D ESIGNING G AMES WITH A P URPOSE By Luis von Ahn and Laura Dabbish

I NTRODUCING GAMES WITH A PURPOSE Many tasks are trivial for humans, but very challenging for computer programs People spend a lot of time playing games Idea: Computation + Game Play People playing GWAPs perform basic tasks that cannot be automated. While being entertained, people produce useful data as a side effect.

R ELATED WORK Recognized utility of human cycles and motivational power of gamelike interfaces Open source software development Wikipedia Open Mind Initiative Interactive machine learning Incorporating game-like interfaces

Wanna Play???

THE QUESTION IS … How to design these games such that… …People enjoy playing them! …They produce high quality outputs!

B ASIC STRUCTURE ACHIEVES SEVERAL GOALS Encourage players to produce correct outputs Partially verify the output correctness Providing an enjoyable social experience

M AKE GWAPS MORE ENTERTAINING … H OW ? Introduce challenge Introduce competition Introduce variation Introduce communication

E NSURE OUTPUT ACCURACY … H OW ? Random matching Player testing Repetition Taboo outputs

O THER DESIGN ISSUES Pre-recorded Games More than two players

H OW TO JUDGE GWAP SUCCESS ? Expected Contribution = Throughput  Average Lifetime Play

C ONCLUSION AND FUTURE WORK First general method for integrating computation and game play! (Everyone could/should contribute to AI progress!) Other GWAP game types? How do problems fit into GWAP templates? How to motivate not only accuracy but creativity and diversity? What kinds of problems fall outside of GWAP approach?

Q UESTIONS ? C OMMENTS ? What do you think of this approach in general? Which problems are suitable for this approach? What do you love about these games? What are the inefficiencies in these games? How do we make these games more enjoyable and more efficient in producing correct results?

A GAME-THEORETIC ANALYSIS OF THE ESP GAME By Shaili Jain and David Parkes

T WO D IFFERENT P AYOFF M ODELS Match-early preferences Want to complete as many rounds as possible Reflect current scoring function in ESP game Low effort is a Bayes-NE Rarest-words-first preferences Want to match on infrequent words How can we accomplish this?

How can we assign scores to outcomes to promote desired behaviours? ?

T HE M ODEL Universe of words Words relevant to an image The game designer is trying to learn this Dictionary size Sets of words for a player to sample from Word frequency Probability of word being chosen if many people were asked to state a word relating to this image Order words according to decreasing frequency Effort level Frequent words correspond to low effort

T HE M ODEL CONTINUED Two stages of the game: 1 st stage: choose an effort level 2 nd stage: choose a permutation on sampled dictionary Only consider the strategies involving playing all words in the dictionary Only consider consistent strategies: Specify a total ordering on elements and applying that ordering to the realized dictionary Complete strategy = effort level + word ordering

M ORE D EFINITIONS A match – first match Probability of a match in a particular location Outcome = word + location Valuation function: a total ordering on outcomes Utility

M ATCH -E ARLY P REFERENCES Lemma 1: Playing ↓ is not an ex-post NE. Proof: Player 2, D2 = {w2, w3}s2: play w2, then w3 Player 1, D1 = {w1, w2}s1: play w1, then w2 But, player 1 is better off playing w2 first!

M ATCH -E ARLY P REFERENCES Definition 6: stochastic dominance for 2 nd stage strategy (Lemma 2, 3) Stochastic dominance is sufficient and necessary for utility maximization. (Lemma 5, 6) Playing ↓ is a strict best response to an opponent who plays ↓ Theorem 1: (↓, ↓) is a strict Bayesian-Nash equilibrium of the 2 nd stage of the ESP game for match-early preferences.

M ATCH -E ARLY P REFERENCES Definition 6: stochastic dominance for 2 nd stage strategy Fix opponent’s strategy s2, stochastic dominance: Strategy s stochastically domiantes s’  P(s, 1) + … + P(s, k) >= P(s’, 1) + … + P(s’, k), for all 1 < k < d

M ATCH -E ARLY P REFERENCES (Lemma 2, 3) Stochastic dominance is sufficient and necessary for utility maximization. Proof by induction Inductive step uses inductive hypothesis and stochastic dominance to establish result

MATCH-EARLY PREFERENCES Key result (Lemma 4) Given effort level e, D = {x, …}, D’ = {x’, …}, f(x) < f(x’) D and D’ only differ by the element x and x’ P(sampling D’) > P(sampling D) for effort level e

M ATCH -E ARLY P REFERENCES (Lemma 5, 6) Playing ↓ is a strict best response to an opponent who plays ↓ Proof by induction Base case (Lemma 5): the probability of a first match in location 1 is strictly maximized when player 1 plays her most frequent word first. Inductive step (Lemma 6): Suppose player 2 plays ↓. Given that player 1 played her k highest frequency words first, the probability of a first match in locations 1 to k is strictly maximized when player 1 players her (k+1)st highest frequency word next.

M ATCH -E ARLY P REFERENCES Proof for Lemma 5 and 6 (Idea: use Lemma 4) Want Pr(sampling D in A) > Pr(sampling D in B) f(w i ) > f(w i+1 ) A (w i highest word) = C (no w i+1 ) and D (has w i+1 ) B (w i+1 highest word) 1-to-1 mapping between C and B P(sampling D in C) > P(sampling D in B)

M ATCH -E ARLY P REFERENCES (Lemma 5, 6) Playing ↓ is a strict best response to an opponent who plays ↓ Theorem 1: (↓, ↓) is a strict Bayesian-Nash equilibrium of the 2 nd stage of the ESP game for match-early preferences.

MATCH-EARLY PREFERENCES CONT’D Definition 7: stochastic dominance for complete strategy (Lemma 7, 8) Stochastic dominance is sufficient and necessary for utility maximization (Lemma 12) Playing L stochastically dominates playing M. Theorem 2: ((L, ↓), (L, ↓)) is a strict Bayesian- Nash equilibrium for the complete game.

MATCH-EARLY PREFERENCES CONT’D (Lemma 12) Playing L stochastically dominates playing M Randomized mapping from D M to D L  D in D M is transformed by: Take low words in D M, continue sampling from D L until we get enough words

MATCH-EARLY PREFERENCES CONT’D (Lemma 12) Playing L stochastically dominates playing M Lemma 10: Each dictionary in D M is mapped to a dictionary in D L which is at least as likely to match against the opponent’s dictionary Lemma 11: The probability of sampling D from D L is the same as the probability of getting D by sampling D’ from D M and then transform D’ into D under the randomized mapping.

M ATCH -E ARLY P REFERENCES Theorem 2: ((L, ↓), (L, ↓)) is a strict Bayesian-Nash equilibrium for the complete game.

RARE-WORDS-FIRST PREFERENCES Definition 8: Rare-words first preferences (Lemma 13, 14) Stochastic dominance is still sufficient and necessary for utility maximization (Lemma 15) Suppose player 2 is playing ↓. For any dictionary, no consistent strategy of player 1 stochastically dominates all other consistent strategies. (Lemma 16) Suppose player 2 is playing ↑. For any dictionary, no consistent strategy of player 1 stochastically dominates all other consistent strategies.

R ARE -W ORDS -F IRST P REFERENCES Idea for proving Lemma 15 (and 16) U = {w 1, w 2, w 3, w 4 }d = 2 D 1 = {w 1, w 2 } s 1 : w 1, w 2 s 2 : w 2, w 1 x = Pr(D 2 = {w 2, w 3 } or D 2 = {w 2, w 4 }) y = Pr(D 2 = {w 1, w 2 }) z = Pr(D 2 = {w 1, w 3 } or D 2 = {w 1, w 4 }) s 1 : (0, x, y+z, 0)s 1 ’: (x, y, 0, z) Neither s 1 nor s 1 ’ stochastically dominates the other

F UTURE W ORK Sufficient and necessary conditions for playing ↑ with high effort being a Bayesian-Nash equilibrium? Incentive structure for high effort? - To extend the labels for an image Other types of scoring functions? Rules of Taboo words? Consider entire sequence of words suggested rather than only focusing on the matched word?

Q UESTIONS ? C OMMENTS ? What do you think of the model? Does everything in the model make sense? Can you suggest improvements to the model? What incentive structure could possibly lead to high effort? Would the use of Taboo words be useful for this purpose?