1 Combinatorial Agency with Audits - PowerPoint Presentation

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Combinatorial Agency with Audits

Raphael EidenbenzETH Zurich, Switzerland

Stefan Schmid

TU Munich, Germany

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IntroductionGrid Computing...Distributed project orchestrated by one serverServer distributes tasksAgents compute subtask

Results are sent back to serverServer aggregates result

Server / Principal

AgentsSlide3

Raphael Eidenbenz, GameNets ‘09

3Introduction: Grid Computing

What are an agent‘s incentives?Payment, fame, altruismWhy not cheat and return a random result?Will principal find out?Not reallyIndividual computation is a hidden actionPrincipal can only check whether entire project failed

Server / Principal

AgentsSlide4

Raphael Eidenbenz, GameNets ‘09

4Introduction: Grid Computing

Project failedWho did a bad job?Whom to pay?Maybe project still succeedsif only one agent exerts low effortIf more than 2/3 of the agents exert high effort...Whom to pay?

Server / Principal

AgentsSlide5

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Binary Combinatorial Agency [Babaioff, Feldman, Nisan 2006]1 principal , n selfish risk-neutral agentsHidden actions={high effort, low effort}High effort  subtask succeeds with probability δLow effort

 subtask succeeds with probability γ

Combinatorial project success functionAND: success if all subtasks succeed

OR: success if at least one subtask succeedsMAJORITY: success if more than half of the agents succeedPrincipal contracts with agentsIndividual payment pi depending on entire project‘s outcomeAssume Nash equilibrium in the created gameSlide6

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Results [Babaioff, Feldman, Nisan 2006]AND technologyPrincipal either contracts with all agents or with noneDepending on her valuation vOne transition point where optimal choice changesOR technologyPrincipal contracts with k agents,

0· k

· nWith increasing valuation

v, there are n transition points where the optimal number k increases by 1Slide7

Raphael Eidenbenz, GameNets ‘09

7Combinatorial Agency with Audits

Grid computing: server can recompute a subtaskActions are observable at a certain cost κ.Principal conducts k random audits among the l contracted agentsAgent i is audited with probability Sophisticated contractsIf audited and convicted of low effort ! p

i=0 even if project successful

Server / Principal

Agents

Slide8

Raphael Eidenbenz, GameNets ‘09

8Some Observations

The possibility of auditing can never be detrimentalNash Equilibrium if principal contracts l and audits k agentspayment piprincipal utility uagent utility uiSlide9

Raphael Eidenbenz, GameNets ‘09

9AND-Technology

Project succeeds if all agents succeedδ: agent success probability with high effortγ: agent success probability with low effort

There is one transition point

v

*for v· v*, contract no agentfor v¸

v*, contract with all agents and conduct

k* audits

Transition earlier with the leverage of audits

TheoremSlide10

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10AND-Technology (2 Agents): Principal Utility Slide11

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11AND-Technology: Benefit from Audits in %Slide12

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12OR-Technology

Project succeeds if at least one agent succeedsδ: agent success probability with high effortγ: agent success probability with low effort

There are

n

transition point v1*,v2*, ... ,v

n*

for

v ·

v

1

*

,

contract no agent

for

v

l-1

*

·

v

·

v

l

*

, contract with

l

agents, conduct

k

*

(l)

audits

for

v

¸

v

n

*

, contract with all agents and conduct

k

*

(n)

audits

Conjecture

LemmaSlide13

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13OR-Technology (2 Players): Benefit from Audits in %Slide14

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14Conclusion

If hidden actions can be revealed at a certain cost, the coordinator may improve cooperation and efficiency in a distributed systemAND technologyGeneral solution to optimally choose pi, l and k One transition point with increasing valuationOR technologyFormula for number of audits to conduct if number of contracts givenPrincipal can find optimal solution in O(n)Probably n transition pointsTransition points occur earlier with the leverage of auditsSlide15

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15OutlookTest results in the wild

Accuracy of the model?Does psychological aversion against control come into play?Non-anonymous technologiesWhich set of agents to audit?Solve problem independent of technologyAre there general algorithms to solve the principal‘s optimization problem for arbitrary technologies?What is the complexity?Total rationality unrealistic

Thank

you!Slide16

Raphael Eidenbenz, GameNets ‘09

16Bibliography[Babaioff, Feldman, Nisan 2006]:

Combinatorial Agency. EC 2006.[Babaioff, Feldman, Nisan 2006]: Mixed Strategies in Combinatorial Agency. WINE 2006.[Monderer, Tennenholtz]: k-Implementation. EC 2003.[Enzle, Anderson]: Surveillant Intentions and Intrinsic Motivation. J. Personality and Social Psychology 64, 1993.[Fehr, Klein, Schmidt]: Fairness and Contract Design. Econometrica 75, 2007.Slide17

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17Outline

Introduction: Grid ComputingCombinatorial AgencyBinary ModelResults by Babaioff, Feldman, NisanCombinatorial Agency with AuditsFirst FactsAND technologyOR technologyConclusionOutlookSlide18

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18Anonymous TechnologiesSuccess function

t depends only on number of agents exerting high efforttm: success probability if m agents exert high effortOptimal paymentsPrincipal utilityOptimal #auditsSlide19

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19AND-Technology

Project succeeds if all agents succeedSuccess function tm=δm¢γn-m

There is one transition point v

*for v

· v*, contract no agentfor v¸ v*, contract with all agents and conduct k

* audits

TheoremSlide20

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20AND-Technology: Principal Utility Slide21

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21MAJORITY TechnologyOptimal payment

wherePrincipal utility