Heuristics for Dealing with a Shrinking Pie in Agent Coalition Formation

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. 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 • Complete task more quickly

3. Skilled Request For Proposal (SRFP) Environment Inspired by RFP (Kraus, Shehory, and Taase 2003) • Provide set of tasks T = {T1…Ti…Tn} • Divided into multiple subtasks • requiring skill/level • Has a payment value V(Ti) • Service Agents, A = {A1…Ak…Ap} • Associated cost fk • skill/level • Manager Agent • Distributes tasks to service agents

4. Auctioning Protocol • Variation of a reverse auction • Agents compete for opportunity to perform 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,…,rz} • Our version is cyclic – so agents later in list are not disadvantaged

5. Cyclic Auction

6. 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. 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. Coalition Calculation Algorithms • Calculating all possible coalitions • 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 • Divide into two steps 1) Task Selection 2) Other Agents Selected for Team • polynomial time algorithms

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

10. Two Step Coalition Calculation • Task Selection • Individual Profit • 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 • Co-opetitive

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

12. 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. • Co-opetitive Task Selection • Select the best fit task if profit is within P% of the maximum profit available

13. Costs by Level

14. 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 • Compare best proposal with best offer • Use utility based on agent type

15. 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 unaware • Monetary • Compromising

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

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

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

22. 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. 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. • bargain buy: bargain may not be possible • hiring a PhD. Shooting too high can backfire. • Others are as smart as you are!

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

25. Big surprise – discount unawaredoes not consider, but sees discount

26. 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. Monetary agents • lower tasks 1st round • later complete more • good deals gone → more reasonable expectations

28. 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. Questions?

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

32. Global tasks completed – same pattern

33. Accepting First Proposal

34. 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. What does it mean? • Competitive Proposal - could be accepted by Aware agent • your estimation of worth matches others’ estimation. • good price • demand for skill • 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.”