Heterogeneity, stability, and efficiency in distributed systems

This paper explores the increasing the heterogeneity of an agent population to stabilize decentralized systems by adding bias terms to each agent´s expected payoffs. Two approaches are evaluated, corresponding to heterogeneous preferences and heterogeneous transaction costs; empirically, the transaction cost case provides stability with near optimal payoffs under certain conditions. Theoretically, in the idealized case of an infinite number of agents, it is proven that the system with added heterogeneous preferences has a fired point different from that of the unbiased system, guaranteeing suboptimal perfomance, while the transaction cast case is demonstrated to have a fixed point identical to that of the unbiased system, and it is further shown to be a contraction mapping, guaranteeing convergence. This contraction mapping allows us to conceptualize the model with heterogeneous transaction costs as a decentralized root finding system