Regret-Based Econometrics in Repeated Games

1. Regret-Based Econometrics
in Repeated Games
Arash Pourdamghani
Sharif CE Algorithms Lab
Fall 2017

2. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Review
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Game
Theory

3. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Auction
There are a goods for sell.
Auctioneers want to maximum their profit.
Buyer wants to minimum its payoff.
Each Buyer has a value for a good.
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4. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Case study: Bing
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5. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Question outline
Estimate players unknown(private) parameters.
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6. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Econometrics
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Observed
values
Model Non-
observer
parameters

7. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Econometrics
7
Observed
values
Model Non-
observer
parameters
Which model
should we use?

8. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Case study: Google
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9. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Sponsored Search Auction
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1- Probability of clicking on ad
 Which is based on the
1. Content of ad
2. Placement of ad
2- Payment rule is a usually general second-price
 Highest bidder pay second price, the next one third …..
𝑢𝑡𝑖𝑙𝑖𝑡𝑦𝑖 𝑏; vi = vi. Pi b − Ci(b)

10. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Assumption
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Nash equilibrium
𝑢𝑡𝑖𝑙𝑖𝑡𝑦𝑖 𝑥, 𝑏−𝑖 ≤ 𝑢𝑡𝑖𝑙𝑖𝑡𝑦𝑖(𝑏)
Randomness
𝑃𝑖 𝑎𝑛𝑑 𝐶𝑖 𝑎𝑟𝑒 𝑑𝑖𝑓𝑓𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒
Convergence
V and B are bounded
together!

11. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Importance of experiment
The Assumptions are wrong!
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12. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Almost infinitely repeated games
Why not one-shot game ?
Why not finite?
Is it really infinite ?
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13. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Sophisticated bidding tools
Learning Algorithms wins!
 Adopt opponents
 No prior knowledge
 Take advantage of playing badly!
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14. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Regret
 Minimizing maximum distance to best response
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𝑅 𝑥, 𝑇 =
1
𝑇
Σ 𝑡 𝑢𝑡𝑖𝑙𝑖𝑡𝑦 𝑥, 𝑎−𝑖
𝑡
−
1
𝑇
Σ 𝑡 𝑢𝑡𝑖𝑙𝑖𝑡𝑦 𝑎𝑖
𝑡
< 𝜖

15. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Approach
∀𝑥:
1
T
Σ 𝑡 𝑢𝑡𝑖𝑙𝑡𝑦𝑖 𝑥, 𝑏−𝑖
𝑡
, 𝑣𝑖 <
1
𝑇
Σ 𝑡 𝑢𝑡𝑖𝑙𝑖𝑡𝑦𝑖 𝑎 𝑡
, 𝑣𝑖 − 𝜀
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∀𝑥: 𝑣𝑖. Δ𝑃 𝑖 − Δ𝐶 𝑖 < 𝜖

16. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Is this good enough?
Not Really, at least for humans !
Nisan & Noti showed that it only had a minor improvement in a
controlled experiment.
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17. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Let’s start Over
Nash Eq:
𝑝𝑥 = 9𝑝 + 1 − 𝑝 10
𝑥 =
10
𝑝
− 1
𝑥 =
10
.68
− 1 ≈ 13.7
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18. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Next step
Min-regret : 13
The answer is 10 !
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19. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Quantal Regret
Regret curves seem to have shallower left side, so just finding
minimum is not the answer.
Therefor Quantal Regret form a weighted average on regret curve.
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20. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Next step
Min-regret : 10.7
The answer is 10 !
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21. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Data Gathering
5 players
Each time assigned a random value
25 minutes simulation
1 auction per second →
1500 auctions in a game
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22. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Data Gathering
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23. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Reduction of regert
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24. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Quantal Regret Results
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25. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Conclusion & future work
Nikpelov et al. have introduced a new model that covers the
concerns of learning agent, but Nisan & Noti showed that it wasn’t
powerful enough, therefore introduce Quantal that had better
performance.
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26. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
References
Nekipelov, Denis, Vasilis Syrgkanis, and Eva Tardos. "Econometrics for learning
agents." Proceedings of the Sixteenth ACM Conference on Economics and
Computation. ACM, 2015.
Nisan, Noam, and Gali Noti. "A “Quantal Regret” Method for Structural
Econometrics in Repeated Games."Proceedings of the Eighteenth ACM
Conference on Economics and Computation. ACM, 2017.
Nisan, Noam, and Gali Noti. "An experimental evaluation of regret-based
econometrics." Proceedings of the 26th International Conference on World Wide
Web. International World Wide Web Conferences Steering Committee, 2017.
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27. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games
Thank You
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