We here introduce a beauty contest game with negative feedback and interior equilibrium in a multi-period experiment. This game is isomorphic to classical BCG but fit economic situations such as crop production or professional investment better. The game is still being analysed from the eductive point of view and with respect to the attempt to establish a typology of players according to their depths of reasoning. Our main contribution to the understanding of this game is the formalization of the process by which the information is processed. Using the Shannon entropy criterion, we evaluated information and made a link between the Sperber analysis of reflective and intuitive beliefs and numerical psychological research (Dehaene, 1993). Information that players take into account in their choices is denoted useful information. As this depends on the exploitation of the strategy interval, it will be higher in BCG- than in BCG+ in the first iterations, because strategies are numbers that are naturally scanned several times. As argued by Sperber (1997), there is a point in the reasoning process starting from which reflective beliefs become intuitive. In order to determine the exact location of the specific point from which players in the BCG- can jump to the REE, we assume that sophisticated reasoning is costly. Therefore, an agent stops calculating at step k which is obtained by the intersection between his marginal cost function and his marginal benefit (information) function. However, there are individuals who are not able to reach that point, because their cognitive constraint is saturated beforehand. There are also individuals for whom the cognitive constraint is saturated for a value higher that k, but who stop at step k because, given the structure of the population, they can win the game at a smaller cost. Therefore, a guess in this game corresponds to the solution of the system comprising these two constraints. For our experiments, we found a depth of reasoning smaller than 3, which can, however, be optimal. Results show that the k-step thinking with k<3 is "a fact of human nature" (Bosch and al., 2000) and not an arbitrary modelling restriction. Even if subjects start with a low degree of sophistication, the final winning numbers are very close to the equilibrium in the BCG-. This is possible, as observed by Guesnerie (1992) on the crop producers market, because situations of negative feedback are stable; therefore, "human nature" is likely to better succeed when confronted with such situations: eductive reasoning is "helped" to stay on the convergence path.