On the Evolution of Memory Size in the Minority Game (extended abstract)

This work presents a study on the effects of different memory sizes in the Minority Game (MG) market model [Zhang, 1998]. We analyse the effects on an agent’s performance when this agent is endowed with a different memory size with respect to other agents in the game. Our aim is to identify in which situations a large or small memory might be advantageous in the game. From the obtained results we argue that there exist convergence to and evolutionary stability around certain memory sizes and we consider an evolutionary setup which confirms our hypothesis. The MG is defined as an odd number of agents (N ) which must choose at each turn of the game whether they will be in one of two possible groups. After all agents have made their choices, agents in the minority group are rewarded. In order to make a decision, agents use an inductive learning algorithm in order to try to exploit patterns from previous outcomes. The number of past turns that agents consider to decide defines their memory size (M ). One of the main properties in a MG is its efficiency, which is evaluated by the statistical variance (σ) of the number of agents in a group [Moro, 2004]. Efficiency is known to be a function of a control parameter α = 2 M N [Manuca et al., 2000]. For N fixed, M becomes the main control parameter of the game. Figure 1 shows σ for a range of memory sizes. Three regions are observed: (i) for small M variance is very high, above the expected for the random case game (which we will call inefficient region); (ii) for high values of M , variance is exactly the one expected for the random case game (random case region); (iii) for intermediate M the system presents small variances (efficient region).