Block withholding attack is an action where a miner who has found a legal block chooses not to submit it but rather directly abandons it. This attack makes the mining pool lose all bitcoin rewards contained within the block. In this paper, we construct a generalized model where two participants can choose to either cooperate with each other or employ a block withholding attack in the mining pool. To make the model more realistic, we consider both the cost of partial proof of work and the cost of cooperation. We also calculate the reward-per-time instead of profit-per-time to better measure the payoffs of each party. Further, we discuss the case where the payoff function and cost function are directly related to the computational power. The pure strategy and mixed strategy are analyzed respectively and the segmentations of the equilibrium are shown. We demonstrate that increasing the information asymmetry by utilizing information conceal mechanisms could lower the occurrence of the BWH attack. 1. Introduction The concept of Bitcoin was originally proposed by Nakamoto [1], and it is basically known as an open source software and a P2P network constructed on the software. Unlike most existing currencies, Bitcoin does not rely on a specific currency institution for its creation and distribution. Instead, it is generated by a large number of calculations based on a specific algorithm. The Bitcoin economy uses a distributed database of nodes in the entire P2P network to confirm and record all transaction behaviors, and it employs cryptographic design to ensure the security of all aspects of currency circulation. The advantages of this new economy include decentralization, worldwide circulation, exclusive ownership, lower transaction costs, no hidden costs and crossplatform mining. Swan [2] performed a detailed introduction to blockchain, which includes the concepts, features and functionality of Bitcoin and how one can use the blockchain for automated tracking of all digi

This paper investigates a novel two-phase preventive maintenance policy for a single-component system with an objective of maximizing the revenue generated by the performance-based contracting (PBC). The system undergoes a defective state before failure, and produces signal hinting the condition. The maintenance policy consists of two phases: imperfect maintenance phase followed by postponed replacement phase. In the imperfect maintenance phase, inspection is performed to reveal the defective state, leading to a possible repair. Both the inspection and the repair are imperfect. In the postponed replacement phase, preventive replacement is performed during the upcoming scheduled maintenance window, before which no inspection or repair is executed. The expected net revenue under PBC is maximized via the joint optimization of the inspection interval, number of inspection and preventive replacement interval. We apply the model to a case from a steel converter plant, and the results show that our proposed maintenance policy outperforms some existing maintenance policies in terms of the net revenue.

This paper studies the defense strategy for a parallel system subject to an unintentional impact and an intentional impact. Existing research assumes that system damage is caused by either natural disasters (unintentional impacts) or strategic attackers (intentional impacts). However, in practice, the defender may encounter diverse scenarios, where these two kinds of impacts can happen in a sequential order.Without knowing the precise occurrence sequence, the defender must allocate its limited resources against two successive impacts. In each contest, the defender can construct redundant elements and protect them from damage, to minimize the expected loss from system destructions. Illustrative examples of the optimal strategy are presented in three cases: first, where the unintentional impact comes first; second, where the intentional impact comes first; and third, where the two impacts come in an uncertain order. Supplemental protection is considered in the model extension, where the defender can allocate additional protection resources to those elements that have survived after the first impact.

Linear consecutive-k-out-of-n systems are frequently used to model vacuum systems, telecommunication networks, oil pipeline systems, and the photographing of nuclear accelerators. Substantial research has been devoted to analyzing the reliability of such systems, using many different approaches and assumptions. Nevertheless, existing reliability formulas may not be suitable for all real systems. This paper therefore proposes a nonrecursive closed-form expression for a consecutive-k-out-of-n system that is made up of three types of nonidentical components. The corresponding dynamic survival function and mean time to failure are derived for the suggested system, and numerical experiments are carried out to illustrate its application.

This paper incorporates the abort policy into the routing problem of unmanned aerial vehicles (UAV). In order to serve a number of targets, some UAVs can be deployed each visiting part of the targets. Different from other works on routing of UAVs, it is assumed that each UAV may experience shocks during the travel. In order to reduce the expected cost of UAV destruction, it is allowed that a UAV aborts the mission if it is found to have undergone too many shocks after it finishes serving a certain number of targets. The optimal routing plan together with the abort policy for each UAV are studied, with the objective to minimize the total cost consisting of the expected cost of UAV destruction and the expected cost for unvisited targets. Test case is used to illustrate the application of the framework.