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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
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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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