1 Who Works Together in Who Works Together in Agent Coalition Agent Coalition Formation? Formation? Vicki Allan – Utah State Vicki Allan – Utah State University University Kevin Westwood – Utah State Kevin Westwood – Utah State University University CIA 2007 CIA 2007
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1 Who Works Together in Agent Coalition Formation? Vicki Allan – Utah State University Kevin Westwood – Utah State University CIA 2007.
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Who Works Together in Agent Who Works Together in Agent Coalition Formation?Coalition Formation?
Vicki Allan – Utah State UniversityVicki Allan – Utah State University
Kevin Westwood – Utah State UniversityKevin Westwood – Utah State University
CIA 2007CIA 2007
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OverviewOverview
Tasks: Various skills and numbersTasks: Various skills and numbers
How do policies interact?How do policies interact?
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Multi-Agent CoalitionsMulti-Agent Coalitions
““A coalition is a set of agents that work together A coalition is a set of agents that work together to achieve a mutually beneficial goal” (Klusch to achieve a mutually beneficial goal” (Klusch and Shehory, 1996)and Shehory, 1996)
Reasons agent would join CoalitionReasons agent would join Coalition Cannot complete task aloneCannot complete task alone Complete task more quicklyComplete task more quickly
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Skilled Request For Proposal Skilled Request For Proposal (SRFP) Environment(SRFP) Environment
Inspired by RFP (Kraus, Shehory, and Taase 2003)Inspired by RFP (Kraus, Shehory, and Taase 2003)
Provide set of tasks T = {TProvide set of tasks T = {T11…T…Tii…T…Tnn} } Divided into multiple subtasksDivided into multiple subtasks In our model, task requires skill/levelIn our model, task requires skill/level Has a payment value V(THas a payment value V(Tii) )
Service Agents, A = {AService Agents, A = {A11…A…Akk…A…App}} Associated cost fAssociated cost fk k of providing serviceof providing service In the original model, ability do a task is In the original model, ability do a task is determined probabilistically – no two agents alike.determined probabilistically – no two agents alike. In our model, skill/levelIn our model, skill/level Higher skill is more flexible (can do any task with lower level skill)Higher skill is more flexible (can do any task with lower level skill)
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Why this model?Why this model?Enough realism to be interestingEnough realism to be interesting An agent with specific skills has realistic An agent with specific skills has realistic
properties.properties. More skilled More skilled can work on more tasks, (more can work on more tasks, (more
expensive) is also realisticexpensive) is also realistic
Not too much realism to harm analysisNot too much realism to harm analysis Can’t work on several tasks at once Can’t work on several tasks at once Can’t alter its costCan’t alter its cost
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Auctioning ProtocolAuctioning ProtocolVariation of a reverse auctionVariation of a reverse auction
Agents compete for opportunity to perform servicesAgents compete for opportunity to perform services Efficient way of matching goods to servicesEfficient way of matching goods to services
Central Manager (ease of programming)Central Manager (ease of programming)1)1) Randomly orders AgentsRandomly orders Agents
2)2) Each agent gets a turnEach agent gets a turnProposes or Accepts previous offer Proposes or Accepts previous offer
3)3) Coalitions are awarded taskCoalitions are awarded task
Multiple Rounds {0,…,rMultiple Rounds {0,…,rzz}}
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Agent Costs by LevelAgent Costs by Level
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 10
Skill Level
Co
sts
General upward trend
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05
10152025
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Agent 3 Agent 2 Agent 5
Costs
Agent Cost Profit
0
5
10
15
20
25
30
35
Agent 11 Agent 2 Agent 5
Costs
Agent Cost Profit
Agent costAgent costBase cost derived from skill and skill levelBase cost derived from skill and skill level Agent costs deviate from base cost Agent costs deviate from base cost
Agent paymentAgent paymentcost + proportional portion of net gaincost + proportional portion of net gain
Only Change in coalition
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How do I decide what to propose?
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DecisionsDecisions
If I make an offer…If I make an offer…What task should I propose doing?What task should I propose doing?What other agents should I What other agents should I recruit?recruit?
If others have made me an offer…If others have made me an offer…How do I decide whether to How do I decide whether to accept?accept?
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Coalition Calculation AlgorithmsCoalition Calculation AlgorithmsCalculating all possible coalitionsCalculating all possible coalitions Requires exponential timeRequires exponential time Not feasible in most problems in which Not feasible in most problems in which
tasks/agents are entering/leaving the systemtasks/agents are entering/leaving the system
Divide into two stepsDivide into two steps1) Task Selection 1) Task Selection
2) Other Agents Selected for Team2) Other Agents Selected for Team polynomial time algorithmspolynomial time algorithms
Why not always be greedy?Why not always be greedy?Others may not accept – your membership is Others may not accept – your membership is questionedquestioned
Individual profit may not be your goalIndividual profit may not be your goal
Co-opetitionCo-opetition Phrase coined by business professors Phrase coined by business professors
Brandenburger and Nalebuff (1996),Brandenburger and Nalebuff (1996), to to emphasize the need to consider both emphasize the need to consider both competitive and cooperative strategies.competitive and cooperative strategies.
Co-opetitive Task SelectionCo-opetitive Task Selection Select the best fit task if profit is within P% of Select the best fit task if profit is within P% of
the maximum profit availablethe maximum profit available
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What about accepting offers?What about accepting offers?Melting – same deal gone laterMelting – same deal gone later
Compare to what you could Compare to what you could achieve with a proposalachieve with a proposal
Compare best proposal with Compare best proposal with best offerbest offer
Use utility based on agent typeUse utility based on agent type
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Some amount of compromise is necessary…
We term the fraction of the total possible you demand – the compromising ratio
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Resources ShrinkResources Shrink
Even in a task rich environment the Even in a task rich environment the number of tasks an agent has to choose number of tasks an agent has to choose from shrinksfrom shrinks Tasks get takenTasks get taken
Number of agents shrinks as others are Number of agents shrinks as others are assignedassigned
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Resources Task Rich
010
2030
4050
6070
80
1 2 3 4 5 6 7 8 9 10 11 12
Rounds
Availab
le R
eso
urc
es
My Tasks
Total Tasks
Total Agents
My tasks parallel total tasks
Task Rich: 2 tasks for every agent
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Scenario 1 – Bargain BuyScenario 1 – Bargain Buy
Store “Bargain Buy” Store “Bargain Buy” advertises a great priceadvertises a great price
300 people show up300 people show up
5 in stock5 in stock
Everyone sees the Everyone sees the advertised price, but it just advertised price, but it just isn’t possible for all to isn’t possible for all to achieve itachieve it
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Scenario 2 – selecting a spouseScenario 2 – selecting a spouse
Bob knows all the Bob knows all the characteristics of the characteristics of the perfect wifeperfect wife
Bob seeks out such a Bob seeks out such a wifewife
Why would the perfect Why would the perfect woman want Bob?woman want Bob?
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Scenario 3 – hiring a new PhDScenario 3 – hiring a new PhD
Dilemma for second tier Dilemma for second tier universityuniversity
offer to “a” studentoffer to “a” student
likely rejectedlikely rejected
delay for acceptancedelay for acceptance
““b” students are goneb” students are gone
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Affect of Compromising RatioAffect of Compromising Ratio
equal distribution of each agent typeequal distribution of each agent type
Vary compromising ratio of only one type Vary compromising ratio of only one type (local profit agent)(local profit agent)
Shows profit ratio = profit achieved/ideal Shows profit ratio = profit achieved/ideal profit (given best possible task and profit (given best possible task and partners)partners)
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Local Profit Agents (Task Rich)
0
0.1
0.2
0.3
0.4
0.5
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Compromising Ratio of Local Profit
Pro
fit/
Idea
l Agent/Task .5
Agent/Task 1
Agent/Task 2
Agent/Task 3
Achieved/theoretical bestNote how profit is affect by load
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Profit only of scheduled agentsProfit only of scheduled agents
Scheduled Agent Profit (Task Rich)
0.440.46
0.480.5
0.520.54
0.560.58
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Compromising Ratio of Local Profit
Pro
fit/
Idea
l LocalProf
GlobProf
Coopet
BestFit
Only Local Profit agentschange compromising ratio
Yet others slightly increase too
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NoteNote
Demanding local profit agents reject the Demanding local profit agents reject the proposals of others.proposals of others.
They are blind about whether they belong They are blind about whether they belong in a coalition.in a coalition.
They are NOT blind to attributes of others.They are NOT blind to attributes of others.
Proposals are fairly goodProposals are fairly good
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Balanced Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
Rat
io t
o E
xpec
ted
LocalProf
GlobProf
Coopet
BestFit
For every agent type, the most likely proposer For every agent type, the most likely proposer was a Local Profit agent.was a Local Profit agent.
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Balanced Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
Rat
io t
o E
xpec
ted
LocalProf
GlobProf
Coopet
BestFit
No reciprocity: Coopetitive eager to accept Local Profit proposals, No reciprocity: Coopetitive eager to accept Local Profit proposals, but Local Profit agent doesn’t acceptbut Local Profit agent doesn’t acceptCoopetitive proposals especially wellCoopetitive proposals especially well
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Balanced Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
Rat
io t
o E
xpec
ted
LocalProf
GlobProf
Coopet
BestFit
For every agent type,For every agent type,Best Fit is a strong acceptor.Best Fit is a strong acceptor.
Perhaps because it isn’t accepted well as a proposerPerhaps because it isn’t accepted well as a proposer
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Coopetitive agents function better as Coopetitive agents function better as proposers to Local Profit agents in proposers to Local Profit agents in balanced or task rich environment.balanced or task rich environment. When they have more choices, they tend to When they have more choices, they tend to
propose coalitions local profit agents likepropose coalitions local profit agents like More tasks give a Coopetitive agent a better More tasks give a Coopetitive agent a better
sense of its own profit-potentialsense of its own profit-potential
Load balance seems to affect rolesLoad balance seems to affect roles
Coopetitive Agents look Coopetitive Agents look at fit as long as it isn’t too bad at fit as long as it isn’t too bad
Coopetitive accepts most proposals Coopetitive accepts most proposals from agents like itselffrom agents like itself
in agent rich environmentsin agent rich environments
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Do agents generally want to work with Do agents generally want to work with agents of the same type? agents of the same type? Would seem logical as agents of the same Would seem logical as agents of the same
type value the same things – utility functions type value the same things – utility functions are similar.are similar.
Coopetitive and Best Fit agents’ proposal Coopetitive and Best Fit agents’ proposal success is stable with increasing percentages success is stable with increasing percentages of their own type and negatively correlated to of their own type and negatively correlated to increasing percentages of agents of other increasing percentages of agents of other types. types.
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Look at function with increasing Look at function with increasing numbers of one other type.numbers of one other type.
Local Profit, Task Rich
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Proposers
Joiners
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What happens as we change What happens as we change relative percents of each agent?relative percents of each agent?
Interesting correlation with profit Interesting correlation with profit ratio. ratio.
Some agents do better and Some agents do better and better as their dominance better as their dominance increases. Others do worse.increases. Others do worse.
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Individual Profit Ratio (std dev 5)
0.58
0.59
0.6
0.61
0.62
0.63
0.64
0% 20% 40% 60% 80% 100%
Agent %
Ind
ivid
ual
Pro
fit
Rat
io
Individual Profit
Global Profit
Best Fit
Co-opetitive
shows relationship if all shows relationship if all equal percentequal percent
Best fit Best fit does better does better and better and better as more as more
dominant in dominant in setset
Best fit Best fit does better does better and better and better as more as more
So who joins and who proposes?So who joins and who proposes?
Agents with a wider range of acceptable Agents with a wider range of acceptable coalitions make better joiners.coalitions make better joiners.
Fussier agents make better proposers.Fussier agents make better proposers.
However, the joiner/proposer roles are However, the joiner/proposer roles are affected by the ratio of agents to work.affected by the ratio of agents to work.
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ConclusionsConclusions
Some agent types are very good in Some agent types are very good in selecting between many tasks, but not as selecting between many tasks, but not as impressive when there are only a few impressive when there are only a few choices. choices.
In any environment, choices diminish In any environment, choices diminish rapidly over time.rapidly over time.
Agents naturally fall into role of proposer Agents naturally fall into role of proposer or joiner.or joiner.
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Future WorkFuture Work
Lots of experiments are possibleLots of experiments are possible
All agents are similar in what they value. All agents are similar in what they value. What would happen if agents deliberately What would happen if agents deliberately proposed bad coalitions?proposed bad coalitions?