Explaining the emergence of cooperative traits: An axiomatic theory of accumulation

Abstract

In this dissertation I construct an axiomatic theory of action that explains how originally selfish individuals form aggregations and develop cooperative abilities. This theory is more general than the two most widespread biological explanations of the emergence of cooperation: kinship theory and game theoretic models. In particular, it introduces the notions of space and time that are more general (individual specific) than standard physical notions on which biological theories mostly rely. While predictions of my theory agree, in principle, with predictions of other main theories of aggregation, its scope goes well beyond that of any other theory of aggregation. For instance, I am able to show that two different arguments about properties of optimal size aggregations do in fact follow from a single set of assumptions, namely those of my theory of accumulations. I am also able to explain a paradoxical empirical finding on genetic variation. More specifically, Sibly (1983) has shown that under a certain type of a fitness function individuals will form aggregations with fitness optimizing group size being larger than the eventually emerging in equilibrium group size. In a response to Sibly, Giraldeau and Gillis (1984) presented a type of fitness function where the optimal group size is equal to the equilibrium group size. Both arguments rely, however, on fitness functions that are postulated ad hoc. In my theory I show how both of these functions can be derived analytically from a set of more fundamental assumptions. This shows that claims of Sibly and Giraldeau's and Gillis' while seemingly contradictory, were in fact consistent. Another example of an application of my theory concerns a genetic puzzle posed by Hedrick and Parker (1997). Hedric and Parker have observed that genetic variation in eusocials is not only a higher than predicted by kinship but even higher than in solitaries. This empirical observation, paradoxical in the light of standard biological explanations, can in fact be explained by my theory.