OPENING QUESTIONS 1 Discuss in pairs What does this paper - PowerPoint PPT Presentation

OPENING QUESTIONS 1

Discuss in pairs • What does this paper accomplish? • What is the mechanism they propose? • What is its output? • Is it budget balanced? • Why does this mechanism not require a common prior? • How do results we’ve seen rely on this assumption? 2

Mike Ruberry & Victor Shnayder TRUTHFUL SURVEYS 3

The story 4

The story 1 0 1 5

The story 1 0 1 6

The story 1 0 1 7

Hill climbing 1 0 8

Hill climbing 1 Payoffs: 0 9

Hill climbing Q: What’s the Nash equilibrium of this game? Q: What is the expected value of the game? 10

n-player Hill climbing 1 0 11

Hill climbing (with a hill) 1 0 1 12

Hill climbing (with a hill) 1 0 1 13

Hill climbing questions: • Q: We have a hill, it’s common knowledge, and now we’re asking people to report an x— what’s the equilibrium of this game? 14

Hill climbing (with a hill) 1 0 1 15

Hill climbing questions: • Q: Now what if instead of knowing the hill, a trusted party (or Nature) provides you with a uniformly at random sample of the function. Is everyone reporting this sample a Nash equilibrium? 16

Hill climbing questions: • Q: Does this method work for any distribution? 17

Hill climbing questions: • Q: If one hill is common knowledge or uniformly at random sampled from, intuitively why would we expect play relative to this function instead of some arbitrary other one? Both are Nash equilibria. 18

The (truthful) survey 19

Implied distribution 1 0 1 20

Hill climbing 1 0 1 21

Hill climbing 1 0 1 22

Two players in the survey 1 0 1 23

The mechanism 1 1 2 3 4 5 6 7 8 9 10 0 1 24

The mechanism 1 1 2 3 4 5 6 7 8 9 10 0 1 25

Questions • How is this different from the hill climbing game we portrayed earlier? • Is the equilibrium unique? • Given the other players in your group are playing as expected, what’s your best response(s)? 26

The trusted survey mechanism 1 H 1 H 2 H 3 H 4 H 5 6 7 8 9 10 0 1 27

The trusted survey mechanism 1 H 1 H 2 H 3 H 4 H 5 6 7 8 9 10 0 1 28

Trusted survey questions • Is reporting honestly a unique equilibrium? 29

The story (again) 30

The story (again) 1 0 1 31

The story (again) 1 0 1 32

The story (again) 1 0 1 33

Discussion 34

ERRATA 35

Learning signal distribution % population with at least this signal 0 1 Signal 36

Learning signal distribution % population with at least this signal and its derivative 0 1 Signal 37

Learning signal distribution 1 Probability of receiving a signal, realized distribution compared to beliefs 0 1 Signal 38