Optimal bubble riding: a mean field game with varying entry times

We propose a game-theoretic model on optimal liquidation in the presence of an asset bubble. Our setup allows the influx of players to fuel the price of the asset and excessive selling to trigger the burst. The popularity of asset bubbles suggests a large-population setting, which naturally leads to a mean field game (MFG) formulation. We introduce a class of extended MFGs with varying entry times whose equilibria depend on the entry-weighted average of conditionally optimal strategies. We prove existence of such equilibria and show that these strategies can be decomposed into before- and after-burst segments, each part containing only the market information. Some numerical simulations are included to shed light on the relationship between the bubble burst and equilibrium strategies.