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Multiagent Coordination Using a Distributed Combinatorial Auction Jose M. Vidal University of South Carolina AAAI Workshop on Auction Mechanisms for Robot Coordination, 2006

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Combinatorial auctions are a great way to represent and solve distributed allocation problems. Problem: most of the winner determination solutions that exists are centralized. Multiagent Coordination Using a Distributed Combinatorial Auction

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This paper suggest using The (the Progressive Adaptive User Selection Environment )PAUSE auction which is an increasing-price combinatorial auction and the problem of winner determination is distributed amongst the bidders. is providing a bidding algorithm for agents in a PAUSE auction, the PAUSEBID algorithm. This algorithm always return the bid which is maximizing the bidders utility.

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Combinatorial auction PAUSE auction PAUSEBID algorithm analysis test

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Combinatorial Auctions has been the most widely used auction in multiagent systems. agents can place bids for sets of items instead of just placing one bid for each item for sale. has been used in many systems where there is a set of tasks need to distributed between agents with different preferences.

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Example for Combinatorial Auctions PriceBid items $1Beast Boy $3 Robin $5Raven, Starfire $6Cyborg, Robin $7Cyborg, Beast Boy $8Raven, Beast Boy correct solution :accept both the $8 bid and the $6 bid.

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Researchs on Combinatorial Auctions CA is applicable to a large number of distributed allocation problems and multiagent coordination problems (Cramton, Shoham, & Steinberg 2006). Centralized Winner determination algorithms 1. CASS (Fujishima, Leyton-Brown, & Shoham 1999) 2. Bidtree (Sandholm 2002) 3.CABOB (Sandholm et al. 2005)

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Researches on Combinatorial Auctions These centralize actions don’t fit multiagent systems where: 1.Agents own computational resources 2.Agents have localized information PAUSE auction has been developed and distribute the winner determination problem among agents

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The PAUSE Auction m stages for m items Stage 1: simultaneous ascending price open-cry auctions for each individual item Stage k =2, 3,...,m: bidders must submit sets of bids that cover all goods but each one of the bids must be for k goods or less.

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The PAUSE Auction Each bid b composed of b items :the set of items the bid is over b value : the valueor price of the bid b agent : the agent that placed the bid b {b items, b value, b agent } At the end of each stage k, set B { b1, b2,b3,..} of the current best bids is generating and all agents know the best bid for every subset of size k or less.

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The PAUSE Auction at each stage k>1 : bidders can use bids from other agents from previous round. The sum of bid prices in each submitted bid set should be bigger than currently winning bid set. There will be a set of currently winning bids which maximizing the revenue.

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The PAUSE Auction also at each stage the goal of each agent i is to maximizing it’s utility where v i is the value function for this agent is : Agent i must find g* such that and

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The PAUSE Auction the final winning bid set will be one such that no agent can propose a better bid set. PAUSE auction has been shown to be envy-free since no bidder would prefer to exchange his allocation with that of any other bidders.

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Eliminating the auctioneer To eliminate the auctioneer, all bids are broadcast when an agent receives a bid from another agent 1.it updates the set of best bids. 2.Determine if the new bid is better than the current winning bid.

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Formulation g is a set of bids all taken from B such that g covers all the items. g* is a set of bids such that:

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Bidding Algorithm

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Search Algorithm

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Analysis The PAUSEBID algorithm implement the same strategy as English auction such that the agents places the bid which maximize its own utility and has the revenue greater than the current winning bid.

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Analysis The PAUSEBID algorithm has certain weaknesses: the agent surplus has been distributed(proportionately to the agent’s valuation for items) across his bids on g* Example solution: change the surplus solution method to include some randomness

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Analysis because of these weaknesses: The PAUSEBID strategy Is not a dominant strategy. But when its called, it returns the bid that increase and maximize the agents utility. If the whole system use it, the solution would be the same as the one by a centralize winner determination algorithm.

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Testing the PAUSE Auction Tested where a a set of agents must perform a set of tasks but there are cost savings for particular agents if they can bundle together certain subsets of tasks. The result was in 95% of runs similar to the result from CASS. The revenue of PAUSE auction is always smaller.

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Future work Improve the performance of the PAUSEBID algorithm by using caching techniques similar to centralized algorithm(CABOB). Developing ways that agents may cooperate in order to minimize any redundant work. Eliminating the need for the agent to constantly broadcast new bids and use multicasting method instead.

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