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                <term xml:lang="en">Multi-objective optimization Multi-criteria decision-making Weighted sum method Bargaining game theory Nash bargaining solution Bi-objective assignment problem</term>
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              <p>&lt;div&gt;&lt;p&gt;Bi-objective combinatorial optimization (BOCO) is a particular case of multi-objective optimization where a decision-maker (DM) must simultaneously optimize two conflicting objectives over a finite feasible set of decision vectors. Arising in many real-world scenarios, BOCO poses significant challenges due to the discrete nature of the decision space and the inherent trade-offs between the objectives. Existing methods for BOCO can be broadly categorized into a posteriori methods, which identify the Pareto front comprehensively, and a priori methods, which incorporate DM's preferences into the optimization and return only the solutions satisfying these preferences. While a posteriori methods provide a diverse set of trade-offs, a priori methods are more computationally efficient and closely aligned with the decision-making process.&lt;/p&gt;&lt;p&gt;Cooperative game theory and multi-objective optimization intersect in finding acceptable solutions amidst conflicting goals. The solution concepts in bargaining games are well-suited for solving multi-objective optimization problems because both involve resolving trade-offs among competing interests (players or objectives). In this paper, we propose a novel approach to BOCO by applying the idea of the Nash Bargaining Solution (NBS), a fundamental concept from cooperative game theory, to the selection of preferred solutions from the Pareto front. We extend this concept by introducing generalized NBS (ρ-NBS), which incorporates the DM's relative priority between two objectives by a given positive parameter ρ.&lt;/p&gt;&lt;p&gt;We first introduce the ρ-NBS concept for BOCO. Then, we develop an exact algorithm to identify the ρ-NBS within the set of supported efficient solutions. These solutions lie on the convex hull of the Pareto front, providing valuable insights into its structure. Finally, we apply our theory and algorithm to the Bi-Objective Assignment Problem, a class of BOCO.&lt;/p&gt;&lt;/div&gt;</p>
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