arXiv subjects

Gurkirat Wadhwa

Publications and source records attributed to Gurkirat Wadhwa.

6 recordsLinked to original sources

arXiv2026

What should the encroaching supplier do?: A Stackelberg Game Approach

Suppliers often encroach downstream by operating in-house production-units while continuing to supply independent production-units. We study the optimal configuration, including optimal pricing, for an encroaching supplier that balances these dual roles through a Stackelberg game. The integrated supplier determines the wholesale price charged to the outsourced production unit and the retail price of its own product, while the outsourced unit responds optimally. Customer demand-response incorporates both price-based substitutions (of the two production-units) and loyalty (towards individual units). With strong customer loyalty and luxury products, at the optimal choice for the coalition, both units co-exist profitably. In contrast, when the products become essential, the optimal strategy depends upon customer-fallback rates (fraction of the exiting production-unit's market that falls-back to other). Under low fallback, the coalition either sustains co-existence at maximum prices or disciplines the out-house to operate at break-even---with high fallback it is optimal to shut-down the in-house or eliminate the out-house---we derive two factors that identify the above. We further develop a numerical procedure to identify the optimal regime for any given set of parameters. Two surprising results are---higher market potential of the out-house can become a reason for it to operate at break-even---and the coalition may find it beneficial to operate its in-house at losses, particularly for products that are neither highly essential nor in the luxury category.

econ.EM↗

arXiv2026

Dual-Channel Closed Loop Supply Chain Competition: A Stackelberg--Nash Approach

In many consumer electronics and appliance markets, manufacturers sell products through competing retailers while simultaneously relying on take-back programs to recover used items for remanufacturing. Designing such programs is challenging when firms compete on prices and consumers differ in their willingness to return products. Motivated by these settings, this paper develops a game theoretic framework to analyze pricing and take-back decisions in a dual-channel closed loop supply chain (CLSC) with two competing manufacturers and two competing retailers. Manufacturers act as Stackelberg leaders, simultaneously determining wholesale prices and consumer take-back bonuses, while retailers engage in Nash competition over retail prices. The model integrates three key elements: (i) segmented linear demand with cross-price effects, (ii) deterministic product returns, and (iii) an inertia responsiveness allocation mechanism governing the distribution of returned products between manufacturers. Closed form Nash equilibria are derived for the retailer subgame, along with symmetric Stackelberg equilibria for manufacturers. We derive a feasibility threshold for take-back incentives, identifying conditions under which firms optimally offer positive bonuses to consumers. The results further demonstrate that higher remanufacturing value or return rates lead the manufacturers to lower wholesale prices in order to expand sales and capture additional return volumes, while high consumer inertia weakens incentives for active collection. Numerical experiments illustrate and reinforce the analytical results, highlighting how consumer behavior, market structure and product substitutability influence prices, bonuses, and return volumes. Overall, the study provides managerial insights for designing effective take-back programs and coordinating pricing decisions in competitive circular supply chains.

econ.EM↗

arXiv2025

On Analyzing the Conditions for Stability of Opportunistic Supply Chains Under Network Growth

Even large firms such as Walmart, Apple, and Coca-Cola face persistent fluctuations in costs, demand, and raw material availability. These are not \textit{rare events} and cannot be evaluated using traditional disruption models focused on infrequent events. Instead, sustained volatility induces opportunistic behavior, as firms repeatedly reconfigure partners in absence of long-term contracts, often due to trust deficits. The resulting web of transient relationships forms opportunistic supply chains (OSCs). To capture OSC evolution, we develop an integrated mathematical framework combining a Geometric Brownian Motion (GBM) model to represent stochastic price volatility, a Bayesian learning model to describe adaptive belief updates regarding partner reliability, and a Latent Order Logistic (LOLOG) network model for endogenous changes in network structure. This framework is implemented in an agent-based simulation to examine how volatility, trust, and network structure jointly shape SC resilience. Our modeling approach identifies critical volatility threshold; a tipping point beyond which the network shifts from a stable, link-preserving regime to a fragmented regime marked by rapid relationship dissolution. We analytically establish monotonic effects of volatility on profitability, trust, and link activation; derive formal stability conditions and volatility-driven phase transitions, and show how these mechanisms shape node importance and procurement behavior. These theoretical mechanisms are illustrated through computational experiments reflecting industry behaviors in fast fashion, electronics, and perishables. Overall, our contribution is to develop an integrated GBM-Bayesian-LOLOG framework to analyze OSC stability and our model can be extended to other OSCs including humanitarian, pharmaceutical, and poultry networks.

econ.GN↗

arXiv2025

Price equilibria with positive margins in loyal-strategic markets with discrete prices

In competitive supply chains (SCs), pricing decisions are crucial, as they directly impact market share and profitability. Traditional SC models often assume continuous pricing for mathematical convenience, overlooking the practical reality of discrete price increments driven by currency constraints. Additionally, customer behavior, influenced by loyalty and strategic considerations, plays a significant role in purchasing decisions. To address these gaps, this study examines a SC model involving one supplier and two manufacturers, incorporating realistic factors such as customer demand segmentation and discrete price setting. Our analysis shows that the Nash equilibria (NE) among manufacturers are not unique, we then discuss the focal equilibrium. Our analysis also reveals that low denomination factors can lead to instability as the corresponding game does not have NE. Numerical simulations demonstrate that even small changes in price increments significantly affect the competitive dynamics and market share distribution.

q-fin.GN↗

arXiv2025

What should the encroaching supplier do in markets with some loyal customers? A Stackelberg Game Approach

Considering a supply chain with partial vertical integration, we attempt to seek answers to several questions related to the cooperation competition based friction, abundant in such networks. Such an SC can represent a supplier with an inhouse production unit that attempts to control an outhouse production unit via the said friction. The two production units can have different sets of loyal customer bases and the aim of the manufacturer supplier duo would be to get the best out of the two customer bases. Our analysis shows that under certain market conditions, an optimal strategy might be to allow both units to earn positive profits particularly when they hold similar market power and when customer loyalty is high. In cases of weaker customer loyalty, however, the optimal approach may involve pressurizing the outhouse unit to operate at minimal profits. Even more intriguing is the scenario where the outhouse unit has a greater market power and customer loyalty remains strong here, it may be optimal for the inhouse unit to operate at a loss just enough to dismantle the downstream monopoly.

econ.GN↗

arXiv2024

Partition-form Cooperative Games in Two-Echelon Supply Chains

Competition and cooperation are inherent features of any multi-echelon supply chain. The interactions among the agents across the same echelon and that across various echelons influence the percolation of market demand across echelons. The agents may want to collaborate with others in pursuit of attracting higher demand and thereby improving their own revenue. We consider one supplier (at a higher echelon) and two manufacturers (at a lower echelon and facing the customers) and study the collaborations that are `stable'; the main differentiator from the existing studies in supply chain literature is the consideration of the following crucial aspect -- the revenue of any collaborative unit also depends upon the way the opponents collaborate. Such competitive scenarios can be modeled using what is known as partition form games. Our study reveals that the grand coalition is not stable when the product is essential and the customers buy it from any of the manufacturers without a preference. The supplier prefers to collaborate with only one manufacturer, the one stronger in terms of market power; further, such collaboration is stable only when the stronger manufacturer is significantly stronger. Interestingly, no stable collaborative arrangements exist when the two manufacturers are nearly equal in market power.

econ.TH↗