Abstract
This paper introduces a theoretical framework for collective decision making to describe fluctuations and transitions in financial markets. Investors are assumed to be boundedly rational, using a limited set of information including past price history and expectation on future dividends. Investment strategies are dynamically changed based on realized returns within a game theoretical scheme with Nash equilibria. In such a setting, markets behave as complex systems whose payoff reflect an intrinsic financial symmetry that guarantees equilibrium in price dynamics (fundamentalist state) until the symmetry is broken leading to bubble or anti-bubble scenarios (speculative state). We model such two-phase transition in a micro-to-macro scheme through a Ginzburg-Landau-based power expansion leading to a market temperature parameter which modulates the state transitions in the market. Via simulations we prove that complex market dynamics can be phenomenologically explained by the number of traders, the strategies used by agents and the past price history, all included in our market temperature parameter.
Highlights
In this paper we develop a theoretical framework for financial markets based on this phenomenological reasoning: the pen in the symmetric state is equivalent to price fluctuations around their fundamental value, whereas the pen falling is equivalent to price trends towards herding seen in a bubble phase or antibubble phase of the market
As discussed in Ref. [38], financial systems are complex adaptive system, in which the micro interactions translate into macro dynamics through bottom-up mechanisms, followed by topdown feedback between the macro and the micro
In this paper we introduced a novel theoretical framework to describe financial market macro-dynamics in which single agents interact in non-linear and complex ways
Summary
In submitting buy and sell orders, agents can use: (1) technical analysis strategies, trying to profit from past price trends, and (2) fundamental analysis strategies, based on expectation of future dividends. The formulation of the decision making process of speculators and fundamentalists via the $-Game leads to a financial market modeling based on 5 parameters:
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