DESIGNING GAMES WITH A PURPOSEBy 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 preferencesWant to complete as many rounds as

possibleReflect current scoring function in ESP

gameLow effort is a Bayes-NE

Rarest-words-first preferencesWant to match on infrequent wordsHow 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 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

THE MODEL CONTINUED Two stages of the game:

1st stage: choose an effort level 2nd 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 of a match in a particular location

Outcome = word + location

Valuation function: a total ordering on outcomes

Utility

MATCH-EARLY PREFERENCES Lemma 1: Playing ↓ is not an ex-post NE.

Proof:

Player 2, D2 = {w2, w3} s2: play w2, then w3Player 1, D1 = {w1, w2} s1: play w1, then w2

But, player 1 is better off playing w2 first!

MATCH-EARLY PREFERENCES Definition 6: stochastic dominance for 2nd 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 2nd stage of the ESP game for match-early preferences.

MATCH-EARLY PREFERENCES Definition 6: stochastic dominance for 2nd

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

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 2nd 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 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 = {w1, w2, w3, w4} d = 2 D1 = {w1, w2} s1: w1, w2 s2: w2, w1

x = Pr(D2 = {w2, w3} or D2 = {w2, w4}) y = Pr(D2 = {w1, w2}) z = Pr(D2 = {w1, w3} or D2 = {w1, w4})

s1: (0, x, y+z, 0) s1’: (x, y, 0, z) Neither s1 nor s1’ 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?