DESIGNING GAMES WITH A PURPOSE By Luis von

DESIGNING GAMES WITH A PURPOSE By Luis von Ahn and Laura Dabbish

INTRODUCING 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.

RELATED 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!

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

MAKE GWAPS MORE ENTERTAINING… HOW? Introduce challenge Introduce competition Introduce variation Introduce communication

ENSURE OUTPUT ACCURACY… HOW? Random matching Player testing Repetition Taboo outputs

OTHER DESIGN ISSUES Pre-recorded Games More than two players

HOW TO JUDGE GWAP SUCCESS? Expected Contribution = Throughput Average Lifetime Play

CONCLUSION 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?

QUESTIONS? COMMENTS? 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

TWO DIFFERENT PAYOFF MODELS 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?

THE MODEL Universe of words Words relevant to an image The game designer is trying to learn this Dictionary Sets Word size of words for a player to sample from 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

THE MODEL 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

MORE DEFINITIONS A match – first match Probability Outcome = word + location Valuation Utility of a match in a particular location function: a total ordering on outcomes

MATCH-EARLY PREFERENCES Lemma 1: Playing ↓ is not an ex-post NE. Proof: Player 2, D 2 = {w 2, w 3} s 2: play w 2, then w 3 Player 1, D 1 = {w 1, w 2} s 1: play w 1, then w 2 But, player 1 is better off playing w 2 first!

MATCH-EARLY PREFERENCES 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.

MATCH-EARLY PREFERENCES Definition Fix 6: stochastic dominance for 2 nd stage strategy opponent’s strategy s 2, stochastic dominance: s stochastically domiantes s’ P(s, 1) + … + P(s, k) >= P(s’, 1) + … + P(s’, k), for all 1 < k<d Strategy

MATCH-EARLY PREFERENCES (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

MATCH-EARLY PREFERENCES (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.

MATCH-EARLY PREFERENCES Proof for Lemma 5 and 6 (Idea: use Lemma 4) Want Pr(sampling D in A) > Pr(sampling D in B) f(wi) > f(wi+1) A (wi highest word) = C (no wi+1) and D (has wi+1) B (wi+1 highest word) 1 -to-1 mapping between C and B P(sampling D in C) > P(sampling D in B)

MATCH-EARLY PREFERENCES (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 strategy 7: stochastic dominance for complete (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 DM to DL D in DM is transformed by: Take low words in DM, continue sampling from DL until we get enough words

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

MATCH-EARLY PREFERENCES 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.

RARE-WORDS-FIRST PREFERENCES 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) Neither s 1 nor s 1’: (x, y, 0, z) stochastically dominates the other

FUTURE WORK 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?

QUESTIONS? COMMENTS? 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?