Constraints on reciprocity for non-sessile organisms |
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Authors: | Michael Mesterton-Gibbons Michael J Childress |
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Institution: | (1) Department of Mathematics 3027, Florida State University, 32306-3027 Tallahassee, FL, U.S.A.;(2) Department of Biological Science 2043, Florida State University, 32306-2043 Tallahassee, FL, U.S.A. |
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Abstract: | Previous game-theoretic models of reciprocity have assumed that populations are large and organisms effectively sessile. This
paper analyzes an iterated prisoner's dilemma among non-sessile organisms in a finite population, on the assumption that an
individual's chance of remaining in one place is not influenced by a partner's behavior. This mode of interaction is suitable
for analyzing potentially cooperative behaviors that are secondary to the advantage of group formation, e.g. allogrooming
among social mammals. The analysis yields necessary conditions for stable reciprocity in terms of three parameters, namely,
a benefit/cost ratio, the probability of further interaction and the probability of partner retention. The results suggest
that, in highly mobile organisms such as fish, birds and mammals, reciprocity may be stable only if the population is small
and the relative benefit and future interaction probability are both large. |
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