Computational Mechanism Design Chapter 3

G pro t no attention is given to the incentives of

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Unformatted text preview: rmation revelation. In the theory of teams MR72 , Radner and Marschak provide a computational account of the organization of management structures and teams, considering in particular the efcient use of information within a decentralized organization. One important assumption made in the theory of teams is that all agents share a common goal e.g. pro t, no attention is given to the incentives of agents. The goal is to compare the e ciency decision quality of di erent information structures under the assumption that each structure will be used optimally. The theory of teams proposes a two-step method to measure the e ectiveness of a particular organizational structure: 1 nd the optimal mode of functioning given a structure and compute the e ciency; 2 subtract the costs of operation. The second step in this methodology has not been done because there has traditionally been no good way to assess the cost of communication. One method suggested to side-step this problem is to compare the performance of di erent communication structures for a xed number of messages. The work of Feigenbaum et al. FPS00 certainly starts to integrate communication complexity analysis into mechanism design. Radner Rad87 compares the e ciency of four classic models of resource allocation, and asks which is the minimal su cient structure to compute e cient solutions. Extensions to consider agent incentives are also discussed. Recently, Radner Rad92, Rad93 has considered a decision-theoretic model of a rm, in which managers are modeled as bounded-rational decision makers, able to perform some information processing and communicate. The model considers distributed decision problems in which agents must perform local computation with local information because of bounded-rationality and limited computation. One useful concept proposed by Radner is that of a minimally e cient" network, which is the minimal communication network 81 e.g. in terms of the number of links that does not introduce delay the decentralized decision making of agents. Green & La ont GL87 consider the impact of limited communication on the performance of incentive-compatible mechanisms. Starting with direct-revelation mechanisms, which assume that agents can transmit information messages that are su ciently detailed to describe fully all their private information, Green & La ont consider the e ect of reducing the dimensionality" of an agent's message space. In their abstract model the decision problem is to select an x 2 Rn , an agent's preferences are 2 Rm , and the communication space is R 2 Rl . The authors characterize the e ect of reducing the message dimension l, while trying to maintain incentive-compatibility and decision optimality. There is a well developed theory on the minimal communication complexity required to implement e cient allocations Hur72, MR74, Rei74 . Mount & Reiter compare the communication requirements at the equilibrium of di erent market structures, in which communication cost is measured in terms of the size of the message space that is used in a mechanism. However, most models compare the costs in equilibrium, without consider communication costs along the adjustment process, and without any attention to the computation cost on agents and on the mechanism infrastructure Mar87 . A central question in the literature is: what is the minimal equilibrium message size required to implement a particular social choice function? Classic results argue that the competitive mechanism", which implements allocations in equilibrium the mechanism announces a set of prices and agents self-select which bundles they will consume, is informationally e cient. This provides a good theoretical basis for the attention to equilibrium solutions to distributed combinatorial optimization problems in this dissertation. Of course, I also carefully consider information revelation in the adjustment process as well as in equilibrium, in addition to the computational complexity of the agents and the auctioneer. 82...
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This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.

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