Johannes Berg

 Statistical mechanics of the single asset model

 

 Asset models are frequently used in economics to examine the behaviour of interacting agents in a simple model of a market. Here we analyze the single-asset model, which consists of a large number of agents investing a fraction of their wealth in an asset. The asset gives a return $R^\omega$ in the 'state of the world' $\omega$. At each timestep the state of the world is chosen randomly out of the $\Omega$ possible states. The price and consequently the amount of asset a player obtains for his investment are given by the market clearing condition. We find two distinct phases of the model: For &\Omega/N<\alpha_c$ the agents quickly settle into a stationary state where the return equals the investment at each timestep. For $\Omega/N>\alpha_c$ no such state exists and the system remains non-stationary. Using methods from the statistical mechanics of disordered systems the critical point $\alpha_c$ and many thermodynamic properties of the system may be calculated analytically.

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