Second Thoughts on Bubbles and Global Games

In models of asset-price bubbles, we show that introducing second thoughts (reconsideration) makes the bubbly equilibrium a unique equilibrium. We reformulate the model of bubbles as a simultaneous game, in which we introduce the second thought stage, where some players can change their strategies after observing the strategies chosen by other players. With a second thought stage, only the bubbly equilibrium survives the backward elimination of weakly dominated strategies (BEWDS). We can also show that when one player reconsiders and the other player then also reconsiders, the bubbly equilibrium becomes a unique subgame-perfect equilibrium. The uniqueness result can also be replicated in a macroeconomic binary action game with a continuum of players, which is typically analyzed in the global game literature, and is modified so that individual agents can interact bilaterally and have second thought stages. Our result implies that the second thought mechanism could be an effective method of equilibrium selection, which could be a promising alternative to the global game.