  Much research has been conducted arguing that tipping points at which complex
systems experience phase transitions are difficult to identify. To test the
existence of tipping points in financial markets, based on the alternating
offer strategic model we propose a network of bargaining agents who mutually
either cooperate or where the feedback mechanism between trading and price
dynamics is driven by an external "hidden" variable R that quantifies the
degree of market overpricing. Due to the feedback mechanism, R fluctuates and
oscillates over time, and thus periods when the market is underpriced and
overpriced occur repeatedly. As the market becomes overpriced, bubbles are
created that ultimately burst in a market crash. The probability that the index
will drop in the next year exhibits a strong hysteresis behavior from which we
calculate the tipping point. The probability distribution function of R has a
bimodal shape characteristic of small systems near the tipping point. By
examining the S&P500 index we illustrate the applicability of the model and
demonstate that the financial data exhibits a hysteresis and a tipping point
that agree with the model predictions. We report a cointegration between the
returns of the S&P 500 index and its intrinsic value.
