Game Theory and the Self-Interested Nash Equilibrium against the Altruistic Berge Equilibrium in the Framework of the Ethical Perspective

Authors

1 Department of Economics Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

2 PhD in Economics, Allameh Tabataba'i University, Tehran, Iran.

3 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Abstract

Game theory is based on assumptions about players' preferences and their mutual expectations about the behavior of others. From this set of assumptions, game theorists make predictions about game outcomes and interactions between players. The basis of this theory was analyzed by Von Neumann and Morgenstern (1944) in a book titled "Game Theory and Economic Behavior", and then John Nash developed this theory between 1950-1953. On the other hand, ethics is a normative discipline that is obtained from reflection on moral behavior and attitudes. The relationship between the ethical approach and game theory is considered as two emerging areas in research and study activities in social sciences and humanities. The application of game theory in ethics dates back to 1954, when Richard Braithway (1954) gave a lecture on "Game Theory as a Tool for Moral Philosophy".
There are two very important concepts related to game theory and ethics, which are related to altruistic (altruistic) behaviors or preferences or behaviors based on personal interest. However, in the framework of the ethical approach, self-interested preferences are known as the approach of egoism or individual rationality, and altruistic behavior is known as the approach of others or group rationality. The concepts of self-interest and altruism are at the center of all kinds of philosophical and social discussions, and their roots go back to the sophists and philosophers of ancient Greece, who considered "self" to be the center of moral issues.
Method
One of the important concepts in game theory when modeling socio-economic behavior and human interactions is the concept of Nash equilibrium, which was founded by John Nash (1950,1951). This equilibrium is considered a solution concept in a non-cooperative game, and in the economic literature, this concept corresponds to the perspective of self-interest.
Definition 1: The strategy profile is a Nash equilibrium of  if and only if, for all players and  and all
While the Nash equilibrium is based on selfishness or individualism, that is, each player aims to maximize her efficiency, Berge equilibrium is based on altruism, so that the goal of each player is to maximize the benefit of all other players.
Definition 2: A strategy profile  is a Berge equilibrium of  if and only if, for all players  and all
An adjusted logistic function was used to design a game between two policymakers. This approach reflects the interdependence between economic growth and inflation on one hand, and macroeconomic policy tools, such as monetary and financial policies, on the other hand. The basic logistic function can be displayed in the following form:




(1)

 



Based on this equation, represents the maximum value of the curve and  is the logistic growth rate and slope of the curve. Also, in this equation, when , the function is uniform, and on the other hand, the range of changes of the function is in the [0,] interval.
 
Results
Therefore, in this study, we investigated the analysis of self-interested and altruistic views in the framework of game theory literature and ethical approaches. We are looking for an answer to the question, which of these two views can bring more social benefits for the whole society? However, the examination of the equilibrium in some famous games shows that the Berge equilibrium, which confirms the golden rule in ethics, can bring higher social welfare and welfare to the whole society, which is in accordance with Islamic views.  By examining the Nash equilibrium and the Berge equilibrium, it can be shown that in this two-policy game, the Nash equilibrium is where the central bank adopts a contractionary monetary policy strategy and the government adopts a contractionary fiscal policy strategy, and therefore the inflation rate is equal to 0.0934 and economic growth is 0.0817. On the other hand, in the Berge equilibrium, it is where the central bank sets a contractionary monetary policy and the government sets an expansionary fiscal policy, and hence inflation is equal to 0.0928 and economic growth is equal to 0.0802.
Discussion and Conclusions
In recent centuries, the principle of personal benefit, which is derived from Adam Smith's point of view, has been proposed as a moral and rational principle in individual and collective decision-making. Nash equilibrium is also proposed by John Nash following the same point of view, in which each player tries to achieve the best outcome against his opponent based on his personal interest and utility. It is also referred to as the point of view of individual rationality or egoism in ethics. However, studies have shown that pursuing personal benefit does not lead to the achievement of the highest utility and outcome, and hence Berge introduces an equilibrium known as altruistic equilibrium, which is opposed to Nash equilibrium. Also, from a moral point of view, this type of balance is also known as group rationality or otherism. In Islamic viewpoints, there is a lot of emphasis on altruistic, selfless, and altruistic behaviors. Therefore, in this study, we investigated the concept of Nash equilibrium and Berge equilibrium in some important and practical games in human sciences, which have important applications in economics, political science, etc. The results of this research show that in many of these important and famous games, altruistic equilibrium following the golden rule and mutual support between players have positive effects on the welfare of society compared to Nash equilibrium. On the other hand, in this study, within the framework of the logistic function, the game between the two monetary and financial policymakers was examined from an empirical aspect, and its results show that in Berge equilibrium, i.e., in the altruistic game between the two policymakers, the level of inflation relative to the Nash equilibrium is stabilized in a lower state.
 
Key words: Game theory, Ethics, Nash equilibrium, Berge equilibrium, Utility
JEL Classification: C70, P40
 
Acknowledgement
In this section, I would like to express my gratitude for the efforts of the executive team and the respected referees of the Journal of Economic Essays: An Islamic Approach.

Keywords

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