The idea to use board games and parlor games as a starting point for analytical purposes is not new. The role of such kinds of games in the birth of the mathematical theory of games is well-known. Let us recall the series of contributions from Zermelo (1912), to Borel (1921; 1924), and Von Neumann himself (1928), where several mathematical properties of the future theory of games have been directly derived from parlor games. Therefore, such games are rightly considered as the cornerstone of a new kind of knowledge expressed in a mathematical format known today as Game theory.
However, the games cannot be reduced to their rules and to the formal problems set by their rules. Aumann himself has recognized that what he has called the “problem solution viewpoint” is not the convenient approach for taking into account the key interactive dimension of a game situation (Aumann and Brandenburger, 1995) (1). Each game is a specific activity where playing refers to a specific cognitive activity of the players which could not be simply deduced from the mathematical solution of its setting problem. Indeed, mathematics offers convenient concepts for modeling logical strategies, but the formal results of an artificial intelligence does not always coincide with the result of players’ mind activity during the play. The Recent development of behavioral psychology and cognitive neuroscience have demonstrated and sometimes explained the distance often observed between the rational solutions strictly deduced from the mathematic formulation and the actual strategy chosen by the players in a game situation. Beyond their discrepancy, the aim of the paper is to show that board games, which have been a fructuous support for the mathematical investigation of interactive systems, can also be used now as useful tools for improving the understanding of brain working in various strategic situations. Therefore, all kinds of games also offer today an opportunity for capturing the mental linkage between the logical and the psychological treatment of the interactive situations.
The first part is devoted to the historical origin of this quest. Indeed, the idea that board games offer stimulating cases for mathematical studies, as well as for exploring the mind capacities takes its roots in a long history, which starts in the end of the seventeen centuries. An overview of this historical background opens the topic. Then, three different questions will be investigated and briefly discussed. Firstly, the impact of learning games on brain capacities and performances which are revealed by the neural differences between the brain activations of the experts by comparison to the novices during the course of different games. Secondly the mental resorts of observed neural activations according to alternative game strategies, as offensive versus defensive, which provide information about how brain works in relation to different strategic position (or posture) in games of strategies as Chess and Go. Thirdly the neural basis of the mental iterations between the self and the others during the plays, which opens the way to new perspective on subjective interactive mechanisms to be related to the psychosocial theory of mind.
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