[/quote]alexpsomi wrote:Αφού δεν με διαφημίζετε εσείς θα διαφημιστώ μόνος μου
- Spoiler: εμφάνιση/απόκρυψη
- [quote]Ayth thn Paraskeuh tha mas milhsei o Alexandros Psomas gia mia koinh mas douleia, pou sthrizetai sthn ptuxiakh tou ergasia, kai h opoia prosfata egine dekth gia dhmosieysh se ena apo ta sunedria ths perioxhs mas. Epistrefoume sthn aithousa A36, omws auth thn Paraskeuh tha einai stis 5 anti gia tis 4 pou einai sinithws. Title: On Worst-Case Allocations in the Presence of Indivisible Goods Abstract: We study a fair division problem, where a set of indivisible goods is to be allocated to a set of n agents. Each agent may have different preferences, represented by a valuation function that is a probability distribution on the set of goods. In the continuous case, where goods are infinitely divisible, it is well known that proportional allocations always exist, i.e., allocations where every agent receives a bundle of goods worth to him at least 1/n. In the presence of indivisible goods however, this is not the case and one would like to find worst case guarantees on the value that every agent can have. We focus on algorithmic and mechanism design aspects of this problem. In the work of Hill 1987, an explicit lower bound was identified, as a function of the number of agents and the maximum value of any agent for a single good, such that for any instance, there exists an allocation that provides at least this guarantee to every agent. The proof however did not imply an efficient algorithm for finding such allocations. Following upon the work of Hill, we first provide a slight strengthening of the guarantee we can make for every agent, as well as a polynomial time algorithm for computing such allocations. We then move to the design of truthful mechanisms. For deterministic mechanisms, we obtain a negative result showing that a truthful 2/3-approximation of these guarantees is impossible. We complement this by exhibiting a simple truthful algorithm that can achieve a constant approximation when the number of goods is bounded. Regarding randomized mechanisms, we also provide a negative result, showing that we cannot have truthful in expectation mechanisms under the restrictions that they are Pareto-efficient and satisfy certain symmetry requirements.
I'll be there!!