Computational Mechanism Design Chapter 3

Given reported types the mechanism solves the

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Unformatted text preview: t of inputs for the auctioneer's existing algorithm, i.e. ^ l : 1  : : :  I ! 1  : : :  I , such that l  provides a new set of preferences ^ for each agent. Given reported types , the mechanism solves the optimization problem ^ with its approximation algorithm once with the inputs , and once with each appeal set ^ of inputs, e.g. li   for the appeal function of agent i, evaluating the outcomes in terms of ^ the reported types . Intuitively, providing an appeal function allows each agent to try to x the approximate nature of the auctioneer's winner-determination algorithm without needing to adjust its reported preferences away from its true preferences. Each agent will try to submit an appeal function to improve the system-wide reported value of the chosen solution. Feasible truthfulness" of the second-chance mechanism is demonstrated, de ned for a suitable restriction on the rationality of agents see below. 70 The appeal functions are very complex and require a high degree of insight on the part of agents. Nisan & Ronen note that the agents themselves could be required to compute the results of their appeal function. The mechanism therefore can be viewed as a method to use decentralized computation to improve the performance of an approximate winnerdetermination algorithm. It is also suggested that agents be given the chance to learn the characteristics of the approximation algorithm, to enable them to generate good appeal functions. Another idea is to integrate successful appeals progressively into the heuristic, to improve its base performance. Rothkopf et al. RPH98 had earlier proposed decentralized computation approaches, with challenges" issued to agents to improve the quality of the auctioneer's solution. Brewer Bre99 also proposes a market mechanism to decentralize computation to agents. Bounded-Rational Implementation Returning to the concept of feasible truthfulness, there is one one sense in which boundedrationality can help in mechanism design. Nisan & Ronen NR00 introduce the concept of a feasible best-response and a feasible dominant action. A feasible best-response is an agent's utility-maximizing action across a restricted set of all possible actions, known as the agent's knowledge set. The knowledge set is a mapping from the actions of other agents to a subset of an agent's own possible actions. An action is then feasible dominant if it is the best-response in an agent's knowledge set for all possible actions of other agents. This is a very similar concept to the maximal-in-range idea introduced as an axiom for strategy-proofness with approximate winner-determination algorithms. Given this concept of feasible dominance, one might design mechanisms in which the strategies that perform better than truth-revelation are in small measure compared to all possible strategies, to make an agent require a lot of knowledge" to have a non truthrevealing dominant strategy, or perform a lot of computation. One can also interpret the myopic best-response strategy, adopted in my own work Par99, PU00a , from the perspective of a bounded-rational agent. Certainly the ass...
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