Who Works Together in Agent Coalition Formation?

Vicki Allan – Utah State University Kevin Westwood – Utah State University CIA 2007 Who Works Together in Agent Coalition Formation?

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

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

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)

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

Auctioning Protocol • Variation of a reverse auction • 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}

Agent Costs by Level General upwardtrend

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

How do I decide what to propose?

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?

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

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

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

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

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

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

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

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

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

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

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?

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

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)

Note how profit is affect by load Achieved/theoretical best

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

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

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

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

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

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.

Agent rich: 3 agents/task Coopetitive accepts most proposals from agents like itself in agent rich environments

Do agents generally want to work with agents of the same type? • Would seem logical as agents of the same type value the same things – utility functions are similar. • Coopetitive and Best Fit agents’ proposal success is stable with increasing percentages of their own type and negatively correlated to increasing percentages of agents of other types.

Look at function with increasing numbers of one other type.

What happens as we change relative percents of each agent? • Interesting correlation with profit ratio. • Some agents do better and better as their dominance increases. Others do worse.

Best fit does better and better as more dominant in set Best fit does better and better as more dominant in set shows relationship if all equal percent Local Profit does better when it isn’t dominant

So who joins and who proposes? • Agents with a wider range of acceptable coalitions make better joiners. • Fussier agents make better proposers. • However, the joiner/proposer roles are affected by the ratio of agents to work.

Conclusions • Some agent types are very good in selecting between many tasks, but not as impressive when there are only a few choices. • In any environment, choices diminish rapidly over time. • Agents naturally fall into role of proposer or joiner.

Future Work • Lots of experiments are possible • All agents are similar in what they value. What would happen if agents deliberately proposed bad coalitions?

Who Works Together in Agent Coalition Formation?