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Costly Information in Markets with Heterogeneous Agents: A Model with Genetic Programming

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Abstract

We analyze the value of costly information in agent-based markets with nine distinct information levels. We use genetic programming where agents optimize how much information to buy and how to process it. We find that most agents first buy high information levels, but in equilibrium buy either complete or no information, with the respective shares depending on the information costs. When information is auctioned, markets are first inefficient, so agents raise their bids to buy the highest information levels, before they learn to bid amounts that they can cover with their trading profits. In equilibrium, markets are not fully efficient, but contain just enough noise to allow informed agents to earn their information costs.

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Notes

  1. See also Kirman (2006), who highlights the importance of such charateristics.

  2. See Banzhaf et al. (1998) for a good introduction to genetic programming.

  3. Further advantages of using genetic programming in agent-based modeling are discussed in LeBaron (2006).

  4. Here we use nine distinct information levels, but the model is highly flexible and can easily be applied for any different numbers of signals, information levels, and agents.

  5. We chose a call market over a continuous double-auction, as in the latter computation times are much longer, and results are highly dependent on parameter choices like waiting times between orders, orderbook design, spreads, etc.

  6. We will consider two possible cost-structures in the following, one where prices of information are fixed, and one where the number of agents per information level is fixed and the information is auctioned.

  7. This result is discussed in detail in Hauser and Kaempff (2010).

  8. The costs for \(I=0\), referring to uninformed traders, is always zero.

  9. Note that due to the cumulative structure of information, all information levels \(I>1\) are defined to be a set of several signals. Technically, we assign an information level according to the signal with the highest rank that an agents uses in his trading strategy. Hence, information costs will be identical if an agent, e.g., only processes \(\epsilon _3\), or all three signals \(\epsilon _1, \epsilon _2, \epsilon _3\).

  10. We have chosen those values building on experience from Hauser and Kaempff (2011) and Huber et al. (2010).

  11. Note that in this setting the lowest information level I = 0 will not be assigned.

  12. We also conducted the simulation with a uniform second-price sealed-bid auction, leading to similar results.

  13. As the size and shape of trading strategies can vary considerably, we use genetic programming, which can handle structures of flexible form, for this task. See Hauser and Kaempff (2011) for some examples of trading strategies.

  14. However, we must recognize that sequential optimization cannot perfectly mimic learning in real-world capital markets. For the latter, many traders will adapt strategies simultaniously. For our simulations, (partial) parallel updating of strategies will provide an additional source of chaos for agents, thus hampering the speed of convergence and making simulations become computationally more expensive.

  15. A tournament selection with size 4 will select 4 agents randomly out of the pool of 160 agents. Then the agent with the lowest return (out of the 4 agents) “wins” the tournament and gets selected. We will use this method several times for related tasks below.

  16. In the fixed-costs setting, the choice of the optimal information level of an agent is handled implicitly by genetic programming: for any strategy that evolves we can assign it to a certain information level by determining the highest signal that this strategy processes. This allows us to account for the information costs on the fly when calculating the fitness of a strategy.

  17. The results are insensitive to variation of this initial condition.

  18. As we conduct 2,000 optimization steps, we arrive at 333 strategy optimizations in the trading school. Hauser and Kaempff (2011) showed that this is sufficient in terms of strategy diversity.

  19. Refer to Banzhaf et al. (1998) and Koza (1992) for a detailed description of genetic programming. A good introduction to genetic algorithms is presented by Michalewicz (1998) and Mitchell (1998).

  20. When an agent is optimized for the first time, we use the ramped-half-half method described in Koza (1992) to generate an initial population.

  21. For comparison of real-valued and binary-coded GA’s refer to Herrera et al. (1998).

  22. A profit/loss of 8 would be the theoretical maximum and thus serves as reasonable bound to prevent agents from submitting implausible bids. Test runs showed that this limitation does not affect our results, but enhances the efficiency of our optimization routine.

  23. With free-riding on the information provided by market prices, we do not mean that agents can take the market price into account when calculating their reservation price (this would be impossible since we only allow for simultaneous trading). But if a market is efficient to a large extent, agents may ignore information and submit random orders with very high or low limits. If their price-impact in not too high, and other agents shoulder the processing of information to serve as price-makers, the former agents free-ride on fairly efficient prices.

  24. We implement random strategies by letting agents randomly submit extremely high (or low) bids as explained in Sect. 2.2.

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Correspondence to Florian Hauser.

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Hauser, F., Huber, J. & Kaempff, B. Costly Information in Markets with Heterogeneous Agents: A Model with Genetic Programming. Comput Econ 46, 205–229 (2015). https://doi.org/10.1007/s10614-014-9439-6

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