Vicki Allan 2008

1. Vicki Allan2008 Looking for students for two NSF funded grants

2. Funded Projects 2008-2011 • CPATH – Computing Concepts • Educational • Curriculum Development • Looking for help in the creation of a new introductory course – USU 1360 • COAL – Coalition Formation • Research in Multi-agent systems

3. CPATH • There is a need for more computer science graduates. • There is a lack of exposure to computer science. • Introductory classes are unattractive to many. • Women are not being attracted to computer science despite forces which should attract women – good pay, flexible hours, interesting problems.

4. Create a library of multi-function Interactive Learning Modules (ILMs) • Showcase computational thinking • De-emphasize programming

5. The balls on the left are to be exchanged with the balls on the right by a sequence of moves. Any ball can move into adjacent empty slot. Any ball can jump over a single neighbor to an empty slot. Complexity Algorithm design Abstraction – general purpose rules

6. Need Students • Good programmers to program interactives. Using Java or flash. • Ideas for how to revitalize undergraduate education • TA for next semester to help with USU 1360

7. COAL Second project involves multi-agent systems

8. If two heads are better than one, how about 2000?

9. Monetary Auction • Object for sale: a dollar bill • Rules • Highest bidder gets it • Highest bidder and the second highest bidder pay their bids • New bids must beat old bids by 5¢. • Bidding starts at 5¢. • What would your strategy be?

10. Give Away • Bag of candy to give away • If everyone in the class says “share”, the candy is split equally. • If only one person says “I want it”, he/she gets the candy to himself. • If more than one person says “I want it”, I keep the candy.

11. The point? • You are competing against others who are as smart as you are. • If there is a “weakness” that someone can exploit to their benefit, someone will find it. • You don’t have a central planner who is making the decision. • Decisions happen in parallel.

12. Cooperation • Hiring a new professor this year. • Committee of three people to make decision • Have narrowed it down to four. • Each person has a different ranking for the candidates. • How do we make a decision?

13. Binary Protocol One voter ranks c > d > b > a One voter ranks a > c > d > b One voter ranks b > a > c > d winner (c, (winner (a, winner(b,d)))=a winner (d, (winner (b, winner(c,a)))=d winner (d, (winner (c, winner(a,b)))=c winner (b, (winner (d, winner(c,a)))=b surprisingly, order of pairing yields different winner!

14. If you only wanted to find the first place winner, could you count the number of times a person was ranked first? • a > b > c >d • a > b > c >d • a > b > c >d • a > b > c >d • b > c > d> a • b > c > d> a • b > c > d> a a=19, b=24, c=17, d=10 Just counting first ranks isn’t enough.

15. Borda protocol assigns an alternative |O| points for the highest preference, |O|-1 points for the second, and so on • The counts are summed across the voters and the alternative with the highest count becomes the social choice 15

16. reasonable???

17. Borda Paradox • a > b > c >d • b > c > d >a • c > d > a > b • a > b > c > d • b > c > d> a • c >d > a >b • a <b <c < d a=18, b=19, c=20, d=13 Is this a good way? Clear loser

18. Borda Paradox – remove loser (d), winner changes • a > b > c • b > c >a • c > a > b • a > b > c • b > c > a • c > a >b • a <b <c a=15,b=14, c=13 • a > b > c >d • b > c > d >a • c > d > a > b • a > b > c > d • b > c > d> a • c >d > a >b • a <b <c < d a=18, b=19, c=20, d=13 When loser is removed, second worst becomes winner!

19. Conclusion • Finding the correct mechanism is not easy

20. Vicki Allan – Utah State University Kevin Westwood – Utah State University Presented September 2007, Netherlands (Work also presented in Hong Kong, Finland, Australia, California) CIA 2007 Who Works Together in Agent Coalition Formation?

21. Overview • Tasks: Various skills and numbers • Agents form coalitions • Agent types - Differing policies • How do policies interact?

22. 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

23. 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 • In our model, task requires skill/level • Has a payment value V(Ti) • Service Agents, A = {A1…Ak…Ap} • Associated cost fk of providing service • In the original model, ability do a task is determined probabilistically – no two agents alike. • In our model, skill/level • Higher skill is more flexible (can do any task with lower level skill)

24. Why this model? • Enough realism to be interesting • An agent with specific skills has realistic properties. • More skilled can work on more tasks, (more expensive) is also realistic • Not too much realism to harm analysis • Can’t work on several tasks at once • Can’t alter its cost

25. Auctioning Protocol • Variation of a reverse auction • One “buyer” lots of sellers • Agents compete for opportunity to perform services • Efficient way of matching goods to services • Central Manager (ease of programming) 1) Randomly orders Agents 2) Each agent gets a turn • Proposes or Accepts previous offer 3) Coalitions are awarded task • Multiple Rounds {0,…,rz}

26. Agent Costs by Level General upwardtrend

27. Agent cost • Base cost derived from skill and skill level • Agent costs deviate from base cost • Agent payment • cost + proportional portion of net gain Only Change in coalition

28. How do I decide what to propose?

29. The setup • Tasks to choose from include skills needed and total pay • List of agents – (skill, cost) • Which task will you choose to do?

30. Decisions If I make an offer… • What task should I propose doing? • What other agents should I recruit? If others have made me an offer… • How do I decide whether to accept?

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

32. Task Selection- 4 Agent Types • 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

33. Task Selection- 4 Agent Types • 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

34. Task Selection- 4 Agent Types • 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

35. 4th type: 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

36. What about accepting offers? Melting – same deal gone later • Compare to what you could achieve with a proposal • Compare best proposal with best offer • Use utility based on agent type

37. Some amount of compromise is necessary… We term the fraction of the total possible you demand – the compromising ratio

38. Resources Shrink • Even in a task rich environment the number of tasks an agent has to choose from shrinks • Tasks get taken • Number of agents shrinks as others are assigned

39. Task Rich: 2 tasks for every agent My tasks parallel total tasks

40. 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

41. 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?

42. 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

43. Affect of Compromising Ratio • equal distribution of each agent type • Vary compromising ratio of only one type (local profit agent) • Shows profit ratio = profit achieved/ideal profit (given best possible task and partners)

44. Note how profit is affect by load Achieved/theoretical best

45. Profit only of scheduled agents Only Local Profit agents change compromising ratio Yet others slightly increase too

46. Note • Demanding local profit agents reject the proposals of others. • They are blind about whether they belong in a coalition. • They are NOT blind to attributes of others. • Proposals are fairly good

47. For every agent type, the most likely proposer was a Local Profit agent.

48. No reciprocity: Coopetitive eager to accept Local Profit proposals, but Local Profit agent doesn’t accept Coopetitive proposals especially well

49. For every agent type, Best Fit is a strong acceptor. Perhaps because it isn’t accepted well as a proposer

50. Load balance seems to affect roles Coopetitive agents function better as proposers to Local Profit agents in balanced or task rich environment. • When they have more choices, they tend to propose coalitions local profit agents like • More tasks give a Coopetitive agent a better sense of its own profit-potential Coopetitive Agents look at fit as long as it isn’t too bad compared to profit.