Post on 12-Jan-2016
description
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?