Asymmetries in power, the ability to influence the outcome of conflict, are ubiquitous in social interactions because interacting individuals are rarely identical. It is well-documented that asymmetries in power influence the outcome of reproductive conflict in social groups. Yet power asymmetries have received little attention in the context of negotiations between caring parents, which is surprising given that parents are often markedly different in size. Here we built on an existing negotiation model to examine how power and punishment influence negotiations over care. We incorporated power asymmetry by allowing the more powerful parent, rank 1, to inflict punishment on the less powerful parent, rank 2. We then determined when punishment will be favored by selection and how it would affect the negotiated behavioral response of each parent. We found that with power and punishment, a reduction in one parent’s effort results in partial compensation by the other parent. However, the degree of compensation is asymmetric: the rank 2 compensates more than the rank 1. As a result, the fitness of rank 1 increases and the fitness of rank 2 decreases, relative to the original negotiation model. Furthermore, because power and punishment enable one parent to extract greater effort from the other, offspring can do better, i.e. receive more total effort, when there is power and punishment involved in negotiations over care. These results reveal how power and punishment alter the outcome of conflict between parents and affect offspring, providing insights into the evolutionary consequences of exerting power in negotiations.

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