Formation of Dominance Relationships via Strategy Updating in an Asymmetric Hawk-Dove Game

We develop a model to describe the development of dominance relations between social animals as they use past experiences to inform future interactions. Using the gametheoretic framework of a Hawk-Dove game with asymmetric resource-holding potentials (RHPs), we derive a simple model that describes the social interactions of animals that compete for resources. We then consider a game-playing strategy in which animals acquire information about their RHP asymmetry from the results of their previous contests and subsequently use their asymmetry assessment to inform their behavior in future contests. We examine how directly incorporating the fact that animals have incomplete information in their interactions can lead to outcomes that differ from what would be expected if one considers the situation as a static game in which the animals have perfect information about the asymmetry size. We thereby obtain results that are consistent with observations of dominancehierarchy formation in social animals. We also discuss how increased interactions between animals can speed up the asymmetry assessment process and how this can explain why agJ. K. Grewal Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford Tel.: +44-7877-685096 E-mail: [email protected] C. L. Hall Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford Tel.: +44-1865-280618 Fax: +44-1865-270515 E-mail: [email protected] M. A. Porter Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford CABDyN Complex Centre, University of Oxford Tel.: +44-1865-270687 Fax: +44-1865-270515 E-mail: [email protected] M. S. Dawkins Department of Zoology, University of Oxford Tel.: +44-1865-271234 Fax: +44-1865-310447 E-mail: [email protected] ar X iv :1 30 8. 53 58 v1 [ qbi o. PE ] 2 4 A ug 2 01 3 2 J. K. Grewal, C. L. Hall, M. A. Porter, M. S. Dawkins gression can sometimes decrease as the number of interactions between animals increases over time.