Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T08:57:40.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability distribution of the number of deceits in collective robotics

Part of: Artificial intelligence (68Txx) Special processes

Published online by Cambridge University Press:  14 July 2016

Antonio Murciano ,
Javier Zamora ,
Jesus Lopez-Sanchez  and
Emilia Rodriguez-Santamaria
Antonio Murciano*
Affiliation:
Universidad Complutense de Madrid
Javier Zamora*
Affiliation:
Universidad Complutense de Madrid
Jesus Lopez-Sanchez*
Affiliation:
Universidad Complutense de Madrid
Emilia Rodriguez-Santamaria*
Affiliation:
Universidad Complutense de Madrid
*
∗ Postal address: Departamento de Matemática Aplicada (Biomatemática), Facultad de Biología, Universidad Complutense de Madrid, Avenida Complutense s/n, Madrid 28040, Spain.
∗ Postal address: Departamento de Matemática Aplicada (Biomatemática), Facultad de Biología, Universidad Complutense de Madrid, Avenida Complutense s/n, Madrid 28040, Spain.
∗ Postal address: Departamento de Matemática Aplicada (Biomatemática), Facultad de Biología, Universidad Complutense de Madrid, Avenida Complutense s/n, Madrid 28040, Spain.
∗ Postal address: Departamento de Matemática Aplicada (Biomatemática), Facultad de Biología, Universidad Complutense de Madrid, Avenida Complutense s/n, Madrid 28040, Spain.
Get access Rights & Permissions [Opens in a new window]

Abstract

The benefit obtained by a selfish robot by cheating in a real multirobotic system can be represented by the random variable Xn,q: the number of cheating interactions needed before all the members in a cooperative team of robots, playing a TIT FOR TAT strategy, recognize the selfish robot. Stability of cooperation depends on the ratio between the benefit obtained by selfish and cooperative robots. In this paper, we establish the probability model for Xn,q. If the values of the parameters n and q are known, then this model allows us to make predictions about the stability of cooperation. Moreover, if these parameters are modifiable, it is possible to tune them to guarantee the viability of cooperation.

Keywords

Collective roboticscooperationreciprocal altruismprobability model

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 68T40: Robotics
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 657 - 663
Copyright
Copyright © Applied Probability Trust 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]. Axelrod, R. (1984). The Evolution of Cooperation. Basic Books, New York.Google Scholar
[2]. Dugatkin, L. A. (1991). Dynamics of the TIT FOR TAT strategy during predator inspection in the guppy ( Poecilia reticulata). Behavioral Ecol. Sociobiol. 29, 127–132.Google Scholar
[3]. Krieger, M. J. B., Billeter, J. B., and Keller, L. (2000). Ant-like task allocation and recruitment in cooperative robots. Nature 406, 992–995.CrossRefGoogle ScholarPubMed
[4]. Kube, C. R., and Zhang, H. (1993). Collective robotics: from social insects to robots. Adaptive Behavior 2, 189–218.Google Scholar
[5]. Murciano, A., Millán, J. R., and Zamora, J. (1997). Specialization in multi-agent systems through learning. Biol. Cybernetics 76, 375–382.CrossRefGoogle ScholarPubMed
[6]. Murciano, A. et (1998). Robot autónomo, móvil, con alta capacidad sensorial y de proceso para trabajos cooperativos. Patente 2112190, Oficina Española de Patentes y Marcas.Google Scholar
[7]. Nowak, M. A., and Sigmund, K. (1998). Evolution of indirect reciprocity by image scoring. Nature 393, 573–577.CrossRefGoogle ScholarPubMed
[8]. Sen, S., and Sekaran, M. (1996). Using reciprocity to adapt to others. In Adaptation and Learning in Multi-Agent Systems (Lecture Notes Comput. Sci. 1042), eds Weilk, G. and Sen, S., Springer, Berlin, pp. 206–217.Google Scholar
[9]. Trivers, R. L. (1971). The evolution of reciprocal altruism. Quart. Rev. Biol. 46, 35–57.Google Scholar
[10]. Wilkinson, G. S. (1984). Reciprocal food sharing in the vampire bat. Nature 308, 181–184.Google Scholar
[11]. Zamora, J., Millán, J. R., and Murciano, A. (1998). Learning and stabilization of altruistic behaviors in multi-agent systems. Biol. Cybernetics 78, 375–382.CrossRefGoogle ScholarPubMed