Time-dependent animal conflicts: 1. The symmetric case

Animal conflicts are often characterized by time-dependent strategy sets. This paper considers the following type of animal conflicts: a member of a group is at risk and needs the assistance of another member to be saved. As long as assistance is not provided, the individual which is at risk has a positive, time-dependent rate of dying. Each of the other group members is a potential helper. Assisting this individual accrues a cost, but losing him decreases the inclusive fitness of each group member. A potential helper's interval between the moment an individual finds itself at risk and the moment it assists is a random variable, hence its strategy is to choose the probability distribution for this random variable. Assuming that each of the potential helpers knows the others' strategies, we show that the ability to observe their realizations influences the evolutionarily stable strategies (ESS) of the game. According to our results, where the realizations can be observed ESS always exist: immediate assistance, no assistance and delayed assistance. Where the realizations cannot be observed ESS do not always exist, immediate assistance and no assistance are possible ESS, while delayed assistance cannot be an ESS. We apply our model to the n brothers' problem and to the parental investment conflict.