) scheme with direct links to both the near-user (NU) and the far-user (FU). Both amplify-and-forward (AF) and decode-and-forward (DF) relaying are considered. In this framework, NU and FU combine the signals from BS and R to attain good outage performance and harness a diversity of two without any need for feedback. For the NU, this serves as an incentive to participate in NOMA signalling. For both NU and FU, expressions for outage probability and throughput are derived in closed form. High-SNR approximations to the outage probability are also presented. We demonstrate that the choice of power allocation coefficient and target rate is crucial to maximize the NU performance while ensuring a desired FU performance. We demonstrate performance gain of the proposed scheme over selective decode-and-forward (SDF) CDRT-NOMA in terms of three metrics: outage probability, sum throughput and energy efficiency. Further, we demonstrate that by choosing the target rate intelligently, the proposed CDRT NOMA scheme ensures higher energy efficiency (EE) in comparison to its orthogonal multiple access counterpart. Monte Carlo simulations validate the derived expressions.

scholarly journals Nash versus coarse correlation

2020 ◽  
Vol 23 (4) ◽  
pp. 1178-1204 ◽  
Author(s):  
Konstantinos Georgalos ◽  
Indrajit Ray ◽  
Sonali SenGupta
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Individual Choice ◽  
Pure Nash Equilibrium ◽  
Expected Payoff ◽  
Equilibrium Payoff ◽  
Payoff Dominance ◽  
Dominated Strategies ◽  
Person Game ◽  
Nash Point

Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

EXISTENCE AND UNIQUENESS OF EQUILIBRIUM IN ASYMMETRIC CONTESTS WITH ENDOGENOUS PRIZES

2013 ◽  
Vol 15 (01) ◽  
pp. 1350005 ◽  
Author(s):  
SHUMEI HIRAI ◽  
FERENC SZIDAROVSZKY
Keyword(s):  
Nash Equilibrium ◽  
Existence And Uniqueness ◽  
Financial Constraints ◽  
Pure Nash Equilibrium ◽  
Asymmetric Contests ◽  
Uniqueness Of Equilibrium

This paper considers contests in which the efforts of the players determine the value of the prize. Players may have different valuations of the prize and different abilities to convert expenditures to productive efforts. In addition, players may face different financial constraints. This paper presents a proof for the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with endogenous prizes.

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