A frequent task facing a MAS designer is to efficiently divide resources amongst multiple agents. We consider a setting in which a single divisible resource, a.k.a. "cake", needs to be divided amongst n agents, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions that maximize the social welfare, focusing on divisions where each agent gets a single contiguous piece of the cake. We provide a constant factor approximation algorithm for the problem, and prove that it is NP-hard to find the optimal division, and that the problem admits no FPTAS unless P=NP. These results hold both when the full valuations of all agents are given to the algorithm, and when the algorithm has only oracle access to the valuation functions. In contrast, if agents can get multiple, non-contiguous pieces of the cake, the results vary greatly depending on the input model. If the algorithm is provided with the full valuation functions of all agents, then the problem is easy. However, if the algorithm needs to query the agents for information on their valuations, then no non-trivial approximation (i.e. < n) can be guaranteed.
|Title of host publication||the International conference on Autonomous Agents and Multi-Agent Systems (AAMAS)|
|Number of pages||8|
|State||Published - 6 May 2013|