Abstract
We investigate and generalize an existing model of competitive helping within a biological market, first introduced for a population of competing individuals in which one individual provides help to all others; the rest compete for the help available from this individual by providing help themselves. Our generalized model comprises two strategies in which each individual of a specific type provides the same amount of help as all other individuals of that type. Each individual’s fitness function is dependent on this level of help, the cost of providing the help, and the fact that help is proportionally reciprocated by other individuals. Competitive helping occurs when individuals actively try to help more than other individuals. To assess the emergence of equilibrium help strategies as adopted by proportions of the population, we examine the competition over available help within two settings: replicator dynamics and agent-based numerical simulations. To move one step further in our generalization, we use the agent-based model to study the N-person competitive helping game, where all individuals in the population are heterogeneous with respect to help provided. Our results show that helping does not increase indefinitely with the population size, as concluded previously, and while there are some instances of an increase in help provided as a result of competition, this competition can be detrimental to all individuals and in most cases, one type simply gives up (thus evolving to a “no help” strategy). The degree to which an individual’s help is reciprocated by the others in the population has strong implications in the long-term behaviour of equilibrium help levels of types of individuals (and of individuals themselves); these equilibrium help levels diverge from existing conjectures in current literature. Lastly, small amounts of passively provided (costless) help results in runaway competition among all individuals.
Highlights
Cooperation and the evolution of altruism between non-kin has been the focus of much research in evolutionary biology [1,2,3,4,5]
In order to assess the emergence of equilibrium help strategies as adopted by proportions of the population, we examine the competition over available help within two settings: replicator dynamics and agent-based numerical simulations
Our results, stemming from our analyses below, show that the above conclusions do not hold as stated: i) helping does not increase indefinitely with the population size; ii) we find a different level of help that maximizes payoff in the case examined by [13], and in general, equilibrium help values scale with the maximum fitness benefit, m
Summary
Cooperation and the evolution of altruism between non-kin has been the focus of much research in evolutionary biology [1,2,3,4,5]. Natural selection results in inherent competition between individuals to survive and reproduce, and one would presume only selfish.
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