Much research has been conducted arguing that tipping points at which complex systems experience phase transitions are difficult to identify. [1,2,3,4,5,6,7] To test the existence of tipping points in financial markets, based on the alternating offer strategic model we propose a network of bargaining agents [8,9,10,11,12,13,14] who mutually either cooperate or compete, [18,15,16,17] where the feedback mechanism [19,20] 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.