Other Negotiation Types .1 Auctions

English auction, Dutch auction and double auction are categories of negotiation characterized by sequential decision making and open-bidding. First-price sealed-bid auction and Vickrey auction are characterized by simultaneous decision-making and sealed-bidding [McAfee and McMillan, 1987; Davis and Holt, 1993].

In English auction, an auctioneer opens the auction, and all bidders bid openly (known by others) and sequentially until one active bidder remains (the winner). The winner pays the highest bid he/she submitted. The best strategy for bidders in an English auction is to increase the bid from zero until their private valuation. A bidder’s valuation here means the minimum or maximum acceptable price depending on whether her/his position is as a buyer or a seller, respectively. A study by Roth and Ockenfels [2002]

reports on the sniping strategy (bid near the end of auction) in English-type online auction (e.g. eBay.com).

Buyers in a Dutch auction do not propose a price, but a single seller will lower the price sequentially until a buyer (the winner) stops it. The strategy used in Dutch auction is fairly similar to that used in price sealed-bid auction, because bidders in a first-price sealed-bid auction submit their bids simultaneously. The winner is the bidder who submits the highest bid, and he/she pays the first highest bid (i.e. his/her own bid). First-price sealed-bid auctions in MASs have been studied in [David et al., 2002; Leyton-Brown et al., 2002; Zhu and Wurman, 2002].

Just like in a first-price sealed-bid auction, bidders in a Vickrey auction (or second-price sealed-bid auction) submit their bids simultaneously. The winner is the

bidder who submits the highest bid, but he/she pays the second highest bid. The best strategy for bidders in a Vickrey auction is to bid their true valuation [Vickrey, 1961].

The double auction was introduced by Smith [1962, 1964]. Under double-auction rules, sellers/bidders announce their offers/bids sequentially, i.e. bids are raised and offers are lowered sequentially. In other words, sellers will compete to lower their offers and buyers will compete to raise their bids. Some papers investigating this auction are [Das et al., 2001], [Tesauro and Das, 2001], [Tesauro and Bredin, 2002], [Huang et al., 2002], [Grossklags and Schmidt, 2003], and [Lochner and Wellman, 2004].

In a combinatorial auction (CA) bidders can bid over bundles of items [Rassenti et al., 1982; Rothkopf et al., 1998]. For example, in an auction for an airport time slot, an airline company can submit the bid: <{Monday 8:00-9:30, Saturday 8:00-9:30}, $0.5 million> XOR <{Monday 10:00-11:30, Friday 8:00-9:30}, $0.4 million>, which means they are willing to pay either $0.5 million for time slot {Monday 8:00-9:30, Saturday 8:00-9:30} or $0.4 million for time slot {Monday 10:00-11:30, Friday 8:00-9:30} but not both. After all bidders submit their bids, the seller will determine the optimal allocation to the bidders so as to maximize his profit (optimal winner determination problem).

The optimal winner determination problem in combinatorial auction is NP-hard [Rothkopf et al., 1998], which makes it one of the most challenging problems in MAS [Sandholm, 2002a]. For example, Nisan [2000] and Tennenholtz [2000] attempt to find a class of combinatorial auctions with tractable (solvable by a polynomial time algorithm) optimal allocation. Gonen and Lehmann [2000] use branch and bound search, Sandholm and his colleagues [Sandholm et al., 2001] use heuristic search, Holland and O’Sullivan [2005] use weighted super solutions framework, etc.

2.2.2.2 Contract-net Protocol

Another approach, the contract-net protocol [Smith, 1980], on the other hand, provides a simple but powerful negotiation mechanism for solving a complex task by means of distributed problem solving. The common way to assign a task is to announce it to other agents (e.g. open an auction/bargaining) and assign the task to the winner.

Moreover, every agent can sub-contract/re-contract its (previous) tasks to others who are willing to accept them. Theoretically, an agent will accept a contract if its marginal cost is less than its marginal benefit [Sandholm, 1993]. For example, if an agent already has many tasks to do, then any additional task will generate high marginal cost (e.g., cause slower computation). Theoretically, using this self-organizing mechanism, the system would perform task allocation, which is Pareto optimal when all agents are sincere in reporting their marginal cost and able to swap their tasks with others [Sandholm, 1999a].

Another important issue in the contract-net protocol is whether the agent can de-commit from a contract or not. Leveled de-commitment contract [Sandholm and Lesser, 1995; Sandholm et al., 1999], i.e. a contract where both parties can de-commit by paying a certain penalty, becomes a crucial mechanism in improving the social welfare of the contract-net. Some work with respect to the application of the contract-net protocol includes [Dellarocas and Klein, 2000; Tran and Cohen, 2002].

2.2.2.3 Voting

Another approach to resolving conflicts is through voting. Voting is a social choice mechanism in selecting social preferences over a set of alternatives, e.g. what is the society mostly prefer from available alternatives. One of the applications of voting in a MAS is resource allocation by means of majority voting. For example, in order to use a common resource (e.g. a supercomputer), an agent can broadcast a request to all other

agents to collect access keys from these agents. If two agents compete to use the same resource, then the first who gets the majority votes (>50% of access keys) will be able to access the resource.

Some examples of the application of voting in MAS are [Ephrati and Rosenschein, 1991, 1993; Hunsberger and Zancanaro, 2000]. The voting mechanism is primarily used in making group decisions, in which the choice is simple such as ‘agree’ or ‘disagree’.

However, in other approaches, voting can be very complex, because the voting result can be manipulated [Gibbard, 1973; Satterthwaite, 1975]. For example if the preference of an agent to three alternatives {A, B, C} is A ≻ B ≻ C,² and this agent knows that the chance of A to win is very small, but the chances of B and C are the same, then its best strategy is to vote B, not A. Some examples of current study in a voting protocol are [Guttmann and Zukerman, 2005] in finding better voting policies in the presence of unreliable agents (e.g. lazy, corrupt, selfish, or conservative agents), [Conitzer and Sandholm, 2005] in correcting noisy votes (e.g. irrational votes) by using maximum likelihood estimators, [Pitt et al., 2005] in formalizing the voting protocol using event calculus, and many others.