Regret-Based Econometrics in Repeated Games
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This document discusses regret-based econometrics in repeated games. It introduces regret as minimizing the maximum distance to the best response over time. While initial regret models showed minor improvements, quantal regret forms a weighted average on the regret curve and had better performance in estimating players' unknown parameters from observed data in repeated auctions. The document also describes data gathering from simulations to analyze the reduction of regret over time.
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 2 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. 3
- 4. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Case study: Bing 4
- 5. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Question outline Estimate players unknown(private) parameters. 5
- 6. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Econometrics 6 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 8
- 9. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Sponsored Search Auction 9 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 10 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! 11
- 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 ? 12
- 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! 13
- 14. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Regret Minimizing maximum distance to best response 14 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 15 ∀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. 16
- 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 17
- 18. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Next step Min-regret : 13 The answer is 10 ! 18
- 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. 19
- 20. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Next step Min-regret : 10.7 The answer is 10 ! 20
- 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 21
- 22. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Data Gathering 22
- 23. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Reduction of regert 23
- 24. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Quantal Regret Results 24
- 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. 25
- 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. 26
- 27. Algorithmic Game Theory Regret-Based Econometrics in Repeated Games Thank You 27