John Maynard Smith was the founder of evolutionary game theory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original assumptions. We review modern approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted.
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Our concerns about the consistency of one of the models of Wade and Shuster were first articulated in an unpublished manuscript co-authored by Tamás Székely and James Webb. Our thanks to them for many stimulating discussions of parental care and to the Leverhulme Trust for support.
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Houston, A.I., McNamara, J.M. John Maynard Smith and the importance of consistency in evolutionary game theory. Biol Philos 20, 933 (2005). https://doi.org/10.1007/s10539-005-9016-4
- Arbitrary payoffs
- Evolutionary game theory
- Parental care