Dynamic Bargaining and Time-Consistency in Linear-State and Homogeneous Linear-Quadratic Cooperative Differential Games

Three different solution concepts are reviewed and computed for linear-state and homogeneous linear-quadratic cooperative differential games with asymmetric players. Discount rates can be nonconstant and/or different. Special attention is paid to the issues of time-consistency, agreeability and subgame-perfectness, both from the viewpoint of sustainability of cooperation and from the credibility of the announced equilibrium strategies.

Procurement for Assembly Under Asymmetric Information: Theory and Evidence

We study an original equipment manufacturer (OEM) purchasing two inputs for assembly from two suppliers with private cost information. The OEM can contract with the two suppliers either simultaneously or sequentially. We consider both cases in which the OEM has relatively equal bargaining power (the dynamic bargaining institution) or substantial bargaining power (the mechanism design institution). For the dynamic bargaining institution, we show that in sequential bargaining, the supply chain profit is higher, the OEM earns a lower profit, the first supplier earns a higher profit, and the second supplier may earn a higher or lower profit, than compared with simultaneous bargaining. For the mechanism design institution, we show that all players’ profits are the same in simultaneous and sequential contracting. We also benchmark against a case where the OEM procures both inputs from a single integrated supplier (a dyadic supply chain). We then test these predictions in a human-subjects experiment, which supports many of the normative predictions qualitatively with some deviations: an OEM with relatively equal bargaining power weakly prefers to contract with suppliers simultaneously, whereas an OEM with substantial bargaining power prefers to contract with suppliers sequentially. In addition, the OEM’s profit and supply chain efficiency are higher in the dyadic supply chain than the assembly system. This paper was accepted by Charles Corbett, operations management.

Policy Experimentation in Committees: A Case against Veto Rights under Redistributive Constraints

We study optimal policy experimentation by a committee. We consider a dynamic bargaining game in which committee members choose either a risky reform or a safe alternative each period. When no redistribution is allowed, the unique equilibrium outcome is generically inefficient. When redistribution is allowed (even small amounts), there always exists an equilibrium that supports optimal experimentation for any voting rule without veto players. With veto players, however, optimal policy experimentation is possible only with a sufficient amount of redistribution. We conclude that veto rights are more of an obstacle to optimal policy experimentation than are the constraints on redistribution themselves. (JEL D72, C78, H23, D78, D71)

Leader Selection and Dynamics Analysis under Leader-Based Collective Bargaining for Buyers’ Alliance

This paper focuses on the leader selection from the leader-based collective bargaining system, where buyers form an alliance and designate one of them as the leader to bargain with the supplier for a lower wholesale price of their common component. We construct the dynamic bargaining system consisting of two heterogeneous buyers and one supplier to analyze the influence of the enterprise nature and bargaining power on the leader selection. It was proved that the buyer with stronger bargaining power should be the leader. However, we find that, when the buyers are heterogeneous, the result may be different. In order to explore which factor plays a more important role in the leader selection, we design two rounds of bargaining for comparison. The interesting results imply that whether the bargaining power will reverse the leader selection in the first round depends on its growth rate. The nonlinear dynamics theory is also introduced to analyze the complex behaviors in the dynamic bargaining system. We analyze the influence of adjustment speed on the dynamic bargaining system and obtain the conditions required to maintain system stability. Considering the significance of system stability, the delayed feedback control mechanism is adopted to drive chaos back to stability.

Bottom-up capping (BUC) policy under bargaining techniques for inter-sectoral groundwater trading: a case study from Iran

Cap-and-trade (C&T) policy has led to environmental benefits in some groundwater markets by restricting and economically reallocating water permits. However, top-down approaches for capping permits may face resistance of every affected stakeholder. This paper presents an efficient policy framework to improve the implementation of C&T policies in a real shared aquifer in Iran. To this end, groundwater permits for water-selling farms are capped through a bottom-up capping (BUC) policy. A policy analysis that employs static and dynamic bargaining techniques incorporates farms' utilities. Results reveal that the bargaining techniques propose more acceptable capping strategies than the top-down approach. The BUC policy analysis introduces the proposed strategy by dynamic bargaining as the tradable groundwater permits. The effects of irrigation water sales to the industry sector, evaluated using a cooperative game-based optimization model, show that with the fair reallocation of water trading benefits, the current net benefits of agriculture and industry sectors increase by 55 and 27%, respectively. Furthermore, farms reduce their groundwater withdrawals by 35% compared with the current mode. Therefore, the BUC policy for inter-sectoral groundwater trading under dynamic bargaining can lead to the sustainable use of limited groundwater resources by facilitating the capping strategies and improving the water permits productivity.