Do Prices Coordinate Markets?

Walrasian equilibrium prices can be said to coordinate markets: They support a welfare optimal allocation in which each buyer is buying bundle of goods that is individually most preferred. However, this clean story has two caveats. First, the prices alone are not sufficient to coordinate the market, and buyers may need to select among their most preferred bundles in a coordinated way to find a feasible allocation. Second, we don't in practice expect to encounter exact equilibrium prices tailored to the market, but instead only approximate prices, somehow encoding "distributional" information about the market. How well do prices work to coordinate markets when tie-breaking is not coordinated, and they encode only distributional information? We answer this question. First, we provide a genericity condition such that for buyers with Matroid Based Valuations, overdemand with respect to equilibrium prices is at most 1, independent of the supply of goods, even when tie-breaking is done in an uncoordinated fashion. Second, we provide learning-theoretic results that show that such prices are robust to changing the buyers in the market, so long as all buyers are sampled from the same (unknown) distribution

Image Segmentation Using Graphical Models

Image segmentation is a very important technique in image processing. However, it is a very difficult task and there is no single unified approach for all types of images. This paper uses graphical models to design a segmentation algorithm and tests it on some nature images. First, the algorithm over-segments an image into small regions, called superpixels. For each superpixel, we model the pixels within it by a Markov random field (MRF). Then the parameters of each MRF are estimated. The coarse segmentation of the image is obtained by clustering these superpixels based on their MRF parameters. Then an undirected graphical model, in which each superpixel is a node, is used to add interactions among the superpixels. The result shows that the algorithm can generate decent segmentation for images with clear edge cues.

Truthful approximation schemes for single-parameter agents

We present the first monotone randomized polynomial-time approximation scheme (PTAS) for minimizing the makespan of parallel related machines (Q||Cmax), the paradigmatic problem in single-parameter algorithmic mechanism design. This result immediately gives a polynomialtime, truthful (in expectation) mechanism whose approximation guarantee attains the bestpossible one for all polynomial-time algorithms (assuming P ̸ = NP). Our algorithmic techniques are flexible and also yield a monotone deterministic quasi-PTAS for Q||Cmax and a monotone randomized PTAS for max-min scheduling on related machines.