Transcript Designing Games with a Purpose

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
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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
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Encourage players to produce correct outputs
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Partially verify the output correctness
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Providing an enjoyable social experience
MAKE GWAPS MORE ENTERTAINING…
HOW?
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Introduce challenge
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Introduce competition
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Introduce variation
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Introduce communication
ENSURE OUTPUT ACCURACY… HOW?
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Random matching
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Player testing
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Repetition
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Taboo outputs
OTHER DESIGN ISSUES

Pre-recorded Games
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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?
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QUESTIONS? COMMENTS?


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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

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
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 Effort

level
Frequent words correspond to low effort
THE MODEL CONTINUED
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Two stages of the game:
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1st stage: choose an effort level
2nd stage: choose a permutation on sampled
dictionary
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Only consider the strategies involving playing all
words in the dictionary
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Only consider consistent strategies:

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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
outcomes
 Utility
of a match in a particular location
function: a total ordering on
MATCH-EARLY PREFERENCES
 Lemma
1: Playing ↓ is not an ex-post NE.
Proof:
Player 2, D2 = {w2, w3}
Player 1, D1 = {w1, w2}
s2: play w2, then w3
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:
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
level e
D’) > P(sampling D) for effort
MATCH-EARLY PREFERENCES

(Lemma 5, 6) Playing ↓ is a strict best response to an
opponent who plays ↓
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Proof by induction
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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 BayesianNash 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


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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}
s 1: w 1, w 2 s 2: w 2, w 1

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
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FUTURE WORK

Sufficient and necessary conditions for playing ↑
with high effort being a Bayesian-Nash
equilibrium?
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Incentive structure for high effort? - To extend
the labels for an image
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Other types of scoring functions?
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Rules of Taboo words?
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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?