Abstract
In many game-theoretical results, the reduction axiom and its converse have been regarded as important requirements under axiomatic processes for solutions. However, it is shown that the replicated core counters a specific (inferior) converse reduction axiom under multi-choice non-transferable-utility situations. Thus, two modified reductions and relative properties of the reduction axiom and its converse are proposed to characterize the replicated core in this article.The main methods and relative results are as follows. First, two different types of reductions are proposed by focusing on both participants and participation levels under relative symmetric reducing behavior. Further, relative reduction axioms and their converse are adopted to characterize the replicated core.
Highlights
The reduction axiom and converse reduction axiom are crucial properties of feasible solutions in the characteristic formulation of cooperative situations
Hwang and Liao [9] presented that the replicated core is “not” the unique solution matching individual rationality, non-emptiness and complement-reduction axiom under the domain of multi-choice NTU balanced situations
Different from the reductions due to Hwang and Liao [9], two different types of the reductions are generated in Section 3 by focusing on both participants and participation levels under relative symmetric reducing behavior
Summary
The reduction axiom (reduced game property) and converse reduction axiom (converse reduced game property) are crucial properties of feasible solutions in the characteristic formulation of cooperative situations. Hwang and Liao [9] presented that the replicated core is “not” the unique solution matching individual rationality, non-emptiness and complement-reduction axiom under the domain of multi-choice NTU balanced situations. Whether different types of reductions, related reduction axioms and their converse could be proposed to characterize the replicated core To resolve this motivation, one would build on the results of Hwang and Liao [9]. Different from the reductions due to Hwang and Liao [9], two different types of the reductions are generated in Section 3 by focusing on both participants and participation levels under relative symmetric reducing behavior These reductions are introduced to multi-choice NTU situations and relative reduction axioms and their converse are presented. The findings of this article are compared with existing results
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