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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