Algorithm stickiness and the memory extent delimit the rationality of El Farol attendees

Arthur's paradigm of the El Farol bar for modeling bounded rationality and inductive behavior is undertaken. The memory horizon available to the agents and the selection criteria they utilize for the prediction algorithm are the two essential variables identified to represent the heterogeneity of agent strategies. The latter is enriched by including various rewarding schemes during decision making. Though the external input of comfort level is not explicitly coded in the algorithm pool, it contributes to each agent's decision process. Playing with the essential variables, one can maneuver the overall outcome between the comfort level and the endogenously identified limiting state. Furthermore, we model the behavior of the agents through the use of an expression that scores the local attendance states available to the agents. It incorporates a single parameter that weighs the relative contributions that originate from the external and internal limiting factors. Solving this expression analytically as well as numerically using the Metropolis Monte-Carlo technique enables us to attribute statistical-thermodynamical meanings to the essential variables identified with the agent-based model, and to gain physical insight to the bounds observed in the behavior of the agents. The power of the analytical approach is validated by obtaining a one-to-one correspondence between the agent-based model and the analytical approach within a wide range of thresholds using a single parameter for a given selection criterion. The origin of discrepancies between the two models appearing at extreme thresholds is tracked to the shifts in the distributions of algorithm types actively utilized by the adaptive agents. 16 pages, 4 figures