1. IAT 2006 1 Heuristics for Dealing with a Shrinking Pie in Agent Coalition Formation Kevin Westwood – Utah State University Vicki Allan – Utah State University IAT 2006

2. 2 Multi-Agent Coalitions “A coalition is a set of agents that work together to achieve a mutually beneficial goal” (Klusch and Shehory, 1996) Reasons agent would join Coalition Cannot complete task alone Cannot complete task alone Complete task more quickly Complete task more quickly

3. 3IAT 2006 Skilled Request For Proposal (SRFP) Environment Inspired by RFP (Kraus, Shehory, and Taase 2003) Provide set of tasks T = {T 1 …T i …T n } Divided into multiple subtasks requiring skill/level Has a payment value V(T i ) Service Agents, A = {A 1 …A k …A p } Associated cost f k Associated cost f k skill/level skill/level Manager Agent Distributes tasks to service agents Distributes tasks to service agents

4. 4IAT 2006 Auctioning Protocol Variation of a reverse auction Agents compete for opportunity to perform services Agents compete for opportunity to perform services Efficient way of matching goods to services Efficient way of matching goods to services Central Manager 1)Randomly orders Agents 2)Each agent gets a turn Accepts previous offer or Proposes 3)Coalitions are awarded task Multiple Rounds {0,…,r z } Our version is cyclic – so agents later in list are not disadvantaged Our version is cyclic – so agents later in list are not disadvantaged

5. 5IAT 2006 Cyclic Auction

6. 6IAT 2006 Agent cost Agent costs deviate from base cost Base cost derived from skill and skill level Agent payment cost + proportional portion of net gain

7. 7IAT 2006 Decisions How do I decide whether to accept? If I make an offer… What task should I propose doing? What other agents should I recruit?

8. 8IAT 2006 Coalition Calculation Algorithms Calculating all possible coalitions Requires exponential time Requires exponential time Not feasible in most problems in which tasks/agents are entering/leaving the system and values of tasks are shrinking over time Not feasible in most problems in which tasks/agents are entering/leaving the system and values of tasks are shrinking over time Divide into two steps 1) Task Selection 2) Other Agents Selected for Team polynomial time algorithms polynomial time algorithms

9. 9IAT 2006 Task Selection Individual Profit – obvious, greedy approach Individual Profit – obvious, greedy approach Competitive: best for me Competitive: best for me Why not always be greedy? Why not always be greedy? Others may not accept – your membership is questioned Individual profit may not be your goal Global Profit Global Profit Best Fit Best Fit Co-opetitive Co-opetitive

10. 10IAT 2006 Two Step Coalition Calculation Task Selection Individual Profit Individual Profit Global Profit – somebody should do this task Global Profit – somebody should do this task I’ll sacrifice Wouldn’t this always be a noble thing to do? Task might be better done by others I might be more profitable elsewhere Best Fit – uses my skills wisely Best Fit – uses my skills wisely Co-opetitive Co-opetitive

11. 11IAT 2006 Two Step Coalition Calculation Task Selection Individual Profit Individual Profit Global Profit Global Profit Best Fit – Cooperative: uses skills wisely Best Fit – Cooperative: uses skills wisely Perhaps no one else can do it Maybe it shouldn’t be done Co-opetitive Co-opetitive

12. 12IAT 2006 Co-opetitive Agent Co-opetition Phrase coined by business professors Brandenburger and Nalebuff (1996), to emphasize the need to consider both competitive and cooperative strategies. Phrase coined by business professors Brandenburger and Nalebuff (1996), to emphasize the need to consider both competitive and cooperative strategies. Co-opetitive Task Selection Select the best fit task if profit is within P% of the maximum profit available Select the best fit task if profit is within P% of the maximum profit available

13. 13IAT 2006 Costs by Level

14. 14IAT 2006 What about accepting offers? Compare to what you could achieve with a proposal Worry about shrinking pie Utility gets smaller as the time to form a coalition increases Utility gets smaller as the time to form a coalition increases Compare best proposal with best offer Use utility based on agent type

15. 15IAT 2006 When an offer is received… Compare best proposal with best offer Use utility based on agent type Four acceptance policies Expected Utility, discount aware Expected Utility, discount aware Expected Utility, discount unaware Expected Utility, discount unaware Monetary Monetary Compromising Compromising

16. 16IAT 2006 Probability of acceptance*utility + Probability of rejection *future utility Other agents – must estimate probability Desperation Desperation Empathy Empathy Interaction History Interaction History Expected Utility

17. 17IAT 2006 Four acceptance policies 1. Expected Utility, discount aware future utility: probabilities, discount, time to close deal future utility: probabilities, discount, time to close deal accepts an offer it is as good as it can expect accepts an offer it is as good as it can expect 2. Expected Utility, discount unaware future utility same as current future utility same as current 3. Monetary wants the highest profit, won’t accept less wants the highest profit, won’t accept less 4. Compromising accepts if offer is within 10% of best accepts if offer is within 10% of best

18. 18IAT 2006 Scenario 1 – Bargain Buy Store “Bargain Buy” advertises a great price 300 people show up 5 in stock Everyone sees the advertised price, but it just isn’t possible for all to achieve it

19. 19IAT 2006 Scenario 2 – selecting a spouse Bob knows all the characteristics of the perfect wife Bob seeks out such a wife Why would the perfect woman want Bob?

20. 20IAT 2006 Scenario 3 – hiring a new PhD Universities ranked 1,2,3 Students ranked a,b,c Dilemma for second tier university offer to “a” student likely rejected delay for acceptance “b” students are gone

21. 21IAT 2006 Test Setup 40 Tasks 3 Subtasks each 3 Subtasks each Skills, 1-10 Skills, 1-10 Skill levels, 1-10 Skill levels, 1-10 Payment – (100-200%) of base cost Payment – (100-200%) of base cost 60 Agents Matched to tasks or Random Matched to tasks or Random Agent base costs (5,10,…50) based on skill level Agent base costs (5,10,…50) based on skill level 4 agent types 4 agent types 5000 tests

22. 22IAT 2006 Shows global profit ratio: profit achieved/system optimal When Discount is greater than 50, there is likely no second round – curve flattens as shows what is achieved in one round Aware and unaware similar for low discounts Monetary worse Compromise 90% is the best for low discounts

23. 23IAT 2006 Why? Monetary just too idealistic. “Bargain Buy” may not really be possible. Discount aware/unaware not much different when low discounts. Compromising 90% works well picking a spouse. Others know my worth. picking a spouse. Others know my worth. bargain buy: bargain may not be possible bargain buy: bargain may not be possible hiring a PhD. Shooting too high can backfire. hiring a PhD. Shooting too high can backfire. Others are as smart as you are! Others are as smart as you are!

24. 24IAT 2006 Tasks per round – obvious trend: higher discount → earlier acceptance

25. 25IAT 2006 Big surprise – discount unaware does not consider, but sees discount

26. 26IAT 2006 How Discount affects choices Offers (some from previous round) Possible Tasks Even though agent doesn’t compute discount, sees discount comparing choices from two rounds

27. 27IAT 2006 Monetary agents lower tasks 1 st round later complete more good deals gone → more reasonable expectations

28. 28IAT 2006 Conclusions Situation is complicated Shrinking occurs because of discount Shrinking also occurs as agents and tasks form coalitions and leave Knowing best “possible” may be misleading

29. 29IAT 2006 Questions?

30. 30IAT 2006 Coalition Selection Best Profit – pick other agents to maximize total profit. (Also maximizes local profit, because of way profits are divided) Best Fit – pick other agents to use their skills well (not pick a more qualified agent if it happens to be cheaper)

31. 31IAT 2006 How do we pair the task and coalition selection methods? Individual Individual Profit Profit Global Profit Global Profit Co-opetitive Co-opetitive Best Fit Best Fit Best Profit Coalition formation Best Fit coalition selection

32. 32IAT 2006 Global tasks completed – same pattern

33. 33IAT 2006 Accepting First Proposal

34. 34IAT 2006 Accept First Proposal Mixture of agent types, but only Aware acceptance policy. Measure what achieved when first proposal is accepted. Measure what achieved when first proposal is not accepted

35. 35IAT 2006 What does it mean? Competitive Proposal - could be accepted by Aware agent your estimation of worth matches others’ estimation. good price good price demand for skill demand for skill proposer picked that task and you over all other choices proposer picked that task and you over all other choices Likely get another proposal if first fails Not about whether or not you should accept first, but “Agents who are competitive enough to receive a strong first offer are competitive enough to do well.”