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Parental care as a differential game: A dynamic extension of the Houston–Davies game |
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| Authors: | Christian-Oliver Ewald John McNamara Alasdair Houston |
| Affiliation: | aDepartment of Economics, University of St. Andrews, St. Salvator’s College, St. Andrews, Fife KY16 9AL, Scotland, UK bDepartment of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK cSchool of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK |
| Abstract: | An interpretation of the conflict between male and female parents during the process of caring for their common offspring by means of Game Theory was given in Houston and Davies. [A.I. Houston, N.B. Davies, The evolution of cooperation and life history in the dunnock Prunella modularis, in: R.M. Sibly, R.H. Smith (Eds.), Behavioral Ecology, Blackwell Scientific Publications, 1985, pp. 471–487]. Mathematically, this model represents a static game with continuous strategy sets. Recently, this model was reconsidered in a dynamic discrete time framework which also included state dependencies [J.M. McNamara et al., A dynamic game-theoretic model of parental care, J. Theor. Biol. 205 (2000) 605–623]. In this article, we give an interpretation of the parental care conflict in continuous time by means of a differential game with state dependent strategies. |
| Keywords: | Models of parental care Behavioral ecology Differential games Game theory |
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