Abstract: Mechanism design has received attention in supply chain management for its ability to effectively address the problem of supply chain inefficiency caused by asymmetric information. Specifically, retailers may not know the exact cost structure of suppliers, such as raw material costs, labor costs, etc., while suppliers have knowledge of their own cost information. In order to maximize their expected profits, retailers can design a contract menu, which includes multiple contracts, each specifying wholesale prices and order quantities based on different suppliers’ costs. The design of the contract menu depends on the rationality of the decision-maker. This study investigates the optimal contract menu design problem for a rational retailer when a supplier has bounded rationality.
Quantal Response Equilibrium (QRE) is an extension of Nash equilibrium under bounded rationality. This study introduces quantal response equilibrium into the model of supply chain incentive mechanism design, establishes a probabilistic selection analysis framework based on response functions, and modifies incentive compatibility and participation constraints that depend on complete rationality of decision-makers. Firstly, the optimal strategy under complete rationality is analyzed. Then, the quantal response equilibrium model is introduced to analyze the incentive mechanism design under bounded rationality. Finally, the incentive mechanism design of quantal response equilibrium under incomplete information is studied. This study further examines the impact of bounded rationality on the performance of the optimal mechanism in the supply chain. Through theoretical analysis and numerical examples, the following results are obtained.
First, we find the optimal strategy under complete rationality: When the market size is small, the optimal mechanism only trades with low-cost type suppliers; When the market size is large, it can trade with two types of suppliers, and can always achieve channel optimality when facing low-cost type suppliers, while the optimal order quantity deviates from channel optimality when facing high-cost type suppliers. Secondly, we obtain the optimal strategy under bounded rationality. Under complete information, the optimal order quantity always maintains channel optimality, and the optimal wholesale price first increases and then decreases with the degree of suppliers’ rationality, and converges to the optimal strategy under complete rationality. Under incomplete information, when the market size is small, the optimal mechanism only provides contracts that generate positive profits for low-cost type suppliers, and the optimal wholesale price first increases and then decreases with the degree of suppliers’ rationality; When the market size is large, with the increase of suppliers’ rationality, the optimal mechanism gradually presents three states: Providing a single contract that generates positive profits for low-cost type suppliers, providing a single contract that generates positive profits for two types of suppliers, and providing a contract menu that generates positive profits for two types of suppliers. If the degree of suppliers’ rationality tends to infinity, the optimal mechanism converges to the optimal strategy under complete rationality.
The impact of bounded rationality on the performance of the supply chain under the optimal mechanism is as follows. Firstly, the overall channel profit of the supply chain under bounded rationality is smaller than that under complete rationality, indicating that bounded rationality leads to a decline in supply chain channel performance. Then, under complete information, the expected profits of retailers and the channel increase monotonously with the increase of rationality degree, while the expected profits of suppliers are relatively low when their rationality degree is extremely low or high. Finally, under incomplete information, the expected profits of the channel increase monotonously with the increase of rationality degree, the expected profits of retailers are higher when the suppliers’ rationality degree is extremely low or high, and the expected profits of suppliers are relatively low when their rationality degree is extremely low or high. The above results mainly stem from the fact that when the suppliers’ rationality degree is extremely low, they may accept contracts with extremely small or even negative profits, resulting in lower expected profits for suppliers, while when the suppliers’ rationality degree is extremely high, they accept contracts with extremely small profits, allowing retailers to obtain a greater profit margin.
This study mainly considers the design of incentive mechanisms by retailers under bounded rationality, where upstream suppliers have private cost information (consisting of wholesale prices and order quantities). Based on this, further extensions can be made in many aspects. For example, under bounded rationality, different types of mechanism designs could be examined, including revenue-sharing contracts or buyback contracts,different types of asymmetric information, where downstream retailers may have private market demand information, etc. The behavioral theory on incentive mechanism design in this study provides a reference framework for other mechanism design research that considers behavior.

Key words: incentive mechanism, quantal response equilibrium, supply chain management, bounded rationality

摘要： 随机反应均衡是在有限理性条件下对纳什均衡的拓展。本文将随机反应均衡引入到供应链激励机制设计的模型中,建立依据反应函数的概率选择分析框架,修正依赖于决策者完全理性的激励相容和参与约束。通过理论分析和数值算例研究发现,随着供应商理性程度的不同,最优机制设计的形式发生变化,且对供应链渠道绩效产生显著影响。零售商和供应链渠道的期望利润随着供应商理性程度的提高而增加,而供应商的期望利润在其理性程度极低或极高时均较少。

关键词: 激励机制, 随机反应均衡, 供应链管理, 有限理性