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Price Trends in a Simplified Model of the Wealth Game

We consider a simplified version of the Wealth Game, which is an agent-based financial market model with many interesting features resembling the real stock market. Market makers are not present in the game so that the majority traders are forced to reduce the amount of stocks they trade, in order to have a balance in the supply and demand. The strategy space is also simplified so that the market is only left with strategies resembling the decisions of optimistic or pessimistic fundamentalists and trend-followers in the real stock market. A dynamical phase transition between a trendsetters' phase and a bouncing phase is discovered in the space of price sensitivity and market impact. Analysis based on a semi-empirical approach explains the phase transition and locates the phase boundary. A phase transition is also observed when the fraction of trend-following strategies increases, which can be explained macroscopically by matching the supply and demand of stocks.