Do software agents know what they talk about? Agents and Ontology dr. Patrick De Causmaecker, Nottingham, March

Negotiation

Nottingham, March 2005Agents and Ontology How can we arrive at an agreement? Sum zero games are not realistic We try to find win-win solutions There is no supervising authority We use negotiation and argumentation

Nottingham, March 2005Agents and Ontology Negotiation scenario’s Mechanisms, protocols Rules of an encounter (Rosenschein, Zlotkin 1994) Mechanism-design is the art to craft protocols that satisfy certain conditions Once the protocol has been defined, we look for strategies that the agents can use

Nottingham, March 2005Agents and Ontology Mechanism-design Wanted ( Sandholm 1999): Guarantee for succes Maximal social wellfare Pareto efficiency Individual rationality Stability Simplicity Distribution

Nottingham, March 2005Agents and Ontology Auctions Pro: very simple, easy to understand, easy to automate Pro: stimulates research for optimal strategies Contra: too simple

Nottingham, March 2005Agents and Ontology Parties at an auction Auctioneer: tries to sell the goods at the optimal price Bidders: try to buy the goods at the optimal price, which should be below the value of their estimate

Nottingham, March 2005Agents and Ontology Important points Has the good a well known public value? Has the good a well known private value? Has the good a correlated value for at least one of the bidders?

Nottingham, March 2005Agents and Ontology Dimensions How is the winner determined Highest bidder, own price: first-price auctions Highest bidder, second price: second-price auctions How to bid? secretly: sealed bid open: open cry What is the bidding procedure? ascending descending one shot

Nottingham, March 2005Agents and Ontology English auction First-price, open cry, ascending There is a reservation price, nobody can go below this price Each bid must be above the previous one. If no agent wants to bid higher, the las bidder wins

Nottingham, March 2005Agents and Ontology Strategy at an English auction The dominant strategy is to bid the minimum above the last bid until the private value is reached. If the value of the good is uncertain The winning agent is happy: he won The winning agent is concerned: he may have paid too much. => Winners curse

Nottingham, March 2005Agents and Ontology Dutch auctions First-price, open cry, descending Auctioneer starts artificially high Auctioneer lowers the price until somebody bids First bidder wins Winners curse…

Nottingham, March 2005Agents and Ontology First price, sealed bid First-price, sealed bid One shot Highest bidde wins Strategy? If every agent bids its own private value, the winner gets it at his price The delta with the second bid is what the winner pays too much. One should bid less than one’s private value, but more than the second’s value. No optimal strategy is known.

Nottingham, March 2005Agents and Ontology Vickrey auctions Second-price, sealed bid One-shot, winner pays second price Pro: The optimal strategy is to bid the real private value Above it, one risks to pay too much. Below does not make sense, you pay the second price anyhow.

Nottingham, March 2005Agents and Ontology Vickrey auctions Display interesting properties, but are not well understood by human bidders. Antisocial behaviour is possible if one knows the amount that a higher bidder wants to spend on the good.

Nottingham, March 2005Agents and Ontology Lies and conspiracies Conspiracy is not prevented by the protocol. Lying by the auctioneer is difficult to prevent, especially in claused and Vickrey auctions. Auctioneer can send someone to bid falsly…

Nottingham, March 2005Agents and Ontology MAFIA

Nottingham, March 2005Agents and Ontology Negotiation Limitations of auctions: Goods, no collaboration Only price, not value Rosenschein en Zlotkin pioneered (1994).

Nottingham, March 2005Agents and Ontology Negotiation Concepts The negotiation set The protocol The strategies The rule of agreement

Nottingham, March 2005Agents and Ontology Negotiation procedure Each agent makes one proposal per round Acording to the own strategy, following the rules of the protocol Once agreement is reached, the outcome is fixed Otherwise we move to the next round

Nottingham, March 2005Agents and Ontology Negotiation encounters One to one Many to one Many to many Simple Multiple Complexity rises exponentially with the number of properties

Nottingham, March 2005Agents and Ontology Task negotiations A set of tasks, a set of agents and a cost function define task negotiation c:  (T)  is monotonous: T 1  T 2  c(T 1 )  c(T 2 ) An encounter is a sequence of sets of tasks, one assigned to each agent.

Nottingham, March 2005Agents and Ontology Negotiations We discuss only one to one encounters., a deal is with D 1  D 2 = T 1  T 2 The cost for agent i of  = is cost i (  ), the cost for a set of actions is c (T i ). We have: utility i (  ) = c (T i ) - cost i (  )

Nottingham, March 2005Agents and Ontology Dominant deals Deal  1 dominates deal  2 iff  i  {1,2}, utility i (  1 )  utility i (  2 )  i  {1,2}, utility i (  1 ) < utility i (  2 ) A dominant deal is preferable for both partners. A deal that is not dominated is called pareto optimal. A non pareto optimal deal can be improved for both negotiators.

Nottingham, March 2005Agents and Ontology Rationality The initial assignment is called the conflict deal. It will be the result of a faulty negotiation process in which no agreement is reached. A deal is individually rational if it weakly dominates the conflict agreement.

Nottingham, March 2005Agents and Ontology The negotiation set The set of reasonable deals is Pareto optimal Individualy rational How should an agent start?

Nottingham, March 2005Agents and Ontology Monotonous procedure Protocol Both agents make a proposal Agreement rule utility 1 (  1 )  utility 1 (  2 ) or utility 2 (  2 )  utility 2 (  1 ) Case 1 leads to  2, case 2 leads to  1. If no agreement is reached, agent i is allowed to make a proposal that is worse for him. If no agent proposes, the conflict agreement is reached.

Nottingham, March 2005Agents and Ontology Zeuthen strategy An agent makes the best proposal possible. The degree of acceptability of the conflictagreement determines who has to bid An agent makes the minimal concession to force the opponent to bid

Nottingham, March 2005Agents and Ontology Risk analysis Degree of acceptability of the conflict agreement: Risk i = 0 if the present proposal is the conflict agreement Risk i = (utility i (  i )-utility i (  j ))/utility i (  i )

Nottingham, March 2005Agents and Ontology How good is this No guarantee of succes It does end Does not maximise social wellfare Is pareto optimal Individually rational No central authority Nash equilibrium (tie resolution at random) Complex, sometimes heuristics are needed