An Artificial Limit Order Book Market Splits into Two Long-Run Price Outcomes

Even when every trader starts from the same place, a market can still end up in two very different worlds: one where prices collapse to zero, and another where they settle at a persistent positive level. This paper studies an artificial stock market exchange with endogenous, myopic traders — traders who react only to the market they can see right now — interacting through a limit order book. The authors find that the price dynamics have intrinsic bistability, meaning the system has two stable long-run states built into its trading rules, not created by randomness. They also identify a metastable region, a middle zone with elevated volatility, sitting between the two basins of attraction that pull trajectories toward different endings. The paper reports distinct transient behaviors on the way to each equilibrium and says the system is neither entirely regular nor fully chaotic. The big takeaway is that uniform beginnings can still produce sharply different market outcomes, revealing strong path dependence in artificial stock markets.

If you rewound a market to the same start, you would expect the same end. This model refuses that rule. The same opening conditions can still lead to two very different futures. One future ends at zero. The other keeps a price above zero. That split comes from the market rules, not from luck. It is the kind of surprise that makes a toy market feel unsettlingly real.

Why the same market can end two ways

This model studies an artificial stock market exchange, or ASME. The traders are myopic, which means they act on the latest market signs. The market uses a limit order book, a live list of buy and sell orders. From the same start, prices fall into two stable long-run states. One is a zero-price end that appears without chance. The other is a persistent positive-price equilibrium, a point where the market keeps settling above zero. Between them sits a metastable zone, a middle stretch that looks active but does not last. The paths into those ends also look different on the way down.

How the split grows from simple trading rules

Simple trading rules build the model. Traders watch the order book, the running list of buy and sell orders. They do not plan far ahead. They react to the state in front of them. The system also starts with fixed money and fixed stock counts spread across traders. That setup lets the same rules play out again and again. It also makes the market's path, not just its start, matter a lot.

Why the middle zone matters

That middle zone is not a boring pause. It is where price swings get larger. Metastable means it looks temporary and unsettled. The system also shows distinct transient behavior, which means its short-life path depends on which end it will reach. A basin of attraction is the set of starts that pull a system to one end state. That idea helps explain why identical starts can still split apart. The result adds a clean picture of path dependence in artificial markets.

What to test next

The next test is the same ASME with traders who are not myopic. That means they would react to more than the latest order book. If the two-end split still holds, the result will look very robust. If it fades, the split may depend on short-sight trader behavior. Either way, the key surprise survives: identical starts are not enough to tell one market story. In this model, the route matters as much as the opening cash and stock count.