We introduce a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs. We characterize the time-invariant solutions of a heat equation involving a (weighted) Tarski Laplacian operator, defined for max-plus matrix-weighted graphs, as approximate equilibria of the trading system. We study algebraic properties of the solution sets as well as convergence behavior of the dynamical system. We apply these tools to the "economic problem" of allocating scarce resources among competing uses. Our theory suggests differences in competitive equilibrium, bargaining, or cost-benefit analysis, depending on the context, are largely due to differences in the way that transaction costs are incorporated into the decision-making process. We present numerical simulations of the synchronization algorithm (RRAggU), demonstrating our theoretical findings.

翻译：我们提出一种去中心化机制，用于在交易成本约束下为替代方案定价与交换。通过定义最大加矩阵加权图上的（加权）塔尔斯基拉普拉斯算子，我们刻画了包含该算子的热方程的时间不变解，并将其视为交易系统的近似均衡。我们研究了解集的代数性质及该动力系统的收敛行为。将这些工具应用于稀缺资源在竞争性用途间配置的“经济问题”。我们的理论表明，竞争性均衡、议价或成本效益分析之间的差异（取决于具体情境）主要由交易成本纳入决策过程的方式不同所致。我们呈现了同步算法（RRAggU）的数值模拟结果，以验证理论发现。