Effect of detailed information in the minority game: optimality of 2-day memory and enhanced efficiency due to random exogenous data

Abstract

In the Minority Game (MG), an odd number of heterogeneous and adaptive agents choose between two alternatives and those who end up on the minority side win. When the information available to the agents to make their choice is the identity of the minority side for the past m days, it is well-known that emergent coordination among the agents is maximum when m ∼ log 2 (N ). The optimal memory-length thus increases with the system size. In this work, we show that, in MG when the information available to the agents to make their choice is the strength of the minority side for the past m days, the optimal memory length for the agents is always two (m = 2) for large enough system sizes. The system is inefficient for m = 1 and converge to random choice behaviour for m > 2 for large N . Surprisingly, providing the agents with uniformly and randomly sampled m = 1 exogenous information results in an increase in coordination between them compared to the case of endogenous information with any value of m. This is in stark contrast to the conventional MG, where agent's coordination is invariant or gets worse with respect to such random exogenous information.

Dynamics of Cooperation in Minority Games in Alliance Networks

“…In this section, we present the numerical simulation results and discussion. We consider a population with N = 101 [47,53,60,61,71,72] placed on three types of initial network topology: random networks, SF networks, and SW networks. To conduct numerical simulations, we consider combinations of different generating parameters (different p er for ER networks (0.05, 0.075, and 0.1), different numbers of neighbors (5, 7, and 10) for SW networks, and different numbers of added nodes for values of the aversion coefficient α (0.9 for aversion, 1 for neural policy, 1.1 for stubbornness), rounds of games T (from 500 to 5000, with steps of one), and different score strategies (global, local cumulative, and local).…”

When big data fails: Adaptive agents using coarse-grained information have competitive advantage

“…Figure S3: The average payoffs P1, P2 of Type 1 (shown in blue) and Type 2 agents (red) comprising a population of size N (=255) for different population fractions f1 and memory length m1 of Type 1 agents. As Type 2 agents with sufficiently large memory length (m2 > 2) effectively use random choice strategy [17], here the Type 2 agents are assumed to be randomly choosing between the two possible options. The contours separate the regions in the (m1, f1) parameter space where Type 1 agents have a relative advantage over Type 2 agents and vice versa.…”

“…When the memory length of the Type 2 agents is increased to m 2 = 2 (see Supplementary Information), the Type 1 agent is no longer observed to have a higher payoff than the rest of the population, regardless of its memory length m 1 . Note that Type 2 agents attain the highest degree of emergent coordination among themselves for m 2 = 2 independent of N [17]. Thus, it is not surprising that the lone Type 1 agent will not be able to outperform the optimally coordinated population of Type 2 agents.…”

“…However, as we shall show below, introducing multiple Type 1 agents makes it possible for these mutually competing individuals to develop emergent coordination within themselves by which they can outperform Type 2 agents with m 2 = 2. If m 2 > 2, the behavior of the Type 2 agents is indistinguishable from agents randomly choosing between A and B [17]. As there is no predictability in the time-series available to the Type 1 agent that it can exploit, it will on average receive essentially the same payoff as the rest of the population.…”

“…For example, an agent with k = 2, the coarsest level of resolution, can only distinguish between N A > N/2 and N A < N/2 (i.e., whether A was chosen by the majority or not) in a particular round [14]. Conversely, the finest level of resolution corresponds to k = N + 1, for which an agent can determine the exact number of agents N A opting for A in a round [17]. Any value of k between these two extremes represents intermediate levels of coarse-graining where the agent can only distinguish whether, in each round, N A belongs to any one of the intervals [iN/k, (i + 1)N/k] where i = 0, .…”