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：我们提出了一种在交易成本约束下对替代品进行定价与交换的去中心化机制。我们刻画了涉及（加权）Tarski拉普拉斯算子的热方程的时间不变解——该算子针对最大加矩阵加权图定义——并将其表征为交易系统的近似均衡。我们研究了解集的代数性质以及该动力系统的收敛行为。将这些工具应用于“将稀缺资源配置于竞争性用途”的经济学问题。我们的理论表明，竞争均衡、议价或成本效益分析中的差异（取决于具体情境）在很大程度上源于交易成本被纳入决策过程的方式不同。我们呈现了同步算法（RRAggU）的数值模拟结果，以验证我们的理论发现。