BIDDING STRATEGIES FOR FANTASY-SPORT AUCTIONS BY ANAGNOSTOPOULOS - - PowerPoint PPT Presentation

BIDDING STRATEGIES FOR FANTASY-SPORT AUCTIONS

BY ANAGNOSTOPOULOS ET AL.

Alireza Amani Hamedani Sepehr Mousavi

§ Introduction § Absence of Nash equilibrium § Fair-Price Bidding

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§ Type of online game § Participants as virtual managers of professional athletes § Choosing players and modifying rosters over the course of a season § Fantasy points obtained based on statistical performance of the athletes in actual

games

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§ Fantasy Points

§ Converted athlete statistics from real-life games

§ Calculation

§ Manually by league commissioner § Online platforms tracking game results

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§ Users (team managers) add, drop, and trade athletes over the course of the season

§ In response to changes in athletes’ potentials

§ Pivotal event is the player draft

§ Initiates the competition

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§ Multi-billion dollar industry § In 2017, 59.3 million users in the USA and Canada § On average, fantasy sport players spend $556 over a 1-year period

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Fig 1. Number of Fantasy Sports Users by Year (in millions) in the USA and Canada

§ Snake vs Auction § Snake Draft

§ Teams taking turns choosing players based on pre-determined order § Once each round is over, the draft snakes back on itself § Used in majority of fantasy leagues

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Fig 2. Snake draft with 12 teams and 15 rounds

§ Auction Draft

§ Each team has an initial budget and each player has a price § The number of rounds mirrors the number of roster spots § Instead of drafting a player in your turn, you place a player on the auction block and start

the bidding at an amount of your choice.

§ Focus of this paper

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§ Fantasy sports league composed of:

§ 𝑙 team managers, or users, with 3 ≤ 𝑙 ≤ 20

§ 𝑣(, 𝑣*, … , 𝑣,

§ 𝑜 athletes (or players)

§ 𝑄

(, 𝑄 *, … , 𝑄 /

§ Each team composed of 𝑛 athletes

§ Depends on the sport and fantasy games provider 11

§ Snake vs Auction

§ Choice made by the initiator of the league

§ Snake Draft

§ No bidding or competition, just a pre-determined order of teams to draft

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§ Auction Draft

§ Fixed budget of 𝐶 § Managers taking turns successively, in some pre-determined order, nominating athletes

for bidding via an English auction

§ Default bid is $1. Can be raised higher within the budget § Managers given a fixed amount of time to place higher bid

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§ Auction Draft

§ Leftover money cannot be used § Managers should be able to complete their rosters § Each athlete has a fixed position and each team must meet a fixed distribution of positions

§ Depends on the sport and fantasy games provider 14

§ Simplifying assumptions

§ Team managers agree on the value of every athlete.

§ Each athlete 𝑄

2 has an associated value 𝑤2

§ 𝑤2: Expected number of fantasy points 𝑄

2 will earn throughout the season

§ 𝑤2 is a shared belief, common to all managers 15

§ Simplifying assumptions

§ Auction draft is a sealed-bid auction

§ Arbitrary fractional bids § In case of a tie, athlete is given out with equal probability § Exception when all managers place the minimal bid. Athlete given to nominating manager 16

§ Simplifying assumptions

§ For each position the player pool has exactly the number of athletes required to complete

each team

§ 𝑜 = 𝑙𝑛 § Fair share:

𝑊 = 1 𝑙 7 𝑤2

/ 28(

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§ Pure strategy subgame perfect Nash equilibria do not generally exist in the fantasy

auction model

§ 9

: worst case with athletes automatically nominated in decreasing order of their

values

§ 9

(; worst case for the general case in which nominations are made in a general

adaptive fashion according to manager strategies

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§ Due to competitive and strategic environment, it is natural to take game theoretic

approach.

§ Generally there will not even exist any pure strategy subgame perfect equilibria in

fantasy draft auctions

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§ Example:

§ Two users with equal budgets § Each team roster has two slots § Four athletes, two of unequal positive value, and two of value 0

§ Claim: In the above example, if the lower (positive) value athlete is nominated first,

there exists no pure strategy Nash equilibrium forward from that point

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§ Simple but not good approach § Generalized good approach § Fair-Price bidding in arbitrary nomination order

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§ Define fair share of total value as below: § Define fair price for athlete 𝑄2: §

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§ Not a good result in this case:

§ 𝑤( = 𝑤* = ⋯ = 𝑤,>( = 𝑊 1 − 𝜁 𝑏𝑜𝑒 𝑤, = 𝑤,C( = … = 𝑤,D =

9((C,F>F) ,D>,C(

§ The value of the final team for our manager:

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§ § Expected value of the final team at least 9

: with 𝛽 = 1.5

§ Regardless of the other managers’ bidding strategies

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§ Valuable athletes with 𝑤2 ≥ 9

L

§ Three scenarios:

1.

One valuable athlete is bought

2.

No valuable athlete, at least at one point, not enough budget

3.

No valuable athlete, always sufficient budget

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1.

Expected value: 9

L 𝑞

2.

At that point, the value at least 9

*L. So, Expected value: 9 *L 𝑞N

3.

Expected value: 𝑌𝑞NN and,

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§ Examples for other 𝛽 that lead to a result of almost 9

:

§ How to come up with a lower bound for any 𝛽?

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§ Three parameters: 𝛾 > 𝛽 ≥ 1 𝑏𝑜𝑒 𝛿 ≥ 1 § Two groups:

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§ Case 1: Value of group 𝑀 is larger than 𝑇

§ Put all the budget for group 𝑀

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§ Case 2: § Average value per spot: § For available spots, choose an athlete when 𝑄2 in 𝑀, or 𝑄2 in 𝑇 and

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§ Complex proof § Under choices 𝛽 = (;

: , 𝛾 = 8 𝑏𝑜𝑒 𝛿 = 2, Expected value is 9 (;

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§ Results hold for private-value case § The big question: How to fill in the gap between our result and the best one can

hope for.

§ May be competitive in real life!

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