We describe an agent-based model of a market where traders exchange a risky asset whose returns can be partly predicted purchasing a costly signal. The decision to be informed (at a cost) or uninformed is taken by means of a simple learning by imitation mechanism that periodically occurs.
The equilibrium is characterized describing the stationary distribution of the price and the fraction of the informed traders. We find that the number of agents who acquire the signal decreases with its cost and with agents’ risk aversion and, conversely, it increases with the signal-to-noise ratio and when learning is slow, as opposed to frequent. Moreover, price volatility appears to directly depend on the fraction of informed traders and, hence, some heteroskedasticity is observed when this fraction fluctuates.
- Agent-based modeling
- Bounded rationality
- Information in financial markets
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To preserve diversity in the population, we add also a minimal degree of random “mutation” in every period, see the details below.
This result corresponds to a simplified version of equations (8) and \((8')\) of Grossman and Stiglitz . Note, in particular, that our agents are not able to exploit entirely the information revealed by the price \(p_t\) on the signal \(\theta _t\) (hence, on \(u_t\)) as for the fully rational agents in GS.
Clearly, if the pair is formed by two agents that were equally informed or uninformed in the last T periods, no change happens as both members in the couple have the same wealth.
For simulations involving \(T=16\), 12000 periods.
It should be stressed that the result obviously depends also on the other parameters, say \(\alpha \) and c, but the conclusion that the signal-to-noise ratio plays an important role robustly holds for all the combinations we have simulated (specific details are not discussed for brevity).
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Gerotto, L., Pellizzari, P., Tolotti, M. (2019). Asymmetric Information and Learning by Imitation in Agent-Based Financial Markets. In: De La Prieta, F., et al. Highlights of Practical Applications of Survivable Agents and Multi-Agent Systems. The PAAMS Collection. PAAMS 2019. Communications in Computer and Information Science, vol 1047. Springer, Cham. https://doi.org/10.1007/978-3-030-24299-2_14
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