An analysis of Nash, Berge, and Greedy equilibrium in the context of a mixed game involving monetary and financial policymakers in normal form: An application of the prisoner’s dilemma

Purpose: During the last decades, the strategic interaction between the monetary authority, i.e. the central bank, and the financial authority, i.e. the central government, has attracted the attention of many economic policymakers, in both developing and advanced countries. A method that plays an important role in the analysis of the strategic confrontation between these two institutions is analysis based on the game theory. This theory has wide applications in various branches of science, including economics, engineering, biology, political science, and military science. The behaviour of each person or player is not only affected by the individual’s own decisions, but also it depends on the behaviour and decisions of other players.
The government aims to foster robust economic growth through budgetary expenses, while the central bank aims to maintain the stability of inflation through interest rate mechanisms. Studies show that the different goals of the central bank and the government are a challenge for the economic stability of a country. The optimal solution for officials is to coordinate their actions and decisions, because coordination improves the situation of the decision makers in both arenas. In Iran's economy, the issue of coordination or lack of it in the implementation of macroeconomic policies is of particular importance for monetary and financial authorities. Therefore, in this study, the interaction between these two groups of authorities is investigated through the game theory in normal forms.
Methodology: Regarding policy coordination between the government and the central bank, there are two types of strategic interaction, which are very useful and important in the analysis of equilibrium solutions. One includes non-cooperative games between two officials, and the other includes cooperative games. The games in which joint action contracts are applicable are called cooperative games, but the games in which such joint actions are not possible and individual participants must be allowed to act in their own interests are called non-cooperative games.
To establish equilibrium in this game, three concepts are used, including Nash equilibrium, Berge equilibrium and Greedy Scaler equilibrium. In a Nash case, each player individually and self-interestedly seeks to maximize his profit. Conversely, in Berge equilibrium, players exhibit altruistic behaviours versus their opponents. In Greedy equilibrium, however, players engage in a semi-cooperative game, striving to advance their shared interests through the formation of coalitions. Also, the Prisoner’s Dilemma has been investigated for the strategic confrontation of the two groups of policy makers. This game is a classic cooperation and choice problem based on the assumption of selfish human motives. Blinder (1983) designed a policy decision-making problem in the framework of the Prisoner’s Dilemma.
Findings and discussion: The outcomes of this game reveal that, in a two-strategy situation, the Nash equilibrium occurs when both the government and the central bank adopt contractionary policy strategies. In this game, the economy does not enter into the prisoner's dilemma, but it is the Pareto optimal. Conversely, in the Berge equilibrium, the scenario arises where the government pursues an expansionary fiscal strategy while the central bank implements a contractionary monetary strategy. In addition, many situations of Greedy equilibrium include both Nash and Berge equilibria. The results for Iran's economy show that the implementation of a balanced and optimization Nash policy by the government and the central bank (contraction fiscal and monetary policy) brings the most benefits for the government. The implementation of an optimal Berge policy by the government and the central bank involves the most benefits for the central bank. However, the results show that, in the first scenario, based on the reviewed information, there are two Greedy equilibria, Nash equilibrium and Berge equilibrium. The first Greedy equilibrium corresponds to the Nash equilibrium, and the second one corresponds to the Berge equilibrium. Therefore, if the government and the central bank follow a semi-cooperative game, both Nash and Berge equilibria can be reached. The equilibrium extracted from the second scenario is more beneficial than the one from the first scenario. Also, in the semi-cooperative game, a more favourable balance can still be achieved. So, the government and the central bank seek the highest profit by forming a coalition and cooperating with each other.
During the first development plan, the Nash equilibrium brings the most economic growth for the government, and, during the third and fourth development plans, the central bank faces the lowest inflation in the Nash equilibrium. However, in the Berge balance, the government experiences the highest economic growth in the third development plan. In this situation, the central bank sees the lowest level of inflation in both the third and fourth development plans. In addition, in the optimal Nash equilibrium, compared to the other equilibria, the government achieves the maximum result, and, in the optimal policy of the central bank, it will achieve the lowest inflation.
Conclusions and policy implications: It is suggested to the policymakers to pay attention to the type of game designed in adopting their policies. So, if these authorities seek to achieve a non-cooperative game, they should follow the strategy of contractionary monetary and financial policies. Also, to reach an altruistic equilibrium and mutual support, the central bank should follow a contractionary monetary policy, and the government should follow an expansionary fiscal policy. For future studies, it is suggested that the role of a third actor, such as speculators or parliament (legislature), be seen in the game between the government and the central bank.