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Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation [Robin Hanson, 2002] Roi Meron 07-Nov-12Seminar in Information Markets, TAU1

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Outline Scoring Rules Market Scoring Rules Logarithmic Market Scoring Rule(LMSR) Distribution == Cost function Combinatorial Markets 07-Nov-12Seminar in Information Markets, TAU2

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Event 07-Nov-12Seminar in Information Markets, TAU3

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Scoring Rule 07-Nov-12Seminar in Information Markets, TAU4

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Exercise 07-Nov-12Seminar in Information Markets, TAU5

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Exercise 07-Nov-12Seminar in Information Markets, TAU6

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Logarithmic Scoring Rule 07-Nov-12Seminar in Information Markets, TAU7

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Logarithmic Scoring Rule 07-Nov-12Seminar in Information Markets, TAU8

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LSR is local 07-Nov-12Seminar in Information Markets, TAU9

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Properness - simple case proof 07-Nov-12Seminar in Information Markets, TAU10

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Objective We want multiple agents(traders) to share their beliefs – Without paying each one – We want a single(unified) prediction. One option is a standard market(Double auction information markets) – What happens in thin markets? 07-Nov-12Seminar in Information Markets, TAU11

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Market Scoring Rule 07-Nov-12Seminar in Information Markets, TAU12

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Market Scoring Rule(2) Market maker subsidizes the reward for accurate predictions: – Gives incentive to participate and share your knowledge – Increases liquidity – Easy to expand to multiple outcomes 07-Nov-12Seminar in Information Markets, TAU13

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Market Scoring Rule(3) If only one agent participates, it is equivalent to simple scoring rule. If many agents participate, it gives the same effect of a standard information market, at the cost of the payment to the last agent. 07-Nov-12Seminar in Information Markets, TAU14

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Logarithmic Market Scoring Rule (LMSR) 07-Nov-12Seminar in Information Markets, TAU15

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how do we implement a market? 07-Nov-12Seminar in Information Markets, TAU17

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Distribution is equal to Buying and Selling shares 07-Nov-12Seminar in Information Markets, TAU18

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LMSR price function 07-Nov-12Seminar in Information Markets, TAU19

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LMSR price function(2) 07-Nov-12Seminar in Information Markets, TAU20

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LMSR cost function 07-Nov-12Seminar in Information Markets, TAU21

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“How much?” 07-Nov-12Seminar in Information Markets, TAU22

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Equivalence proof 07-Nov-12Seminar in Information Markets, TAU23

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Example 07-Nov-12Seminar in Information Markets, TAU24

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Combinatorial Markets 07-Nov-12Seminar in Information Markets, TAU27

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LMSR local inference rule 07-Nov-12Seminar in Information Markets, TAU28

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Combinatorial Product Space 07-Nov-12Seminar in Information Markets, TAU29

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THANK YOU 07-Nov-12Seminar in Information Markets, TAU30

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