Altruism, fairness and evolution: the case for repeated stochastic games

This paper is an effort to convince the reader that using a stochastic stage game in a repeated setting - rather than a deterministic one - comes with many advantages. The first is that as a game it is more realistic to assume that payoffs in future games are uncertain. The second is that it allows for strategies that make an evolutionary approach possible, while folk theorem strategies do not allow for such an analysis. But the most important feature is that such a setting allows for equilibrium strategies that look very much like human behaviour; altruism and fairness will be shown to feature in a natural way in equilibrium

Hamilton's missing link

Hamilton's famous rule was presented in 1964 in a paper called "The genetical theory of social behaviour (I and II)", Journal of Theoretical Biology 7, 1-16, 17-32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper's central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton's rule does follow from his central result

Why kin and group selection models may not be enough to explain human other-regarding behaviour

Models of kin or group selection usually feature only one possible fitness transfer. The phenotypes are either to make this transfer or not to make it and for any given fitness transfer, Hamilton's rule predicts which of the two phenotypes will spread. In this article we allow for the possibility that different individuals or different generations face similar, but not necessarily identical possibilities for fitness transfers. In this setting, phenotypes are preference relations, which concisely specify behaviour for a range of possible fitness transfers (rather than being a specification for only one particular situation an animal or human can be in). For this more general set-up, we find that only preference relations that are linear in fitnesses can be explained using models of kin selection and that the same applies to a large class of group selection models. This provides a new implication of hierarchical selection models that could in principle falsify them, even if relatedness - or a parameter for assortativeness - is unknown. The empirical evidence for humans suggests that hierarchical selection models alone are not enough to explain their other-regarding or altruistic behaviour

Robustness against indirect invasions

Games that have no evolutionarily stable strategy may very well have neutrally stable ones. (Neutrally stable strategies are also known as weakly evolutionarily stable strategies.) Such neutrally, but not evolutionarily stable strategies can however still be relatively stable or unstable, depending on whether or not the neutral mutants it allows for - which by definition do not have a selective advantage themselves - can open doors for other mutants that do have a selective advantage. This paper defines robustness against indirect invasions in order to be able to discern between those two very different situations. Being robust against indirect invasions turns out to be equivalent to being an element of a minimal ES set, where this minimal ES set is the set that consists of this strategy and its (indirect) neutral mutants. This is useful, because we know that ES sets are asymptotically stable in the replicator dynamics

Evolution in games with a continous action space

Allowing for games with a continuous action space, we deal with the question whether and when static conceptslike evolutionary stability can shed any light on what happens in the dynamical context of a population playingthese games. The continuous equivalents of theorems for the finite case are either harder to prove or simplyuntrue. In some cases that fall within the latter category, sensible additional assumptions can repair the damage.Apart from that it turns out that we can no longer ignore the mutation process; with a continuous action space itmakes quite a difference what kind of shocks we consider to be likely