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Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has at least one Pareto–Nash equilibrium. Then, with the help of BGIP, we obtain the necessary and sufficient conditions for the existence of fuzzy Pareto–Nash equilibrium of MBGFP. Secondly, based on the bilinear programming method for calculating Nash equilibrium in crisp bi-matrix games, we established a bilinear programming method with parameters for calculating fuzzy Pareto–Nash equilibrium. By considering the importance of each objective to the players, MBGFP is transformed into a bi-matrix game with fuzzy payoffs (BGFP). Furthermore, we obtained the necessary and sufficient conditions for the existence of fuzzy weighted Pareto–Nash equilibrium and its calculation method. Finally, a practical example is used to illustrate the effectiveness of our proposed calculation method. Full article

Uncertainty is common in miscellaneous decision-making problems, including bi-matrix games. The uncertainty of bi-matrix games is caused by the complexity of the game environment and the limitations of players’ cognition rather than the asymmetry of information. Therefore, it is hard for players to precisely give their crisp payoff values. In this paper, a new method considering the acceptance degree that the general intuitionistic fuzzy constraints may be violated is developed to solve general intuitionistic fuzzy bi-matrix games (GIFBMGs). In the method, a new asymmetric general intuitionistic fuzzy number (GIFN) and its cut sets are firstly defined. Then, the order relationship of GIFNs and the definitions of α and β-bi-matrix games are proposed. Afterwards, the constructed general intuitionistic fuzzy quadratic program is converted into an interval bi-objective program on the basis of the order relationship of GIFNs. Furthermore, the interval bi-objective program is converted into a multi-objective quadratic program based on the combination of interval order relationship and the player’s acceptance degree. A goal programming approach is put forward to solve the multi-objective quadratic program. Finally, the validity of the proposed method is verified with a numerical example for corporate environmental behavior (CEB), and some comparative analyses are conducted to show the superiority of the proposed method. Full article

The emergence of the modern gig economy introduces a new set of employment considerations for firms and laborers that include various trade-offs. With a game-theoretical approach, we examine the influences of technology, policy and markets on firm and worker preferences for gig labor. Theoretically, we present new conceptual extensions to the replicator equation and model oscillating dynamics in two-player asymmetric bi-matrix games with time-evolving environments, introducing concepts of the attractor arc, trapping zone and escape. While canonical applications of evolutionary game theory focus on the evolutionary stable strategy, our model assumes that the system exhibits oscillatory dynamics and can persist for long temporal intervals in a pseudo-stable state. We demonstrate how changing market conditions result in distinct evolutionary patterns across labor economies. Informing tensions regarding the future of this new employment category, we present a novel payoff framework to analyze the role of technology on the growth of the gig economy. Regarding governance, we explore regulatory implications within the gig economy, demonstrating how intervals of lenient and strict policy alter firm and worker sensitivities between gig and employee labor strategies. Finally, we establish an aggregate economic framework to explain how technology, policy and market environments engage in an interlocking dance, a balancing act, to sustain the observable co-existence of gig and employee labor strategies. Full article

In this article, we introduce a model of bi-matrix games based on crisp parametric payoffs via utilizing the method of interval value function. Then, we get that equilibrium solutions of bi-matrix games on the basis of fuzzy payoffs and equilibrium solutions of the game model are of equal value. Furthermore, it is concluded that equilibrium solutions of the game can be converted to optimal solutions of discrete nonlinear optimization problems with parameters. Lastly, the proposed methodology is illustrated by an example. Full article