Macro meets micro: stochastic (Calvo) revisions in games

Abstract

The timing of moves in conventional games is deterministic. To better capture the uncertainty of many real world situations, we postulate a stochastic timing framework. The players get a revision opportunity at a pre-specified time (common to them) with some known probability (different across them). The probabilistic revisions resemble the Calvo (1983) timing widely used in macroeconomics, and by nesting the standard simultaneous move game and Stackelberg leadership they can serve as a “dynamic commitment” device. The analysis shows how the revision time and probabilities affect the outcomes in games with multiple and/or inefficient equilibria. Unsurprisingly, we show in the Battle of the sexes that commitment – low revision probability relative to the opponent – improves the player’s chances to uniquely achieve his preferred outcome (i.e. to dominate). What may, however, seem surprising is that the less committed (higher revision probability) player may dominate the game under some circumstances (for which we derive the necessary and sufficient conditions). This is in contrast to the intuition of Stackelberg leadership where the more committed player (leader) always does so. The paper then applies the framework to the strategic interaction between monetary and fiscal policies in the aftermath of the Global financial crisis. It is modelled as the Game of chicken in which a double-dip recession and deflation can occur when both policies postpone stimulatory measures – attempting to induce the other policy to carry them out. In order to link our theoretic results to the real world, we develop new indices of monetary and fiscal policy leadership (pre-commitment) and quantify them using institutional characteristics of high-income countries. This exercise shows that the danger of the undesirable deflationary scenario caused by a monetary–fiscal policy deadlock may be high in some major economies.