# Numeric Evaluation of Game-Theoretic Collaboration Modes in Supplier Development
## 1 Introduction  
Manufacturing companies confront procurement costs of raw materials and components of over 50% of the companies' total profit [1, 2]. As a result, manufacturers depend on their suppliers, and the suppliers performance shows a considerable effect on many product aspects, such as cost, quality, and on-time delivery [2]. Consequently, manufacturers place increasing concentration on a more efficient supply chain utilizing supplier development. The purpose of supplier development is enhancing the performance and/or potentials of the supplier to fulfill the supply needs of manufacturers, such as improvement in response to customer needs and market dynamics, increasing customer responsiveness, improvement of quality and reliability of products, manufacturing of new products, reducing costs of production and then ultimately, to increase profit margins [2, 3, 4]. Hence, it is in the interest of manufacturers and suppliers to seek competitive advantages through supplier development. According to the relational perspective, manufacturers invest in supplier development to gain tangible profits like lower cost, higher quality and flexibility, and trustworthy delivery. In these cases, the manufacturer, to achieve the better performance and shared value development, may be determined to support the supplier via information exchange, technological support, training, and through investiture in supplier processes [5]. Supplier development can provide the foundation of cooperation among buyers and suppliers. However, supplier development offers the chance of collaboration among several manufacturing companies as well. Many manufacturing companies, especially the ones that are active in the same industry, tend to order raw materials and components from an assortment of suppliers. As an instance, Whirlpool and General Electric for washing machines' motors, Toyota and Pontiac for automobiles' engines and Dell and Hewlett-Packard for personal computers' PC boards work with the same suppliers [2]. Generally, in such a situation, a manufacturer can choose between various types of relationships, which can be cooperative, non-cooperative, and collaborative [6]. In this paper, we study multi-manufacturer scenarios, which consist of two manufacturers and one supplier to enable us to simulate more realistic settings. We assume four types of relationships between manufacturers that are fully cooperative, collaborative (simultaneous and sequential decision-making) and non-cooperative. Previous studies suggest a wide range of definitions for the cooperative and collaborative relationship in supply chains. In this study, we assume a cooperative relationship where partners act together to achieve a shared goal. In contrast, in a non-cooperative scenario, manufacturers aim to maximize their profit. Furthermore, manufacturers in collaborative relationships generally aim to maximize their own profit, while rendering their decisions separate from each other. We subdivide the collaborative setting in terms of the order of decisions. In a simultaneous setting, both manufacturers make their decisions at the same time, while constantly forwarding their decisions to the other manufacturer. In a sequential setting, one manufacturer makes its decision first and reveals it to the second manufacturer. In this paper, we investigate the effect of centralized and distributed relationships between manufacturers on the overall profit of the supply chain. Furthermore, we attempt to answer the following questions: Are collaboration, cooperation, and non-cooperation good scenarios for manufacturers who intend to develop the same supplier by means of dynamic horizon investment? How can cooperative, collaborative, and non-cooperative settings between manufacturers affect the profit of the supply chain in short-term investments? To answer the mentioned questions, we expand the scenarios of [7; 8] from a monopolistic setting (one manufacturer-one supplier) to a multi-manufacturer setting with two manufacturers and one supplier.