Altruism and reputation: cooperation within groups

arXiv:0903.3902v1 [physics.soc-ph] 23 Mar 2009 Altruism and reputation: cooperation within groups P. Gawro´nski, M. J. Krawczyk and K. Ku lakowski∗ Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Krak´ow, Poland ∗kulakowski@novell.ftj.agh.edu.pl September 7, 2018 Abstract In our recent model, the cooperation emerges as a positive feedback between a not-too-bad reputation and an altruistic attitude. Here we introduce a bias of altruism as to favorize members of the same group. The matrix Fi,j of frequency of cooperation between agents i and j reveals the structure of communities. The Newman algorithm reproduces the initial bias. The method based on differential equations detects two groups of agents cooperating within their groups, leaving the uncooperative ones aside. PACS numbers: 87.23.Ge; 02.50.Le Keywords: cooperation; agents; computer simulation; altruism; reputation 1 Introduction Despite the widespread using of game theory [1, 2] in social sciences, its range of applications remains disputable. The question, to what extent people are rational in their decisions, created a rich set of research points of view, includ- ing the concept of evolutionary thinking [3]. Axelrod discussed this question in terms of the Prisoner’s Dilemma (PD), a famous thought experiment which demostrates that according to game theory in many situations a cooperation is not rational. Then, PD become a common method of real and computational experiments. To complete the list of references is beyond our chance and aim; we refer to [4, 5, 6, 7]. Although the formulation of PD relies on the concepts of payoffs and rational choice, some recent experiments exceed this frame. In 2006 De Cremer and Stouten showed [8] that the conditions of cooperation are trust and some common goal to achieve; the latter was measured with the ’Inclusion of Other with the Self’ scale [9]. In the same year the results of Mulder et al. [10] indicated that sanctioning defection itself can weaken the motivation of players to cooperate. These results, obtained within the scheme of the public good experiment [11, 12], show that a reliable theory of cooperation cannot be limited to the assumption of an idividual and selfish rationality, but it should include some collectivistic attitudes, as for example preserving of social norms. The same conclusion can be drawn from the results of the ultimatum game, when played by members of different societies [13]. Here we are interested in a contribution of cooperation to the process of the formation of social groups. Although in a society this process usually runs 1 in a longer timescale than a standard experiment, some information could be drawn from a search of cooperation in already established groups. Here how- ever, the outcome varies strongly from one particular case to another. Some- times boundaries between groups seem to disappear, as those reported in [14] between Japanese and American students in Hokkaido. The data collected in Bosnia and North Causasus indicate, that the likelihood of intergroup trust and cooperation depends more on cultural and economic status than on per- sonal - often crude - experience [15]. In other cases, as the one with Australian and Singaporean students [16], the results are less conclusive. The difference in timescale, noted above, was to some extent evaded in the PD experiment performed by Goette et al. [17]. The groups investigated there were platoons of males formed for four-week period of officer training in the Swiss army. As individuals were randomly assigned to different platoons, the experiment was free from the confounding effect of self-selection into groups. The intra-group cooperation was found to be clearly stronger than the inter-group one. Also, individuals believed that members of their own platoons were more willing to cooperate. These results are closely akin to those of [8]. Recently we proposed a new model of cooperation, formulated without use of the concepts of payoffand utility [18]. In this model, the only model vari- ables were reputations and altruisms of individual players. Both these variables entered to the expression of the probability of cooperation of one player with another. The only difference between the variables was their time dependence; while the reputation varied in each game, the level of altruism remained con- stant. The aim of this work is to apply the same model to the intra- and inter-group cooperation. Accordingly, we are going to admit that the reputa- tion and the altruism can be different within the group and between the groups. The paper is organized as follows. Next section is devoted to the model, as formulated in [18], and to a brief conclusion of its results for one group. In the same Section we explain how the model is generalized to the case of two groups. In Section 3 we report the way how the group structure is investigated; here we base on methods of [19, 20]. Nu

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