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Crowdsourcing and All-Pay Auctions Milan Vojnović Microsoft Research Joint work with Dominic DiPalantino UC Berkeley, July 13, 2009

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Examples of Crowdsourcing Crowdsourcing = soliciting solutions via open calls to large-scale communities – Coined in a Wired article (06) Taskcn – 530,000 solutions posted for 3,100 tasks Innocentive – Over $3 million awarded Odesk – Over $43 million brokered Amazons Mechanical Turk – Over 23,000 tasks 2

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Examples of Crowdsourcing (contd) Yahoo! Answers – Lunched Dec 05 – 60M users / 65M answers (as of Dec 06) Live QnA – Lunched Aug 06 / closed May 09 – 3M questions / 750M answers Wikipedia 3

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Incentives for Contribution Incentives – Monetary $$$ – Non-momentary Social gratification and publicity Reputation points Certificates and levels Incentives for both participation and quality 4

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Incentives for Contribution (contd) Ex. Taskcn 5 Reward range (RMB) Contest duration Number of submissions Number of registrants Number of views 100 RMB $15 (July 09)

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Incentives for Contribution (contd) Ex. Yahoo! Answers 6 Points Levels Source: http://en.wikipedia.org/wiki/Yahoo!_Answers

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Questions of Interest Understanding of the incentive schemes – How do contributions relate to offered rewards? Design of contests – How do we best design contests? – How do we set rewards? – How do we best suggest contests to players and rewards to contest providers? 7

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Strategic User Behavior From empirical analysis of Taskcn by Yang et al (ACM EC 08) – (i) users respond to incentives, (ii) users learn better strategies – Suggests a game-theoretic analysis 8 User Strategies on Taskcn.com

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Outline Model of Competing Contests Equilibrium Analysis – Player-Specific Skills – Contest-Specific Skills Design of Contests Experimental Validation Conclusion 9

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Single Contest Competition 10 c1c1 c2c2 c3c3 c4c4 R c i = cost per unit effort or quality produced contest offering reward R players

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Single Contest Competition (contd) 11 Outcome -c1b1 -c1b1 R - c 2 b 2 -c 3 b 3 -c 4 b 4 c1c1 c2c2 c3c3 c4c4 b1b1 b2b2 b3b3 b4b4 R

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All-Pay Auction 12 Outcome -b1 -b1 v 2 - b 2 -b 3 -b 4 v1v1 v2v2 v3v3 v4v4 b1b1 b2b2 b3b3 b4b4 Everyone pays their bid

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Competing Contests 13 R1R1 R2R2 RJRJ... RjRj contestsusers 1 2 u N...

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Incomplete Information Assumption Each user u knows = total number of users = his own skill = skills are randomly drawn from F 14 We assume F is an atomless distribution with finite support [0,m]

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Assumptions on User Skill 1) Player-specific skill random i.i.d. across u (ex. contests require similar skills or skill determined by players opportunity cost) 2) Contest-specific skill random i.i.d. across u and j (ex. contests require diverse skills) 15

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Bayes-Nash Equilibrium Mixed strategy Equilibrium Select contest of highest expected profit where expectation with respect to beliefs about other user skills = prob. of selecting a contest of class j = bid 16 Contest class = set of contests that offer same reward

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User Expected Profit Expected profit for a contest of class j = prob. of selecting a contest of class j = distribution of user skill conditional on having selected contest class j 17

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Outline Model of Competing Contests Equilibrium Analysis – Player-Specific Skills – Contest-Specific Skills Design of Contests Experimental Validation Conclusion 18

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Equilibrium Contest Selection m 0 1 2 3 4 5 1 v2v2 v3v3 v4v4 2 3 4 skill levels contest classes 19

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Threshold Reward Only K highest-reward contest classes selected with strictly positive probability 20 = number of contests of class k

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Partitioning over Skill Levels User of skill v is of skill level l if where 21

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Contest Selection User of skill l, i.e. with skill selects a contest of class j with probability 22

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Participation Rates A contest of class j selected with probability 23 Prior-free – independent of the distribution F

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Large-System Limit For positive constants where K is a finite number of contest classes 24

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Skill Levels for Large System User of skill v is of skill level l if where 25

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Participation Rates for Large System Expected number of participants for a contest of class j 26 Prior-free – independent of the distribution F

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Contest Selection in Large System User of skill l, i.e. with skill selects a contest of class j with probability m 0 1 2 3 4 5 1 2 3 4 1/3 27 For large systems, what matters is which contests are selected for given skill

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Proof Hint for Player-Specific Skills 28 Key property – equilibrium expected payoffs as showed v m0v1v1 v2v2 v3v3 g 1 (v) g 2 (v) g 3 (v) g 4 (v)

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Outline Model of Competing Contests Equilibrium Analysis – Player-Specific Skills – Contest-Specific Skills Design of Contests Experimental Validation Conclusion 29

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Contest-specific Skills Results established only for large-system limit Same equilibrium relationship between participation and rewards as for player- specific skills 30

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Proof Hints Limit expected payoff – For each Balancing – Whenever Asserted relations for follow from above 31

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Outline Model of Competing Contests Equilibrium Analysis – Player-Specific Skills – Contest-Specific Skills Design of Contests Experimental Validation Conclusion 32

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System Optimum Rewards 33 maximise over subject to SYSTEM Set the rewards so as to optimize system welfare

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Example 1: zero costs (non monetary rewards) 34 Assume are increasing strictly concave functions. Under player-specific skills, system optimum rewards: for any c > 0 where is unique solution of Rewards unique up to a multiplicative constant – only relative setting of rewards matters

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Example 1 (contd) 35 For large systems Assume are increasing strictly concave functions. Under player-specific skills, system optimum rewards: for any c > 0 where is unique solution of

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Example 2: optimum effort 36 Consider SYSTEM with exerted effort { cost of giving R j (budget constraint) { prob. contest attended { Utility: Cost:

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Outline Model of Competing Contests Equilibrium Analysis – Player-Specific Skills – Contest-Specific Skills Design of Contests Experimental Validation Conclusion 37

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Taskcn Analysis of rewards and participation across tasks as observed on Taskcn – Tasks of diverse categories: graphics, characters, miscellaneous, super challenge – We considered tasks posted in 2008 38

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Taskcn (contd) 39 reward number of views number of registrants number of submissions

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Submissions vs. Reward Diminishing increase of submissions with reward 40 GraphicsCharactersMiscellaneous linear regression

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Submissions vs. Reward for Subcategory Logos Conditioning on the more experienced users, the better the prediction by the model 41 any rate once a monthevery fourth dayevery second day Conditional on the rate at which users submit solutions model

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Same for the Subcategory 2-D 42 any rate once a monthevery fourth dayevery second day model

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Conclusion Crowdsourcing as a system of competing contests Equilibrium analysis of competing contests – Explicit relationship between rewards and participations Prior-free – Diminishing increase of participation with reward Suggested by the model and data Framework for design of crowdsourcing / contests Base results for strategic modelling – Ex. strategic contest providers 43

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More Information Paper: ACM EC 09 Version with proofs: MSR-TR-2009-09 – http://research.microsoft.com/apps/pubs/default. aspx?id=79370 http://research.microsoft.com/apps/pubs/default. aspx?id=79370 44

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