Computational Mechanism Design Optimal Auction Design

The model matches some of the properties of standard

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Unformatted text preview: tegies for agents in each auction. The model matches some of the properties of standard algorithmic techniques for solving hard optimization problems, such as Lagrangian relaxation, depth- rst search, and branch-and-bound. Furthermore, the model supports a mode of interaction between people and software bidding agents that is provided in some current on-line auctions 17 . We do not expect the valuation problems and decision procedures of real agents or real experts to have characteristics that match the precise assumptions e.g. distributional assumptions of our model. However, we believe that the general results from our analysis will hold in many real problem domains for agents with hard valuation problems. Every agent i has an unknown true value vi for a good, and maintains a lower bound v and upper bound v on its value, see Fig 1 a. Agent i believes that its true value is uniformly distributed between its bounds, v  U v; v. Given this belief the expected value for the good is v = v + v=2. As an agent deliberates ^ its bounds are re ned and its belief about the value of the good changes, with expected value v converging to v over time. ^ Let  = v , v denote an agent's current uncertainty about the value of the good. Agents have a deliberation procedure that adjusts the bounds on value, reducing uncertainty by a multiplicative factor , where 0 1. The new bounds are  apart, and consistent with the current bounds but not necessarily adjusted symmetrically, see v0 and v0 in Fig 1 a. For a small the uncertainty is reduced by a large amount, and we refer to 1 ,  as the computational e ectiveness" of an agent's deliberation procedure. Furthermore, we model the new expected value v0 for the good after deliberation as uniformly ^ distributed v0  U v + =2; v , =2, such that the new bounds are consistent ^ with the current bounds. After deliberation an agent believes the value of the good is uniformly distributed between its new bounds. Agents incur a cost C for each deliberation step, that we assume is constant fo...
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This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.

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