[ Game Theory ] A short primer

Transcription

1 [ Game Theory ] A short primer

2 Why game theory?

3 Why game theory?

4 Why game theory? ( Currently )

5 Why game theory?

6 Chorus - Conversational Assistant

7 Chorus - Conversational Assistant

8 Chorus - Conversational Assistant

9 Chorus - Conversational Assistant

10 Chorus - Conversational Assistant YOU:

11 Chorus - Conversational Assistant YOU:

12 Chorus - Conversational Assistant YOU:

13 Chorus - Conversational Assistant ANSWER. RESPONSE.

14 Intro to Game Theory (Just enough to impress your friends at parties)

15 What is game theory? Definition: the study of mathematical models of conflict and cooperation between intelligent rational decision-makers Translation: The study of rational motivation. - A rational player seeks the biggest reward

16 Coordination in Games Cooperative: Contracts / communication allowed - Contract means we re 100% committed to what we claim Non-cooperative: There is uncertainty in other players claimed responses

17 More Game Properties Simultaneous / Sequential: Do the players make decisions at the same time or in order? - Discrete or continuous? Length: Is the game played for 1 round, or 50? 1 minute or 10 days?

18 More Game Properties (Cont.) Perfect / imperfect information: Do the players know everything about what is going on? Symmetry: Are players rewarded the same? Zero-sum / non-zero-sum: Does one player winning mean the other loses?

19 What does a solution look like? A decision or policy. How do we get there? - Compare outcomes P1 Confess Hold Out - Pick the best one Confess Ex: Prisoner s Dilemma (5yr, 5yr) (Free, 10yr) (10yr, Free) (1yr, 1yr) P2 Hold out

20 What does a solution look like? A decision or policy. How do we get there? - Compare outcomes P1 Confess Hold Out - Pick the best one Confess Ex: Prisoner s Dilemma - w/ a dominant policy (5yr, 5yr) (Free, 10yr) P2 Hold out (10yr, Free) (Free, Free)

21 Nash Equilibria Non-cooperative games - Recall: Players cannot make contracts or commitments to play a certain way Stable state: even knowing other players strategies, everyone sticks with their choice

22 Nash Equilibria: Example Stag Hunt Problem: N hunters, N hares, 1 stag Everyone is needed to shoot the stag - Large reward Anyone can shoot a hare alone - Smaller reward

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26 Vote here:

27 Nash Equilibria: Example Stag Hunt Problem - N hunters, N hares, 1 stag Stag-All P1 Stag Hare (200lb, 200lb) (1lb, 0lb) (1lb, 0lb) (1lb, 1lb) P-Rest Hare-Some

28 Nash Equilibria: Example Stag Hunt Problem - N hunters, N hares, 1 stag Why is this an equilibrium solution?

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31 Nash Equilibria: The WRONG way

32 Nash Equilibria: The WRONG way

33 Nash Equilibria: The WRONG way

34 Nash Equilibria: The WRONG way

35 Nash Equilibria: The WRONG way

36 Nash Equilibria: The WRONG way

37 Nash Equilibria: The WRONG way

38 What s wrong with this Nash Equilibria?

39 Understanding the Crowd Explains how rewards affect workers motivation Misaligned motivation = workers misbehave - Common mistakes: -- E.g.: reward for speed, not accuracy -- no reward for better work, do the minimum -- reward for agreement, not when correct

40 Understanding the Crowd The study of rational motivation Where do the values come from? - Payment, psych, comprehension of rules People aren t always rational! - Fairness (E.g., our prisoner example)

41 Intro to Mechanism Design (Just enough to confuse your friends at parties)

42 Changing the Rules of the Game The other side of game theory: writing the rules Influence behavior by setting up the game

43 Applications for Crowd Systems Adjust rewards to elicit responses Build in cooperative and competitive behavior - Coordinate to solve problems, or be the best Make the rules clear to workers!

44 Applications for Crowd Systems Adjust rewards to elicit responses Build in cooperative and competitive behavior - Coordinate to solve problems, or be the best >> Make the rules clear to workers! <<

45 Application: Real-Time Manipulation

46 Reputation Systems Honest P1 Honest Cheat (R + R, R +R ) (R, R +R ) Later Later Later Cheat P2 (R +R, R ) Later (R,R )

47 Reputation Systems (in Collective Intelligence systems) Honest P1 Honest Cheat (R + R, R +R ) (R, R +R ) (R (R + R, R +R ) Later Later Later Cheat P2 +R, R ) Later Later Later

48 Reputation Systems (in Collective Intelligence systems) Honest P1 Honest Cheat (R + R, R +R ) (R, R +R ) Later Later Cheat P2 (R +R, R ) Later Later (RN + RL, RN + RL) (RN, RN) (RN, RN) (RN + RL, (RN, RN) RN + RL) (RN, RN) (RN, RN) (RN + RL, RN + RL) (RN, RN)

49 Reputation Systems (in Collective Intelligence systems) Honest P1 Honest Cheat (R + R, R +R ) (R, R +R ) Later Later Cheat P2 (R +R, R ) Later Later

50 Reputation Systems (in Collective Intelligence systems) Honest P1 Honest Cheat (R + R, R +R ) (R, R +R ) Later Later Cheat P2 (R +R, R ) Later Later

51 Uncertainty of Player Strategies

52 Limitations of Collective Intelligence Mechanisms

53 Example: ESP Game

54 Example: ESP Game Sony MDRAS40EX Sport Over-the-Ear Headphones!

55 Example: ESP Game Headphones...

56 Example: ESP Game Sony MDRAS40EX Sport Over-the-Ear Headphones!

57 Example: ESP Game Headphones...

58 Example: ESP Game Headphones...

59 Expert Example: ESP Game? ^

60 Plenty of Topics We Didn t Cover! Multiple Equilibria Pare to s e r u t c u r t s e k p i Kr Dom Optim inate ality m u i r b quili Ba E h s a N n yesia d Str ateg ies Incentive Compatibility

61 [ paper questions? ]