Sustainable Combination Mechanism for Catalysts: A Game-Theoretical Approach

Abstract

Catalysts, artificially or naturally generated, are often considered to be important factors in numerous chemical processes. Although each catalyst can act under its own characteristics, the efficiency of chemical interactions can be enhanced by a balanced combination of different catalysts. On the other hand, many game-theoretical results have been widely applied to seek the optimal or balanced state for efficiency regulation, resource control, portfolio allocation, and behavior simulation in modern academic literature. Based on game-theoretical approaches under actual chemical and biochemical environments, this article aims to analyze, construct, simulate, and derive the most efficient optimal or balanced combinations for a group of catalysts with different conditions and actions. In this article, a power index is proposed by simultaneously focusing on the factors and its active levels. In order to analyze the accuracy and rationality of this power index, we adopt usual axioms to offer some characterizations. In conjunction with the constructed game-theoretical results that are related to chemical and biochemical environments, this article further analyzes, verifies, and demonstrates the validity, accuracy, feasibility, plausibility, and applicability of the combination of catalysts with different conditions and actions.

Game-Theoretic Dynamic Procedure for a Power Index under Relative Symmetry

“…In the past, combinations were always estimated by empirical rule judgments, literature comparison simulations, circular errata corrections and so on. Although the MLII has been shown to be able to propose a relatively balanced combination ratio for all reacting processes (please see Chen et al [13]), as stated in previous sections, not all experimental procedures will adopt the MLII to analyze the combinations of catalysts at the beginning. On the other hand, although all the participating elements have their own characteristics during the operational processes, they may produce mutual excitation, repulsion, or other interactive effects between each other, which will have a relative impact on the processes and results of entire operational processes.…”

“…By applying the notion of multi-choice circumstance, a toxicity-reacting environment with lofty consistences of mitigating catalysts and heavy metal pollutants can be generalized as (F, b, C). Based on the works of Chen et al [13], it is shown that the MLII could be a stable and sustainable mechanism for generating the most efficient combinations for reacting levels among all elements.…”

“…In order to generate the most efficient combinations for a collection of catalysts, Chen et al [13] introduced a power index under multi-choice circumstances as follows.…”

“…Remark 1. Two axiomatic outcomes are proposed by Chen et al [13] as follows. Let τ be a power index.…”

“…Although each participating catalyst could react under its characteristics, the efficiency of reacting interactions could be raised by a suitable combination of participating catalysts. By applying the game-theoretical outcomes to catalyticreacting environments, Chen et al [13] introduced the multi-choice level-individual index (MLII) to analyze and derive the most efficient combinatorial mechanism for a collection of participating catalysts with different environments under multi-choice consideration. Further, Chen et al [13] adopted the axiomatic procedures to show that the MLII is the only mechanism satisfying the properties of level completeness, the criterion for circumstances property, level equal effect property, level synchronization, and consonance simultaneously.…”