Bitcoin is one of the most popular cryptocurrency in the world. Miners in the Bitcoin network reduce their risks through participating in mining pool. Existing mining pool systems do not consider the cost and strategy of miners. In this paper, we study two mining models: public cost model and private cost model. For the public cost model, we design an incentive mechanism, called Mining game, using a Stackelberg game. We show that Mining game is individually rational, profitable, and has the unique Stackelberg Equilibrium. For the private cost model, we formulate the Budget Feasible Reward Optimization (BFRO) problem to maximize the reward function under the budget constraint, and design a budget feasible reverse auction to solve the BFRO problem, which is computationally efficient, individually rational, truthful, budget feasible, and constant approximate. Through extensive simulations, we evaluate the performance and validate the theoretical properties of our incentive mechanisms.

比特币是世界上最受欢迎的加密货币之一。比特币网络中的矿工通过加入矿池来降低风险。现有的矿池系统没有考虑矿工的成本和策略。本文研究了两种挖掘模型：公共成本模型和私人成本模型。对于公共成本模型，我们使用Stackelberg游戏设计了一种激励机制，称为Mining游戏。我们证明了采矿游戏是个体理性的，可盈利的，并且具有独特的Stackelberg均衡。对于私人成本模型，我们制定了预算可行奖励优化（BFRO）问题以在预算约束下最大化奖励函数，并设计一个预算可行的逆向拍卖来解决BFRO问题，该问题计算效率高，个体有理，真实，预算可行且恒定近似。通过广泛的模拟，我们评估了绩效并验证了激励机制的理论性质。