Designing Games with a Purpose

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Designing Games with a Purpose

• By Luis von Ahn and Laura Dabbish

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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.

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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

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Wanna Play???
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THE QUESTION IS

• How to design these games such that
• People enjoy playing them!
• They produce high quality outputs!

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Basic structure achieves several goals

• Encourage players to produce correct outputs
• Partially verify the output correctness
• Providing an enjoyable social experience

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Make GWAPS more entertaining How?

• Introduce challenge
• Introduce competition
• Introduce variation
• Introduce communication

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Ensure output accuracy How?

• Random matching
• Player testing
• Repetition
• Taboo outputs

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Other design issues

• Pre-recorded Games
• More than two players

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How to judge GWAP success?

• Expected Contribution
• Throughput ? Average Lifetime Play

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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?

• 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?

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A GAME-THEORETIC ANALYSIS OF THE ESP GAME

• By Shaili Jain and David Parkes

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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?

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

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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

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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

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Match-Early Preferences

• 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!

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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.

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Match-Early Preferences

• Definition 6 stochastic dominance for 2nd stage
  strategy
• Fix opponents strategy s2, stochastic dominance
• Strategy s stochastically domiantes s ?
• P(s, 1) P(s, k) P(s, 1) P(s, k),
  for all 1

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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

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MATCH-EARLY PREFERENCES

• Key result (Lemma 4) Given effort level e,
• D x, , D x, , f(x)
• D and D only differ by the element x and x
• P(sampling D) P(sampling D) for effort level e

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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 (k1)st highest
  frequency word next.

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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(wi1)
• A (wi highest word) C (no wi1) and D (has
  wi1)
• B (wi1 highest word)
• 1-to-1 mapping between C and B
• P(sampling D in C) P(sampling D in B)

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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.

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MATCH-EARLY PREFERENCES CONTD

• 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.
  

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MATCH-EARLY PREFERENCES CONTD

• (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

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MATCH-EARLY PREFERENCES CONTD

• (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 opponents 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.

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Match-Early Preferences

• Theorem 2 ((L, ?), (L, ?)) is a strict
  Bayesian-Nash equilibrium for the complete game.
  

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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.

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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, yz, 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?
• 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?

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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?