We present a simple adaptive learning model of a poker-like game, by means of which we show how a bluffing strategy emerges very naturally and can also be rational and evolutionarily stable. Despite their very simple learning algorithms, agents learn to bluff, and the most bluffing player is usually the winner. 1. Introduction Among the concepts formulated and elaborated by the cognitive psychology in the last century, the study of the process of development of problem-solving strategies has enabled a meaningful improvement in the comprehension of the mental activity and its relations with the cerebral circuits. At this level of description, the concept of cognitive process is defined as the interconnected performances of some elementary cognitive activities that operate on and affect mental contents, representing the fundamental issue to bridge at a theoretical level the superior cognitive functions and the human behaviour [1, 2]. Such a concept is used in a wider sense to mean the act of knowing and may be interpreted in a social or cultural sense to describe the emergent development of knowledge, concepts, or strategies. Cognitive psychologists argue that the mind can be understood in terms of information processing, especially when processes as abstraction, categorization, knowledge, expertise, or learning are involved [3–5]. The concept of cognitive process is defined both in terms of result of the parallel elaboration of several well-defined and functionally independent neural moduli and in terms of a sort of “software” able to optimize the integration among different cognitive functions by the adaptation to the different environmental/informational circumstances [6–8]. The target of the present paper is to formulate a cognitive model of a poker-like game in which the players are able to develop strategies by learning from experience. Such a task, better known as problem solving, allows to investigate effectively the relation and coupling between the dynamics of cognitive process and the environment. Moreover, the study of poker is of great and general interest in complex systems, because it is strictly related with sociophysics, decision theory, and behaviour evolution. Actually, the study of human behaviour and, more in general, of social phenomena has been faced in the last years utilizing the tools of complex systems physics [9]. Poker-like games provide a very good instance of strategic dilemma where agents must optimize their income in conditions of imperfect information (see Section 2) or where it is not clear which is the true optimal
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