Crowdsourcing and All-Pay Auctions Milan Vojnovic Microsoft Research Lecture series – Contemporary Economic Issues – University of East Anglia, Norwich, UK, November 10, 2014

This Talk An overview of results of a model of competition-based crowdsourcing services based on all-pay auctions Based on lecture notes Contest Theory, V., course, Mathematical Tripos Part III, University of Cambridge - forthcoming book 2

Competition-based Crowdsourcing: An Example 3 CrowdFlower

Statistics TopCoder data covering a ten-year period from early 2003 until early 2013 Taskcn data covering approximately a seven-year period from mid 2006 until early

Example Prizes: TopCoder 5

Example Participation: Tackcn A month in year players contests

Game: Standard All-Pay Contest 7

Strategic Equilibria A pure-strategy Nash equilibrium does not exist In general there exists a continuum of mixed-strategy Nash equilibrium Moulin (1986), Dasgupta (1986), Hillman and Samet (1987), Hillman and Riley (1989), Ellingsen (1991), Baye et al (1993), Baye et al (1996) There exists a unique symmetric Bayes-Nash equilibrium 8

Symmetric Bayes-Nash Equilibrium 9

Quantities of Interest 10

Quantities of Interest (cont’d) 11

Total vs. Max Individual Effort Chawla, Hartline, Sivan (2012) 12

Contests that Award Several Prizes: Examples KaggleTopCoder 13

Rank Order Allocation of Prizes 14 V. – Contest Theory (2014)

Rank Order Allocation of Prizes (cont’d) 15 V. – Contest Theory (2014)

The Limit of Many Players 16 Archak and Sudarajan (2009)

When is it Optimal to Award only the First Prize? In symmetric Bayes-Nash equilibrium both expected total effort and expected maximum individual effort achieve largest values by allocating the entire prize budget to the first prize. Holds more generally for increasing concave production cost functions Moldovanu and Sela (2001) – total effort Chawla, Hartline, Sivan (2012) – maximum individual effort 17

Importance of Symmetric Prior Beliefs 18 V. - Contest Theory (2014)

Optimal Auction Myerson (1981) 19

Optimal All-Pay Contest w.r.t. Total Effort 20

Optimal All-Pay Contest w.r.t. Max Individual Effort Chawla, Hartline, Sivan (2012) 21

Simultaneous All-Pay Contests players contests 22

Game: Simultaneous All-Pay Contests 23

Mixed-Strategy Nash Equilibrium 24 V. – Contest Theory (2014)

Quantities of Interest 25 V. – Contest Theory (2014)

Bayes Nash Equilibrium DiPalantino and V. (2009) 26

Example: Two Contests Class 1 equilibrium strategyClass 2 equilibrium strategy 27 V. – Contest Theory (2014)

Participation vs. Prize Value Taskcn 2009 – logo design tasks any rate once a monthevery fourth dayevery second day 28 model DiPalantino and V. (2009)

Conclusion A model is presented that is a game of all-pay contests An overview of known equilibrium characterization results is presented for the case of the game with incomplete information, for both single contest and a system of simultaneous contests The model provides several insights into the properties of equilibrium outcomes and suggests several hypotheses to test in practice 29

Not in this Slide Deck Characterization of mixed-strategy Nash equilibria for standard all-pay contests Consideration of non-linear production costs, e.g. players endowed with effort budgets (Colonel Blotto games) Other prize allocation mechanisms – e.g. smooth allocation of prizes according to the ratio-form contest success function (Tullock) and the special case of proportional allocation Productive efforts – sharing of a utility of production that is a function of the invested efforts Sequential effort investments 30

References Myerson, Optimal Auction Design, Mathematics of Operations Research, 1981 Moulin, Game Theory for the Social Sciences, 1986 Dasgupta, The Theory of Technological Competition, 1986 Hillman and Riley, Politically Contestable Rents and Transfers, Economics and Politics, 1989 Hillman and Samet, Dissipation of Contestable Rents by Small Number of Contestants, Public Choice, 1987 Glazer and Ma, Optimal Contests, Economic Inquiry, 1988 Ellingsen, Strategic Buyers and the Social Cost of Monopoly, American Economic Review, 1991 Baye, Kovenock, de Vries, The All-Pay Auction with Complete Information, Economic Theory

References (cont’d) Moldovanu and Sela, The Optimal Allocation of Prizes in Contests, American Economic Review, 2001 DiPalantino and V., Crowdsourcing and All-Pay Auctions, ACM EC 2009 Archak and Sundarajan, Optimal Design of Crowdsourcing Contests, Int’l Conf. on Information Systems, 2009 Archak, Money, Glory and Cheap Talk: Analyzing Strategic Behavior of Contestants in Simultaneous Crowsourcing Contests on TopCoder.com, WWW 2010 Chawla, Hartline, Sivan, Optimal Crowdsourcing Contests, SODA 2012 Chawla and Hartline, Auctions with Unique Equilibrium, ACM EC 2013 V., Contest Theory, lecture notes, University of Cambridge,