Contracts and coordination: Supply chains with uncertain demand and supply

Considering a supply chain with a supplier subject to yield uncertainty selling to a retailer facing stochastic demand, we find that commonly studied classical coordination contracts fail to coordinate both the supplier's production and the retailer's procurement decisions and achieve efficient performance. First, we study the vendor managed inventory (VMI) partnership. We find that a consignment VMI partnership coupled with a production cost subsidy achieves perfect coordination and a win‐win outcome; it is simple to implement and arbitrarily allocates total channel profit. The production cost subsidy optimally chosen through Nash bargaining analysis depends on the bargaining power of the supplier and the retailer. Further, motivated by the practice that sometimes the retailer and the supplier can arrange a “late order,” we also analyze the behavior of an advance‐purchase discount (APD) contract. We find that an APD with a revenue sharing contract can efficiently coordinate the supply chain as well as achieve flexible profit allocation. Finally, we explore which coordination contract works better for the supplier vs. the retailer. It is interesting to observe that Nash bargaining solutions for the two coordination contracts are equivalent. We further provide recommendations on the applications of these contracts. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 305–319, 2016     

建立中国式辩诉交易制度的构想

美国的辩诉交易制度具有重要的理论价值和现实意义。有必要借鉴国外辩诉交易制度的合理因素，建立中国式的辩诉交易制度。建立中国式的辩诉交易制度，应对其适用条件、适用案件的范围及适用程序做出明确规定。     

A sequential auction‐bargaining procurement model

One of the most important decisions that a firm faces in managing its supply chain is a procurement decision: selecting suitable suppliers among many potential competing sellers and reducing the purchase cost. While both auctions and bargaining have been extensively studied in the literature, the research that combines auctions and bargaining is limited. In this article, we consider a combined auction‐bargaining model in a setting where a single buyer procures an indivisible good from one of many competing sellers. The procurement model that we analyze is a sequential model consisting of the auction phase followed by the bargaining phase. In the auction phase, the sellers submit bids, and the seller with the lowest bid is selected as the winning bidder. In the bargaining phase, the buyer audits the cost of the winning seller and then negotiates with him to determine the final price. For this auction‐bargaining model, we find a symmetric equilibrium bidding strategy for the sellers in a closed form, which is simple to understand and closely related to the classical results in the auction and bargaining literature. We also show that the auction‐bargaining model generates at least as much profit to the buyer as the standard auction or sequential bargaining model. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

军事联盟的形成机制与对策

国家间的对抗与合作是国际关系中的最常见的问题,通过引入博弈论中的讨价还价模型和差分方程,分析了联盟的形成机制,并对三国合作、三国竞争以及三国部分合作对抗的情况进行了比较,通过数值仿真对模型分析过程进行了验证,仿真结果表明,不同类型国家的策略选择对博弈结果影响很大,研究内容较好地揭示了国家间矛盾与利益的变化规律,为深入理解国际关系提供了参考。     

Interchange fee rate,merchant discount rate,and retail price in a credit card network: A game‐theoretic analysis

We consider two game‐theoretic settings to determine the optimal values of an issuer's interchange fee rate, an acquirer's merchant discount rate, and a merchant's retail price in a credit card network. In the first setting, we investigate a two‐stage game problem in which the issuer and the acquirer first negotiate the interchange fee rate, and the acquirer and the retailer then determine their merchant discount rate and retail price, respectively. In the second setting, motivated by the recent US bill “H.R. 2695,” we develop a three‐player cooperative game in which the issuer, the acquirer, and the merchant form a grand coalition and bargain over the interchange fee rate and the merchant discount rate. Following the cooperative game, the retailer makes its retail pricing decision. We derive both the Shapley value‐ and the nucleolus‐characterized, and globally‐optimal unique rates for the grand coalition. Comparing the two game settings, we find that the participation of the merchant in the negotiation process can result in the reduction of both rates. Moreover, the stability of the grand coalition in the cooperative game setting may require that the merchant should delegate the credit card business only to the issuer and the acquirer with sufficiently low operation costs. We also show that the grand coalition is more likely to be stable and the U.S. bill “H.R. 2695” is thus more effective, if the degree of division of labor in the credit card network is higher as the merchant, acquirer, and issuer are more specialized in the retailing, acquiring, and issuing operations, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Franchising cooperation through chance cross‐constrained games

This paper explores the role of franchising arrangements in the context of game theory. We assume a single franchisor and a single franchisee channel and address the impact of fixed lump‐sum fees, royalties, wholesale price, and retail price on the franchise contracts. We start with the chance cross‐constrained noncooperative situation where the franchisor, as the leader, first specifies his/her strategies. The franchisee, as the follower, then decides on his/her decision. We then relax the assumption of franchisee's inability to influence the franchisor's decisions and discuss cooperative situation between the franchisor and the franchisee. Nash's bargaining model is utilized to select the best Pareto‐efficient payment scheme for the franchisor and the franchisee to achieve their cooperation. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 669–685, 2000     

On efficiency of multistage channel with bargaining over wholesale prices

This article considers a multistage channel with deterministic price‐sensitive demand. Two systems for pricing decisions, that is, the bargaining system and the leader‐follower system, are compared. We characterize the necessary and sufficient conditions on the power structure, under which the solution of the bargaining system Pareto dominates that of the leader‐follower system. Also, under such conditions, we give a tight upper bound of channel efficiency of the bargaining system, which converges to 100% channel efficiency as the number of stages increases to infinity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 449–459, 2016     

Auctions in the post‐change‐order period

A change order is frequently initiated by either the supplier or the buyer, especially when the contract is long‐term or when the contractual design is complex. In response to a change order, the buyer can enter a bargaining process to negotiate a new price. If the bargaining fails, she pays a cancellation fee (or penalty) and opens an auction. We call this process the sequential bargaining‐auction (BA). At the time of bargaining, the buyer is uncertain as to whether the bargained price is set to her advantage; indeed, she might, or might not, obtain a better price in the new auction. To overcome these difficulties, we propose a new change‐order‐handling mechanism by which the buyer has an option to change the contractual supplier after bargaining ends with a bargained price. We call this the option mechanism. By this mechanism, the privilege of selling products or services is transferred to a new supplier if the buyer exercises the option. To exercise the option, the buyer pays a prespecified cash payment, which we call the switch price, to the original supplier. If the option is not exercised, the bargained price remains in effect. When a switch price is proposed by the buyer, the supplier decides whether or not to accept it. If the supplier accepts it, the buyer opens an auction. The option is exercised when there is a winner in the auction. This article shows how, under the option mechanism, the optimal switch price and the optimal reserve price are determined. Compared to the sequential BA, both the buyer and the supplier benefit. Additionally, the option mechanism coordinates the supply chain consisting of the two parties. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 248–265, 2015     

Inventory transshipment game with limited supply: Trap or treat

Inventory transshipment is generally shown to be beneficial to retailers by matching their excess demand with surplus inventory. We investigate an inventory transshipment game with two newsvendor-type retailers under limited total supply and check whether the retailers are better off than the case without transshipment. We derive the ordering strategies for the retailers and show that unlike the unlimited supply case, a pure Nash equilibrium only exists under certain conditions. Furthermore, contrary to the conventional wisdom, we show that inventory transshipment may not always benefit both retailers. Although one of the retailers is guaranteed to be better off, the other could be worse off. The decision criteria are then provided for the retailers to determine if they will benefit from the exercise of inventory transshipment. Numerical study indicates that the carefully chosen transshipment prices play an important role in keeping inventory transshipment beneficial to both retailers. Subsequently, a coordinating mechanism is designed for the retailers to negotiate transshipment prices that maximize the total profit of the two retailers while keeping each of them in a beneficial position.