This thesis investigates general equilibrium asset prices in non-competitive markets in which monopolistic traders, arbitrageurs, and extrapolators (MAX) coexist. Extrapolators form beliefs about the probability distribution of future asset prices based on sentiment, which is determined by historical asset prices. Arbitrageurs trade on mispricing but experience the limits of arbitrage, and monopolistic traders hold correct beliefs and market power. Chapter 1 provides a research overview. Chapter 2 presents a discrete-time model and investigates monopolistic traders' optimal strategies. We argue that the equilibrium price is determined not by monopolistic traders' current assets alone, but by the sequence of trades that acquired them. Monopolistic traders' decisions of placing a large block order or sequential small orders depend on both market conditions and other agents' strategies. The pump-and-dump and optimal liquidation strategies offer two examples. Results from this study explain many market phenomena, such as asset price bubbles and flash crashes, which have significant implications for financial institutions. Chapter 3 presents a continuous-time model. The model generates asset pricing characteristics, such as high equity premiums and excess volatility, while maintaining the persistence of risk-free rate and the predictability of dividend price ratio. The model proposes hypotheses and provides theoretical foundations for empirical asset pricing research, and can be used to guide profitable investment strategies.