Abreu and Brunnermeier (2003) examine the failure of rational arbitrage in asset markets. They argue that even with rational arbitrageurs, speculative bubbles can persist due to a lack of common knowledge. The model features behavioral traders causing a bubble, which can only be punctured by sufficient selling pressure from rational traders. Stock prices initially rise exponentially, but after a random time t0, they diverge from fundamentals. The bubble's size depends on a function β, which determines the fraction of the price due to fundamentals versus the bubble. Rational traders do not share the same information. Once prices diverge from fundamentals, they become aware sequentially. A significant number of traders must sell for the bubble to burst. The key is that rational traders do not all share the same information, leading to a lack of coordination. This prevents them from selling simultaneously, allowing the bubble to persist. The paper shows that traders use "cut-off" strategies, selling at a specific time based on their beliefs about when the bubble will burst. The optimal selling time depends on the expected burst time and the bubble's size. The model identifies two types of equilibria: one where the bubble bursts exogenously and another where it bursts endogenously due to coordinated selling. The paper also discusses the implications of public news, which can create common knowledge and facilitate coordination. The results show that even with rational traders, bubbles can persist due to the lack of common knowledge and the difficulty in coordinating sales. The uniqueness of the equilibrium is similar to global games analysis, but with differences in coordination and competition. The paper highlights the importance of information and coordination in asset markets.Abreu and Brunnermeier (2003) examine the failure of rational arbitrage in asset markets. They argue that even with rational arbitrageurs, speculative bubbles can persist due to a lack of common knowledge. The model features behavioral traders causing a bubble, which can only be punctured by sufficient selling pressure from rational traders. Stock prices initially rise exponentially, but after a random time t0, they diverge from fundamentals. The bubble's size depends on a function β, which determines the fraction of the price due to fundamentals versus the bubble. Rational traders do not share the same information. Once prices diverge from fundamentals, they become aware sequentially. A significant number of traders must sell for the bubble to burst. The key is that rational traders do not all share the same information, leading to a lack of coordination. This prevents them from selling simultaneously, allowing the bubble to persist. The paper shows that traders use "cut-off" strategies, selling at a specific time based on their beliefs about when the bubble will burst. The optimal selling time depends on the expected burst time and the bubble's size. The model identifies two types of equilibria: one where the bubble bursts exogenously and another where it bursts endogenously due to coordinated selling. The paper also discusses the implications of public news, which can create common knowledge and facilitate coordination. The results show that even with rational traders, bubbles can persist due to the lack of common knowledge and the difficulty in coordinating sales. The uniqueness of the equilibrium is similar to global games analysis, but with differences in coordination and competition. The paper highlights the importance of information and coordination in asset markets.