A Truth Serum for Sharing Rewards

Arthur Carvalho

Kate Larson

Introduction

• A group has accomplished a joint task– Reward

• A crucial question in MAS literature– How to share it?

• Shapley value– Marginal contribution – Individual contributions are objectively defined

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Introduction• Individual contributions are subjective

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Green guy is lazy and deserves nothing

Introduction

• Individual contributions are subjective

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Green guy did an excellent

job.

Introduction

• Sharing rewards based on subjective opinions– Evaluations– Predictions

• Mechanism (sharing function)– Collect opinions– Share the reward

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Outline

• Introduction

• Model

• Mechanism

• Properties

• Conclusion

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Model

• Game-theoretic model

• A set of agents , for

• Reward

• Private information– private signals (truthful evaluations)– – is a parameter of the model

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Model

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....

i

1 3 3 5

5M

....1 i - 1 i + 1 n

Model

• Predictions–

M = 5

9

1 2 3 4 5

0.1 0 0.3 0.5 0.1

Model

• Assumptions– Self-interest– Bayesian-decision makers– Population is large

• Agents report evaluations and predictions– Reported evaluation:– Reported prediction:

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Outline

• Introduction

• Model

• Mechanism

• Properties

• Conclusion

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Mechanism

• Central, trusted entity– Elicit and aggregate opinions as well as to

share the reward

• Formally– – : share received by agent i

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Mechanism

• The share received by each agent has two major components– Aggregated evaluation: – Truth-telling score: –

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Mechanism

• Component 1: – Scale the evaluations reported by each agent

so that they sum up to V • Scaled evaluation given by agent j to agent i

– Aggregating scaled evaluations

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Mechanism

• Component 2: (truth-telling score)– is a score for agent i based on and

– “Bayesian Truth Serum” (Prelec, Science 2004)

–

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Mechanism

• BTS– Multiple-choice questions

• “What is the evaluation deserved by agent j?”

– Answers and predictions• Evaluations and predictions

– Scores based on the surprisingly common criterion

• An answer receives a high score to the extent that it is more common than collectively predicted

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Mechanism

• BTS– False-consensus effect– Collective truth-telling is a strict Bayes-Nash

Equilibrium– Given that the others are telling the truth, the

best (in an expected sense) that an agent can do is also to tell the truth

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Outline

• Introduction

• Model

• Mechanism

• Properties

• Conclusion

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Properties

• Incentive-Compatible– Collective truth-telling is a Bayes-Nash

equilibrium

• Budget-Balanced– It allocates the entire reward back to the

agents

• Tractable– It computes the shares in polynomial time

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Properties

• Sufficient conditions – Individually rational

• All shares are greater than or equal to 0

– Fair• If an agent unanimously receives better

evaluations than a peer, then that agent should also receive a greater share of the joint reward than its peer.

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Outline

• Introduction

• Model

• Mechanism

• Properties

• Conclusion

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Conclusion

• Model for sharing rewards– Individual contributions are subjective– Subjective opinions

• Mechanism– Well-evaluated– Truthfully reporting opinions

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A Truth Serum for Sharing Rewards

Thank you!

Presentation available at:

www.cs.uwaterloo.ca/~a3carval

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