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Computational Mechanism Design Optimal Auction Design

Agents are locked into a deliberation waiting game if

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Unformatted text preview: from other agents. Every agent hopes that another agent will deliberate and place a new bid that increases the price. Agents are locked into a deliberation waiting game". If the price increases above an agent's upper bound v on value the agent can avoid deliberation completely. Agents can be in one of three states, depending on the relative position of the ask price with respect to their beliefs v; v about the value of the good, see Fig 1 c. Agents in state s1 always bid, and therefore the ask price in the auction is always the minimum bid increment above the second-highest lower threshold on deliberation for all agents after a bidding war between all agents in state s1 . Agents in state s3 leave the auction because the ask price is greater than their upper thresholds on deliberation, and can only increase. Agents in state s2 remain active, and are locked into a waiting game. Every active agent will deliberate to prevent the auction closing, but prefers to wait for another agent to deliberate. The unique symmetrical Nash equilibrium of the waiting game has all active agents that are not currently winning the auction play a mixed strategy: deliberate with probability 1=Na , 1 when the auction is about to close, for Na active agents the active agent that is winning the good will not deliberate because it is happy for the auction to terminate.3 When there is a single active agent left the auction terminates, with that agent winning the auction. 4 Empirical Results We model a simple market for a single good, with agents that have true values vi for the good drawn from a uniform distribution, such that vi  U 0; 10. We implement the optimal bidding and metadeliberation strategies for agents in each auction, and compare the performance of each auction, in terms of e ciency, revenue and average utility from participation. Every agent has initial beliefs v = 0 and v = 10, and a deliberation procedure with computational e ectiveness 1 ,  and cost C . We simulate deliberation to match the agents' simple model. After assigning a true value for the good to each agent we use a stochastic procedure to generate new bounds after deliberation such that: 1 the true value remain...
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