Mini Review

Hyper-Rational Choice in Game Theory

Gholamreza Askari¹*, Madjid Eshaghi Gordji¹ and Manuel De la sen²

¹Department of Mathematics, Semnan University, Iran

²Institute of Research and Development of Processes IIDP, Faculty of science and technology, University of the Basque country, Spain

Submission: January 01, 2019; Published: March 12, 2019

*Corresponding author: Gholamreza Askari, Department of Mathematics, Semnan University, Semnan, Iran

How to cite this article: Gholamreza Askari, Madjid Eshaghi Gordji, Manuel De la sen. Hyper-Rational Choice in Game Theory. Biostat Biometrics Open Acc J. 2019; 9(2): 555760. DOI: 10.19080/BBOAJ.2019.09.555757

Abstract

In this paper, a new interpretation of the rationality for modeling in the game theory has been proposed. The advantage of this concept emphasizes the importance of outcomes of other actors in game. The hyper-rationality concept focuses on preferences of actors how seek to maximize benefit or loss of other actors and or seek to maximize his benefit.

Keywords: Rational choice; Game theory;Preferences

Introduction

Game theory was for the first time recognized by Von Neumann and Morgenstern [1] in reference to human economic behavior [1]. This theory is a powerful tool for predicting and analyzing the behavior of various phenomena in different sciences and it helps us understand situations in which decision-makers interact [2,3]. Although there are many branches of game theory: cooperative and non-cooperative game theory are the most common which these two branches are analyzed in the form of dynamic or static games [4]. Recently Eshaghi & Askari [5] introduced a new concept of rational choice called hyper-rational choice. The concept of hyper-rational choice suggests that hyper-rational players have considered three classes of hyper-preferences that help determine how to behave in interactive decisions.

Hyper-rational choice

In the concept of hyper-rationality, the player thinks about profit or loss of other players in addition to his personal profit or loss and then will choose an action which is desirable to him. Here, we consider the set of possible choices of rational individualis shown with Given hyper-preferences, how will a hyper-rational individual behave? We assume that given a set of choicesWe define the weak hyper-preferences of actor i′ over the set 𝐵 as follows:

where relation  is complete and transitive. Considering situations which the individual faces, we define hyper-rationality as follows: Definition : (Hyper-rational) An individual will be called hyper-rational under certainty if is a rational and their hyper-preferences (individual or for others) satisfy at least one of the following conditions: • The actor chooses from the set of available alternatives (actions) based on individual preferences; • The actor chooses from the set of available alternatives (actions) based on preferences for other actors

In order to describe a game, the set of possible choices of rational individual is shown with So,each individual player i has a set of actions iA available to him and a particular element in the set of actions is denoted by

Now, we apply hyper-rational choice theory as a basis and main element of modeling in game theory. With help of hyper-rationality, we analyze conditions of a strategic game. In order to describe a game based on concept of hyper-rational choice, the payoff functions for each player i is given by:

Where jiU shows that if playeri considers profit (loss) of player,j he will choose an action from a set of available actions which will benefit (lose) player,j for every In other words, based on player i′ preferences for player j, he thinks about profit or loss of another player in addition to his personal profit or loss and then will choose an action from a set of available actions which is desirable to him.

Conclusion

The concept of hyper-rationality helps us to more clearly understand cooperation and non-cooperation in games. The hyperrational actor is the person who has concurrently characteristics of Homo-economics actor and Homo-reciprocans actor. Hyperrationality leads to consideration of the nonmaterial benefits. The findings of this research can help to enlarge our understanding of the psychological aspects of strategy choices in games and also provide an analysis of the decision-making process with cognitive economics approach at the same time. The concept of hyper-rational can provide a method that is as a common research language between psychologists and economists.

References

1. Neumann JV, Morgenstern O (2007) Theory of games and economic behavior. Princeton university press, USA.
2. Eshaghi Gordji M, Askari G (2018) Dynamic system of strategic games. Int J Nonlinear Anal Appl 9: 83-98.
3. Nash JF (1950) Equilibrium points in n-person games. Proceedings of the national academy of sciences 36(1): 48-49.
4. Bezalel P, Peter Sudholter P (2007) Introduction to the theory of cooperative games. Springer Science and Business Media, UK.
5. Eshaghi Gordji M, Askari G (2018) Hyper-Rational Choice and economic behavior. Advances in mathematical finance and applications 3: 69-76.