1. A Truth Serum for Sharing Rewards Arthur Carvalho Kate Larson

2. 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 2

3. Introduction Individual contributions are subjective 3 Green guy is lazy and deserves nothing 

4. Introduction Individual contributions are subjective 4 Green guy did an excellent job. 

5. Introduction Sharing rewards based on subjective opinions –Evaluations –Predictions Mechanism (sharing function) –Collect opinions –Share the reward 5

6. Outline Introduction Model Mechanism Properties Conclusion 6

7. Model Game-theoretic model A set of agents, for Reward Private information – private signals (truthful evaluations) – – is a parameter of the model 7

8. Model 8.... i 1i - 1i + 1n

9. Model Predictions – M = 5 9 12345 0.100.30.50.1

10. Model Assumptions –Self-interest –Bayesian-decision makers –Population is large Agents report evaluations and predictions –Reported evaluation: –Reported prediction: 10

11. Outline Introduction Model Mechanism Properties Conclusion 11

12. Mechanism Central, trusted entity –Elicit and aggregate opinions as well as to share the reward Formally – – : share received by agent i 12

13. Mechanism The share received by each agent has two major components –Aggregated evaluation: –Truth-telling score: – 13

14. 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 14

15. Mechanism Component 2: (truth-telling score) – is a score for agent i based on and –“Bayesian Truth Serum” (Prelec, Science 2004) – 15

16. 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 16

17. 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 17

18. Outline Introduction Model Mechanism Properties Conclusion 18

19. 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 19

20. 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. 20

21. Outline Introduction Model Mechanism Properties Conclusion 21

22. Conclusion Model for sharing rewards –Individual contributions are subjective –Subjective opinions Mechanism –Well-evaluated –Truthfully reporting opinions 22

23. A Truth Serum for Sharing Rewards Thank you! Presentation available at: www.cs.uwaterloo.ca/~a3carval 23