Unilateral Support Equilibria in a Mixed Game Among Monetary, Fiscal, and Speculator Policymakers within the Framework of the Modified Logistic Function in Strategic Form

One of the topics that have attracted researchers' attention in recent decades is the analysis of the strategic interaction between fiscal and monetary authorities, with emphasis on the role of a third actor—foreign exchange market interventionists—in achieving stability in key economic indicators, particularly in the foreign exchange market. The purpose of this study is to design a model based on game theory involving three economic actors. In this paper, we aim to minimize the influence of the speculator on the economy. The government aims to achieve maximum economic growth by implementing financial policies. Meanwhile, the central bank focuses on maintaining price stability through its monetary policies. Additionally, speculators look to generate the highest profits by actively intervening in the currency market. To achieve this, we will analyze the Nash equilibrium and the unilateral support equilibria in the game using a modified logistic function. In the Nash equilibrium, each player individually tries to maximize their own benefit. In contrast, in unilateral support equilibria, each player seeks to maximize their own profit (or minimize their own loss) while supporting the player they are backing. The design of this game has been analyzed in six scenarios. The results of this game-theoretic analysis reveal that, among the six designed scenarios, the first and fifth scenarios—specifically, the main game and the scenario where the government and central bank mutually support each other—exhibit the lowest possible level of involvement by currency market speculators. In these cases, unilateral support equilibria emerge, wherein both the government and the central bank adopt contractionary fiscal and monetary policy strategies to minimize their respective losses