In many realistic problems of allocating resources, economy efficiency must be taken into consideration together with social equality, and price rigidities are often made according to some economic and social needs. We study the computational issues of dynamic mechanisms for selling multiple indivisible items under price rigidities. We propose a polynomial algorithm that can be used to find over-demanded sets of items, and then introduce a dynamic mechanism with rationing to discover constrained Walrasian equilibria under price rigidities in polynomial time. We also address the computation of sellers' expected profits and items' expected prices, and discuss strategical issues in the sense of expected profits.
Abstract:Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n, m and N stand for the number of vertices, edges and minimum spanning trees, respectively. Because this algorithm spends more time finding minimum spanning tree, we propose an improved algorithm whose time complexity is O(Nm). The improved algorithm uses disjoint set data structure so that the average time complexity on finding a new minimum spanning tree is O(m/n). The two algorithms are analyzed in detail and the experiment results agree with theoretical analysis.
We study the problem of allocating a set of indivisible goods to multiple agents. Recent work [Bouveret and Lang, 2011] focused on allocating goods in a sequential way, and studied what is the "best" sequence of agents to pick objects based on utilitarian or egalitarian criterion. In this paper, we propose a parallel elicitation-free protocol for allocating indivisible goods. In every round of the allocation process, some agents will be selected (according to some policy) to report their preferred objects among those that remain, and every reported object will be allocated randomly to an agent reporting it. Empirical comparison between the parallel protocol (applying a simple selection policy) and the sequential protocol (applying the optimal sequence) reveals that our proposed protocol is promising. We also address strategical issues.
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