A qualitative game of interest rate adjustments with a nuisance agent

A qualitative game describes a situation in which antagonistic players strive to keep the evolutions of their state variables in predetermined constraint sets. We argue that a qualitative game model is a suitable mathematical representation of the struggle between a domestic central bank of a small open economy and a foreign central bank of a large economy to maintain their respective state variables within an acceptable band regardless of the other player's choices. The actions of the foreign central bank affect the domestic exchange rate and, hence, domestic inflation, output gap and interest rate. However, these actions do not necessarily aim to destabilise the small open economy, nor do they take into account the state of the latter. The domestic bank's problem, therefore, is similar to that of a game against nature. We refer to this type of qualitative game as a nuisance-agent game (or NA-game). We use viability theory to derive satisficing rules (in the sense of Simon) of nominal interest-rate adjustments for the domestic central bank of a small open economy in a qualitative NA-game against the foreign central bank.