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  1. We study the problem of distributed task allocation in multi-agent systems e.g. the division of labor in an ant colony or robot swarm. Suppose there is a collection of agents, a collection of tasks, and a demand vector, which specifies the number of agents required to perform each task.The goal of the agents is to collectively allocate themselves to the tasks to satisfy the demand vector. We study the dynamic version of the problem where the demand vector changes overtime. Here, the goal is to minimize the switching cost, which is the number of agents that change tasks in response to a change in the demand vector. The switching cost is an important metric since changing tasks may incur significant overhead.We study a mathematical formalization of the above problem introduced by Su, Su, Dornhaus, and Lynch [21]. We prove the first non-trivial lower bounds for the switching cost. 
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