Automated Negotiation

Automated Negotiation Sarit Kraus Bar-Ilan, Israel UMD,USA

Plan of the course • Introduction • Rules of Encounters • Strategic Negotiation • Auctions • protocols • strategies • Argumentation

Machines Controlling and Sharing Resources • Electrical grids (load balancing) • Telecommunications networks (routing) • PDA’s (schedulers) • Shared databases (intelligent access) • Traffic control (coordination)

Broad Working Assumption • Designers (from different companies, countries, etc.) come together to agree on standards for how their automated agents will interact (in a given domain) • Discuss various possibilities and their tradeoffs, and agree on protocols, strategies, and social laws to be implemented in their machines

Attributes of Standards • Efficient: Pareto Optimal • Stable: No incentive to deviate • Simple: Low computational and communication cost • Distributed: No central decision-maker • Symmetric: Agents play equivalent roles Designing protocols for specific classes of domains that satisfy some or all of these attributes

Distributed Artificial Intelligence (DAI) • Distributed Problem Solving(DPS) —Centrally designed systems, built-in cooperation, have global problem to solve • Multi-Agent Systems(MAS) —Group of utility-maximizing heterogeneous agents co-existing in same environment, possibly competitive

Phone Call Competition Example • Customer wishes to place long-distance call • Carriers simultaneously bid, sending proposed prices • Phone automatically chooses the carrier (dynamically) AT&T Sprint MCI $0.20 $0.23 $0.18

Best Bid Wins • Phone chooses carrier with lowest bid • Carrier gets amount that it bid MCI Sprint AT&T $0.20 $0.23 $0.18

“Maybe I can bid as high as $0.21...” Attributes of the Mechanism • Distributed • Symmetric • Stable • Simple • Efficient Carriers have an incentive to invest effort in strategic behavior AT&T MCI Sprint $0.20 $0.23 $0.18

Best Bid Wins, Gets Second Price • Phone chooses carrier with lowest bid • Carrier gets amount of second-best price MCI Sprint AT&T $0.20 $0.23 $0.18

“I have no reason to overbid...” Attributes of the Mechanism • Distributed • Symmetric • Stable • Simple • Efficient Carriers have no incentive to invest effort in strategic behavior AT&T MCI Sprint $0.20 $0.23 $0.18

“All female employees making over $50,000 a year.” “All female employees with more than three children.” 2 1 Database Domain Common Database TOD

Negotiation “A discussion in which interested parties exchange information and come to an agreement.” — Davis and Smith, 1977 • Two-way exchange of information • Each party evaluates information from its own perspective • Final agreement is reached by mutual selection

Game Theory--Short Introduction • Game theory is the study of decision making in multi-person situations where the outcome depends on everyone’s choice. • In Decision Theory and the theory of competitive equilibrium from economics the other participants actions are considered as an environmental parameter. The effect of the of the decision-maker’s actions on the other participants is not taken into consideration.

Describing a Game • Essential elements: players, actions, information, strategies, payoffs, outcome, and equilibria. • Ways to present social interactions as a game: • Extensive form:the most complete description. • Strategic form: many details are omitted. • Coalitional form: binding agreements exist.

Example of two players game dindia op deal 0 2- 1 2 deal Dsikh 3- 0 2- 1- blow

Nash Equilibrium • An action profile is an order set a=(a1,…,aN) of one action for each of the N players in the game. • An action profile a is a Nash Equilibrium (Nash 53) of a strategic game, if each agent j does not have a different action yielding an outcome that it prefers to that generated when chooses aj, given that every other player I chooses ai.

2,1- 3-,5 blow op sik yes 2,5 Ind 2,1- 3,4 op blow yes 0.4 sik Ind dealH dealH c 1,4 0.6 Ind sik dealH Ind dealH dealH 1,4 dealH sik op op 4- ,4 -3,0-

Rules of Encounter Jeffrey S. Rosenschein Gilad Zlotkin

Domain Theory • Task Oriented Domains • Agents have tasks to achieve • Task redistribution • State Oriented Domains • Goals specify acceptable final states • Side effects • Joint plan and schedules • Worth Oriented Domains • Function rating states’ acceptability • Joint plan, schedules, and goal relaxation

1 2 Postmen Domain Post Office TOD a   c b   f  e d

“All female employees making over $50,000 a year.” “All female employees with more than three children.” 2 1 Database Domain Common Database TOD

2 1 Fax Domain faxes to send TOD a c b Cost is only to establish connection f e d

1 2 Slotted Blocks World SOD 3 1 2 3 1 2

The Multi-Agent Tileworld WOD hole agents tile B A 2 2 5 5 2 obstacle 4 3 2

Task Oriented Domain (TOD) A tuple < T, A, c > where: • T is the set of all possible tasks • A = A1 , … , An is a list of agents • c is a monotonic function c : [2T ] + An encounter is a list T1 ,…, Tn of finite sets of tasks from T such that agent Ak needs to achieve all the tasks in Tk (also called agent Ak’s goal).

Building Blocks • Domain • A precise definition of what a goal is • Agent operations • Negotiation Protocol • A definition of a deal • A definition of utility • A definition of the conflict deal • Negotiation Strategy • In Equilibrium • Incentive-compatible

Deal and Utility in two-agent TOD • Deal  is a pair (D1, D2): D1  D2 = T1  T2 • Conflict deal:  = (T1, T2) • Utilityi() = Cost(Ti) – Cost(Di)

Negotiation Protocols • Agents use a product-maximizing negotiation protocol (as in Nash bargaining theory); • It should be a symmetric PMM (product maximizing mechanism); • Examples: 1-step protocol, monotonic concession protocol…

Building Blocks • Domain • A precise definition of what a goal is • Agent operations • Negotiation Protocol • A definition of a deal • A definition of utility • A definition of the conflict deal • Negotiation Strategy • In Equilibrium • Incentive-compatible

1 2 Negotiation with Incomplete Information Post Office What if the agents don’t know each other’s letters?  a h b 1 g c e f d   2 1

1 b, f e 2 –1 Phase Game: Broadcast Tasks Post Office Agents will flip a coin to decide who delivers all the letters.  a h b 1 g c e f d   2 1

1 f b e 2 Hiding Letters Post Office  a h b (1) (hidden) g c e f d They then agree that agent 2 delivers to f and e.   2 1

b, c 1 b, c 2 Another Possibility for Deception Post Office They will agree to flip a coin to decide who goes to b and who goes to c. a c b   1, 2 1, 2

1 2 Phantom Letter Post Office b, c, d They agree that agent 1 goes to c. a b, c c  b 1, 2  1, 2  d 1 (phantom)

Negotiation over Mixed Deals Mixed deal (D1, D2) : p The agents will perform (D1, D2) with probability p, and the symmetric deal (D2, D1) with probability 1 – p Theorem: With mixed deals, agents can always agree on the “all-or-nothing” deal

1 f b e 2 Hiding Letters with MixedAll-or-Nothing Deals Post Office They will agree on the mixed deal where agent 1 has a 3/8 chance of delivering to f and e.  a h b (1) (hidden) g c e f d   2 1

1 2 Phantom Letters with Mixed Deals Post Office b, c, d They will agree on the mixed deal where A has 3/4 chance of delivering all letters, lowering his expected utility. a b, c c  b 1, 2  1, 2  d 1 (phantom)

Sub-Additive TODs TOD < T, A, c > is sub-additive if for all finite sets of tasks X, Y in T we have: c(X  Y) c(X) + c(Y)

Sub-Additivity X Y c(X  Y) c(X) + c(Y)

Sub-Additive TODs The Postmen Domain, Database Domain, and Fax Domain are sub-additive. The “Delivery Domain” (where postmen don’t have to return to the Post Office) is not sub-additive.  

c b d Incentive Compatible Mechanisms a  a h b (1) (hidden)  g c Sub-Additive 1, 2  e 1, 2 f d Hidden Phantom    1 (phantom) Pure L L 2 1 A/N T/P T Mix L T/P Theorem: For all encounters in all sub-additive TODs, when using a PMM over all-or-nothing deals, no agent has an incentive to hide a task.

 1  2  1 1  2   1 1 Decoy Tasks Decoy tasks, however, can be beneficial even with all-or-nothing deals Sub-Additive Hidden Phantom Decoy Pure L L L A/N T T/P L Mix L T/P L

Concave TODs TOD < T, A, c > is concave if for all finite sets of tasks Y and Z in T , and X  Y, we have: c(Y  Z) – c(Y) c(X  Z) – c(X) Concavity implies sub-additivity.

Concavity The cost Z adds to X is more than the cost it adds to Y.(Z - X is a superset of Z - Y) Z Y X

Concave TODs The Database Domain and Fax Domain are concave (not the Postmen Domain, unless restricted to trees). Z 1  This example was not concave; Z adds 0 to X, but adds 2 to its superset Y (all blue nodes).  2 X  1 1 2    1 1

Three-Dimensional Incentive Compatible Mechanism Table Theorem: For all encounters in all concave TODs, when using a PMM over all-or-nothing deals, no agent has any incentive to lie. Concave Hidden Phantom Decoy Pure L L L A/N T T T Mix L T T Sub-Additive Hidden Phantom Decoy Pure L L L A/N T T/P L Mix L T/P L

Modular TODs TOD < T, A, c > is modular if for all finite sets of tasks X, Y in T we have: c(X  Y) = c(X) + c(Y) – c(X  Y) Modularity implies concavity.

Modularity c(X  Y) = c(X) + c(Y) – c(X  Y) X Y

Modular TODs The Fax Domain is modular (not the Database Domain nor the Postmen Domain, unless restricted to a star topology). Even in modular TODs, hiding tasks can be beneficial in general mixed deals.

Automated Negotiation