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 the outcomes of games and the interactions between players. The basis of this theory was analyzed by Von Neumann, J., & Morgenstern; O. (1944) in a book entitled "Theory of Games and Economic Behavior" and then developed by John Nash between 1950 and 1953. In contrast, ethics is a normative discipline that arises from reflection on behavior and moral attitudes, and the relationship between the ethical approach and game theory is considered two emerging areas of research and study in the social sciences and humanities. The application of game theory to ethics dates back to 1954 when the Theory of games as a tool for moral philosophy was an inaugural lecture delivered in Cambridge on 2 December 1954.
Two fundamental concepts in game theory and ethics relate to altruistic (sacrificing) behaviors or preferences or behaviors based on self-interest. However, within the framework of the ethical approach, utilitarian preferences are known as the egoistic or individual rationality approach, and altruistic behavior is known as the other-oriented or group rationality approach. The concepts of self-interest and altruism are at the center of a variety of philosophical and social debates, and their roots go back to the sophists and philosophers of ancient Greece, who considered the "self" to be the center of ethical 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 and 1951). This equilibrium is considered a solution concept in a non-cooperative game and in the economic literature this concept corresponds to the self-interest perspective which corresponds to the selfish approach or moral utilitarianism based on Adam Smith's view about the self-interest approach.
Definition 1: The strategy index s^*=(s_1^*,….,s_n^* ) is a Nash equilibrium of G if and only if, for all players and i∈N and all s_i ∈ S_i,
u_i (s^* )≥u_i (s_i,s_(-i)^* )
While the Nash equilibrium is based on egoism or individualism i.e. each player aims to maximize his payoff, the Berg equilibrium is based on altruism i.e. each player aims to maximize the payoff of all other players.
Definition 2: A strategy profile s^*=(s_1^*,….,s_n^* ) is a leaf equilibrium of G if and only if, for all players i∈N and all s_(-i) ∈ S_(-i),
u_i (s^* )≥u_i (s_i^*,s_(-i) )
On the other hand, a modified logistic function was used to design the game between the two policymakers and to reflect the interdependence between economic growth and inflation on the one hand and macroeconomic policy instruments including monetary and fiscal policies on the other. The logistic basis function can be represented in the following form:
(1) f(x)=k/(1+θe^(-φ(x-x_0)) )
where k represents the maximum value of the curve and φ is the logistic growth rate and the slope of the curve. Also, in this equation, when θ>0, the function is uniform, and on the other hand, the range of changes of the function is the interval [0,k].
Results: Therefore, in this study, we analyzed the utilitarian and altruistic perspectives within the framework of game theory literature and the ethical approach, and we seek to answer the question of which of these two perspectives can bring greater social benefits to the entire society. However, examining the equilibrium in some famous games shows that the Berg equilibrium, which also confirms the golden rule in ethics, can bring higher social utility and welfare to the whole society, which is to Islamic views on the ethical approach. By examining the Nash equilibrium and the Berg 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, and hence the inflation rate is 0.0934 and economic growth is 0.0817. On the other hand, in the Berg equilibrium, it is where the central bank adopts a contractionary monetary policy and the government adopts an expansionary fiscal policy, and hence inflation is 0.0928 and economic growth is 0.0802.
Discussion and Conclusion: Over the past centuries, the principle of self-interest, which is derived from Adam Smith's perspective, has been proposed as a moral and rational principle in individual and collective decision-making, and the Nash equilibrium was also proposed by John Nash following this perspective, in which each player, based on personal interest and utility, is trying to achieve the best outcome against his opponent, which is also referred to as the perspective of individual rationality or egoism in ethics. However, studies have shown that pursuing personal interest does not lead to achieving the highest utility and outcome, and hence a balance sheet known as the altruistic or altruistic equilibrium has been introduced, which is placed opposite the Nash equilibrium. Also, from the ethical perspective, this
type of balance is known as group rationality or others. In Islamic perspectives, great emphasis has been placed on altruistic, altruistic, and altruistic behaviors. Therefore, in this study, we examined the concept of Nash equilibrium and Berg equilibrium in some important and applied games in the humanities that 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 and the pursuit of 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 two monetary and fiscal policymakers was examined from an empirical perspective, and the results show that in Berg equilibrium, that is, in an altruistic game between two policymakers, the level of inflation is stabilized at a lower level than in Nash equilibrium.
Keywords: Game theory, Ethics, Nash equilibrium, Berg equilibrium, Utility
Acknowledgements: In this section, I would like to express my gratitude to the efforts of the executive team and also the esteemed referees of the Iranian Quarterly Journal of Economic Research with an Islamic Approach.
JEL classification: C70, P40
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