Abstract
The equilibrium proposed by Nash provides a basis from which group decisions can be selected. This kind of choice establishes a situation in which none of the participants will have any incentive to change their strategy if they are acting rationally, which is the major assumption of game theory. Leoneti proposed a utility function that allows multi-criteria problems to be modeled as games in order to find alternatives that meet the Nash equilibrium conditions for solving conflicts in group decision-making process. The objective of this research was to propose a deviation index from the theoretical rational decision (the Nash equilibrium solution) and to discuss the use of this index as an indicator of the theoretical rationality deviation. In accordance with other results presented in the literature, it was found that the group might not always choose this alternative, deviating from the equilibrium solutions, measured here by a deviation index.
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Notes
- 1.
It is important to stress that this index can be calculated using any equilibrium as reference, which may vary depending on the research purposes.
- 2.
The term “performance matrix” was adopted over other possible classifications to the criteria versus alternative matrix, such as, i.e., “decision matrix”, “consequence matrix”, etc.
- 3.
The game is considered a non-cooperative game since the participants cannot make binding agreements before choosing their alternatives.
- 4.
This alternative is called “ideal” because it contains the maximum absolute value of all criteria considered in the alternative’s evaluation and, therefore, is used as an indicator of direction to the maximum value that each criteria can eventually reach.
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Acknowledgments
The authors thank the National Council of Technological and Scientific Development (CNPq) for Regular Research Grant (458511/2014-5), and the São Paulo Research Foundation (FAPESP) for the Scientific Initiation Scholarship (2014/09540-0) and for the grant for Paper Presentation (2016/03722-5). The authors also acknowledge the helpful comments of two anonymous referees.
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Leoneti, A.B., de Sessa, F. (2017). A Deviation Index Proposal to Evaluate Group Decision Making Based on Equilibrium Solutions. In: Bajwa, D., Koeszegi, S., Vetschera, R. (eds) Group Decision and Negotiation. Theory, Empirical Evidence, and Application. GDN 2016. Lecture Notes in Business Information Processing, vol 274. Springer, Cham. https://doi.org/10.1007/978-3-319-52624-9_8
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