The resource allocation problem consists of the optimal distribution of a budget between agents in a group. We consider such a problem in the context of open systems, where agents can be replaced at some time instances. These replacements lead to variations in both the budget and the total cost function that hinder the overall network's performance. For a simple setting, we analyze the performance of the Random Coordinate Descent algorithm (RCD) using tools similar to those commonly used in online optimization. In particular, we study the accumulated errors that compare solutions issued from the RCD algorithm and the optimal solution or the non-collaborating selfish strategy and we derive some bounds in expectation for these accumulated errors.
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