Computational Mechanism Design Optimal Auction Design

We do not consider the mechanism for example bayesian

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Unformatted text preview: hoc strategy that makes implicit assumptions about the bids from other agents. We do not consider the mechanism for example Bayesian learning with which agents become informed, but provide agents with approximately correct distributional information about the bids from other agents. Informed agents can follow expected-utility maximizing metadeliberation strategies; agents compare the expected utility of placing an optimal bid after deliberation with the expected utility of placing an optimal bid before deliberation, given their beliefs about deliberation, the value of the good, and the bids of other agents. The mapping from expected value v to expected utility for an ^ agent's optimal bid b = v is non-linear, because an agent is more likely to win ^ the auction with a higher bid. Although an agent's mean expected value v0 after ^ deliberation is equal to an agent's expected value v before deliberation, deliber^ ation can have positive utility because of this non-linear mapping. The number of deliberation steps that an agent performs depends on the number of agents in the auction, an agent's current beliefs v; v , and the computational e ectiveness and cost of its deliberation procedure. Agents with large uncertainty and high expected values tend to deliberate more than other agents. 2 The optimal bidding strategy for a risk-neutral agent with an uncertain value for the good is expected-value equivalent" to the optimal bidding strategy for an agent that knows its value for the good. For example, when o ered a good at a xed price p, an agent with beliefs v; v should buy the good for a price p v. Similarly, in a ^ second-price sealed-bid auction an agent should bid v. ^ 5 In a posted-price sequential auction an agent that receives an ask-price p for the good holds an exclusive o er until it accepts or rejects the price. The only uncertainty in an agent's metadeliberation problem is due to the agent's own uncertainty about the value of the good. There is no uncertainty from the actions of other agents in the auction. Although agents that receive the o er can make good metadeliberation decisions, the...
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