The rapid advancement of the Internet has significantly reshaped traditional business models, enabling firms to leverage both online and offline channels to enhance competitiveness and profitability. This study explores the interplay between bundling and pricing strategies within a dual-channel retail system that integrates a physical store and an online shop, utilizing a game-theoretic approach while accounting for network externalities. A two-stage model is proposed: in stage 1, a manufacturer supplies two products with differing network externalities to a retailer, who must decide whether to sell them individually or as a bundle. In stage 2, the manufacturer considers launching its online channel to complement the existing physical channel. Four distinct scenarios are analyzed, examining the bundling and pricing strategies employed by both the manufacturer and the retailer across both channels to maximize their profits. The findings indicate that the integration of physical and online channels is mutually beneficial for both parties, resulting in increased profits that grow alongside stronger network externalities. Moreover, the optimal bundling strategy is contingent upon the nature of the products and their respective externalities. Specifically, when both products demonstrate high network externalities, the manufacturer should implement a mixed strategy—offering the products as a bundle online while selling them individually in physical stores. Numerical analysis emphasizes the importance of network externalities in shaping bundling decisions and profit outcomes, providing actionable insights for firms operating in multi-channel retail environments.

This paper explores the strategic behavior of power generators under green certificate trading policies, considering both renewable and conventional energy generators. Using game theory, we construct a Nash equilibrium model that incorporates the unit price of green certificates, the required quantity of certificates, and the cap on the quantity. By applying the Karush-Kuhn-Tucker conditions, we reform this Nash equilibrium problem as a mixed complementarity system, which can be solved by MATLAB software. Furthermore, we conduct sensitivity analysis and numerical tests on a number of important parameters. The results reveal that, under certain conditions, the unit price of green certificates does not affect the number obtained by renewable energy generators or purchased by conventional energy generators. However, as the required number of certificates for conventional energy generators increases, both the quantity of certificates that renewable generators obtained and conventional generators purchased increase proportionally. Additionally, the outcomes of limiting the quantity of green certificates awarded to renewable energy generators align with government regulations on the purchase requirements for conventional energy generators. This research provides new insights for power generators in ensuring financial viability and optimizing operations under green certificate trading policies. By enhancing carbon emission reduction capacity, these findings may contribute to the effective management of the electrical supply chain.

This paper studies the marketplace channel introduction of contract manufacturers and the response of the platform with an option to introduce a private brand. We develop a game-theoretical model to examine a three-tier e-commerce supply chain including a contract manufacturer (CM), an original equipment manufacturer (OEM) and a platform and derive the equilibrium results. We find that the marketplace channel introduction of the CM and the platform's private brand introduction influence each other. More specifically, marketplace channel encroachment may discourage the platform from introducing a private brand, and this preference is reinforced as the referral fee increases. Interestingly, the introduction of the platform's private brand increases the likelihood of contract manufacturer encroachment, which is mediated by the difference between the two private brands of the CM and platform--as the difference increases, the CM prefers to enter the marketplace channel. Furthermore, only contract manufacturer encroachment (or private brand introduction for the platform) can always benefit the whole supply chain, but the supply chain may be hurt when the platform and the CM perform their strategies simultaneously. In the extension section, in addition to demonstrating the validity of our main results when the CM and the OEM act as a single entity, we also find that the first-mover advantage of the platform may reduce the possibility of the contract manufacturer encroachment.

Most job shops in practice are constrained by both machine and labor availability. Worker assignment in these so-called Dual Resource Constrained (DRC) job shops is typically solved in the literature via the use of meta-heuristics, i.e. “when” and “where” rules, or heuristic assignment rules. While the former does not necessarily lead to optimal results, the latter suffers from high computational time and complexity, especially when there is a large number of workstations. This paper uses game theory to propose a new worker assignment rule for DRC job shops. The Gale-Shapley model (also known as the stable marriage problem) forms a ‘couple’ made up of a worker and machine following a periodic review strategy. Simulation is used to evaluate and compare the proposed model to “when” and “where” rules previously proposed in the literature. Simulation experiments under different conditions demonstrate that the Gale-Shapley model provides better results for worker assignments in complex DRC systems, particularly when the workers have different efficiency levels. The implications of the findings for research and practice are outlined.

In this paper, a stochastic model of a closed-loop supply chain (CLSC) with one risk-averse manufacturer, one risk-averse retailer and one risk-averse third party is developed. To analyze how the members make decisions about wholesale price, collection rate, retail price and sales effort under different decision-making structures, the optimal decision problem under uncertain price and sales effort-dependent demand is studied through development of four game theoretical models. The equilibrium results between various models are compared and the optimal decisions from each member’s perspective are investigated. According to the results, the third party-led model has better performance than manufacturer-led model. The cooperation mode of manufacturer and retailer is beneficial for the whole chain and customers and the cooperation mode of manufacturer and third party is the most effective model to collect the used-product. Finally, to increase the performance of decentralized CLSC compared with the centralized CLSC, a coordination contract is developed. The results indicate that this contract is advantageous for the members of CLSC, the customers, and the environmental issues.

In this paper, we present a hybrid method of game theory and dynamic systems to study the behavior of firms in an oligopoly market. The aim of this study is to build a model for an oligopoly game on the basis of feedback loops and system dynamics approach and to solve the resulted problems under some special conditions where traditional game theory methods are unable to handle. The method includes a combination of qualitative methods including interviews with industry experts to prepare the model and quantitative methods of system dynamics, simulation methodologies and game theory. The results indicate that competitive behavior and the important parameters such as volume of demand, interest rates and price fluctuation will be stabilized after a transition period.

Most of the supply chain models have been developed under symmetric information structure i.e. players have complete knowledge of each other’s policies. But in most of the cases, players do not have complete information about the other players i.e. some information regarding their businesses is hidden. This paper studies supply chain model of imperfect quality items under asymmetric information in which unit price taken by the buyer and unit marketing expenditure are influencing product’s demand. This information is hidden to seller. The seller delivers the supply to the buyer. Each delivered lot goes through an inspection process at the buyer’s side. In the inspection process, the items are divided into two categories. The first category is perfect quality items while the second category is of imperfect quality items. After the inspecting the lots, the perfect quality commodities are to be sold at selling price and the imperfect items are supposed to get sold at a discounted price. The interaction between two constituents of the supply chain is modeled by non-cooperative Seller Stackelberg game approach in which the role of leader is played by the seller while the role of follower is played by the buyer. In our proposed model, the seller does not have information related to market demand but the buyer does. Numerical examples and sensitivity analysis explain the significance of the theory.

In this paper, the issue of cooperative (co-op) promotion efforts is addressed in a two-stage supply chain (SC). The investigated SC includes one monopolistic manufacturer and two duopolistic retailers facing different market demands. The customers’ demand is affected by both advertising efforts of the manufacturer and two retailers. Moreover, the retailers compete with each other on local advertising investments within the market. In order to boost the retailers’ advertising level, it is assumed that the manufacturer pays a ratio of the retailers' advertising expenditures. We propose four non-cooperative game scenarios and one cooperative game. Non-cooperative models are established through both Stackelberg and Nash game between two echelons. Moreover, both Cournot and Collusion behaviors are assumed to be followed by two retailers. We develop a promotion cost sharing contract to achieve the channel coordination. Under cooperation model, all SC members seek to reach the highest profit for the entire SC by considering the bargaining power of the SC participants. In each game scenario the optimal solution and unique equilibrium are determined. In addition, a comparison on the advertising level of all SC members along with the value of participation rate are provided. In addition, the feasibility of the cooperative game is discussed and resulted.

In the era of Industry 4.0, advanced manufacturing systems are increasingly integrating cyber and physical components, making them susceptible to sophisticated cyber-attacks. Addressing these vulnerabilities is crucial for maintaining the integrity and efficiency of manufacturing processes. This study introduces a comprehensive game-theoretic model to tackle cybersecurity challenges in such systems. The interaction between cyber attackers and defenders is modeled as a strategic game, incorporating a cost function that includes production losses, recovery from attacks, and maintaining of defense strategies. Both deterministic and probabilistic approaches are employed: linear programming identifies optimal strategies, achieving Nash equilibrium under ideal conditions, while the Quantal Response Equilibrium (QRE) method captures player behavior under uncertainty. The optimization problem is solved using the CPLEX library in Python, ensuring robust and efficient computation of optimal mixed strategies. The methodology is demonstrated through a numerical example, highlighting the identification of potential vulnerabilities and optimal defense strategies. The analysis reveals that the defender's learning curve is longer and more complex than the attacker's, emphasizing the necessity for advanced and adaptive defense strategies. This comprehensive approach not only predicts attacker behavior but also suggests effective defense mechanisms tailored to specific threats. The findings underscore the importance of strategic decision-making in enhancing the cybersecurity resilience of cyber-physical manufacturing systems, offering valuable insights for mitigating cybersecurity risks effectively. The most significant result indicates the critical need for timely and adaptive defense mechanisms to counter sophisticated cyber threats, ensuring the sustained operation and security of modern manufacturing environments.

With the intensification of market competition, the competition form of firms is evolving from the competition among firms to the competition among supply chains. This paper considers a market with two competing supply chains consisting of one supplier and one manufacturer. The two supply chains compete on products’ quantities and research and development (R & D) level when the two manufacturers conduct technological innovation. This paper analyses the supply chain competition in three scenarios: two decentralized supply chains (DD), one decentralized supply chain and one centralized supply chain (DC) and two centralized supply chains (CC). The results indicate that the production quantity, the R & D level and the total profit of the integrated supply chain in DC scenario are the largest, CC scenario comes second, those of the DD scenario come third and those of the decentralized supply chain in DC scenario are the smallest. CC strategy is the supply chain system’s Nash equilibrium, which is good for the both supply chains, and there is no prisoner & apos; s dilemma.