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Discussion Paper 1019, "Bounded Rationality In Finite Automata", by Christos A. Ioannou

A model of adaptive learning and innovation is used to simulate the evolution of finite automata in the repeated Prisoner's Dilemma stage-game. The automata are prone to two types of errors: (a) implementation errors and (b) perception errors. The computational experiments incorporate different levels of errors in an effort to assess whether and how the distribution of outcomes and structures in the population changes. Under the proposed framework, the incorporation of implementation and perception errors is sufficient to reduce cooperative outcomes. In addition, the study identifies a threshold error-level. At and above the threshold error-level, the prevailing structures converge to the open-loop (history-independent) automaton Always-Defect. On the other hand, below the threshold, the prevailing structures are closed-loop (history-dependent) and diverse. The diversity thus impedes any inferential projections on the superiority of a particular automaton. Yet, the analysis still identifies some broad characteristics of the automata that work "reasonably well" in such environments. In particular, the complexity of the automata is decreasing in the probability of errors. Furthermore, the prevailing structures tend to exhibit low reciprocal cooperation and low tolerance to defections. These results show that the evolution of cooperative automata is considerably weaker than expected, while the change in the model is ecologically plausible: Errors are common in strategic situations. We use a genetic algorithm to simulate the evolution of error-prone finite automata in the repeated Prisoner's Dilemma game. In particular, the automata are subjected to implementation and perception errors. The computational experiments assess whether and how the distribution of outcomes and structures in the population changes with different levels of errors. We find that the complexity of the automata is decreasing in the probability of errors. Furthermore, the prevailing structures tend to exhibit low reciprocal cooperation and low tolerance to defections as the probability of errors increases. In addition, by varying the error-level, the study identifies a threshold. At and above the threshold, the prevailing structures converge to the open-loop (history-independent) automaton Always-Defect. On the other hand, below the threshold, the prevailing structures are closed-loop (history-dependent) and diverse, which impedes any inferential projections on the superiority of a particular machine.

JEL Classification: C72, C80, C90

Keywords: Automata, Repeated Games, Genetic Algorithms, Local Polynomial Regression