Local Bargaining and Supply Chain Instability

We analyze the behavior of a competitive n-tier supply chain system, where agents bargain with each other locally. We study the influence of transaction costs on the convergence of the system to a stationary outcome. In particular, we consider a dynamic bargaining game among a finite set of agents and its replications, and use a limit stationary equilibrium to examine the system’s behavior as the population’s size goes to infinity. The convergence of the system to a limit stationary equilibrium would capture the common belief that as the market gets large, it converges to a competitive and stable outcome. However, we prove that depending on the underlying transaction costs, the system might not converge to such an equilibrium. Interestingly, our result shows that a small increase of the transaction cost at one end of the chain can be greatly amplified, and shifts the system away from the steady state, a phenomenon reminiscent of the well known bullwhip effect. When a limit stationary equilibrium exists, we show that it is unique. We use such an equilibrium outcome to study bid-ask spreads and the split of trade surplus among sellers, buyers and middlemen.