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Towards A Predictive Level-K Thinking Model

Towards A Predictive Level-K Thinking Model. Shengen Zhai. Traditional Game Theory. Nash Equilibrium High cognitive requirements

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Towards A Predictive Level-K Thinking Model

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  1. Towards A Predictive Level-K Thinking Model Shengen Zhai

  2. Traditional Game Theory • Nash Equilibrium • High cognitive requirements • Weakness: it states neither how people do behave nor how they should behave in an absolute sense, but how they could behave in the perfect world to remain the status stable. • Conclusion: Narrative Models

  3. Behavioral Game Theory • Level-K thinking model • Players have different levels of strategic sophistication hence behave heterogeneously • L0 players; L1 players; Lk players; use simplified models that avoid the complexity of equilibrium • Example: Nagel’s “guess the half of average” game

  4. Behavioral Game Theory • Level-K Auction Model • Extend Level-K Model into complicated games • truthful L0 bidder; random L0 bidder • “truthful L1 bidder”, “truthful L2 bidder” … ; “random L1 bidder”, “random L2 bidder” … • Main result is to determine the amount of variance in players’ behavior that could explained by the model • Conclusion: Descriptive Models

  5. Possible Future Game Theory • Limitation of Level-K Thinking Model • Poor transferability of players’ levels across different games • Predictive Level-K Thinking Model • Invariant type underlying every player • Measurable as a combination of cognitive abilities • Exhibited level=f (type, game) • Levels of strategic sophistication predictable based on types and the results from comparable games

  6. Experiment Goals • Main goal • To determine cognitive requirements for each strategy level in different auction mechanisms • To test the transferability of the cognitive requirements among different auction mechanisms • Additional goal • To examine L-0 assumption in Level-K auction model • To examine the assumption of the best responses among adjacent levels

  7. Experiment Implementation • Cognitive Measures: • Bayesian Maturities • Backward Induction Abilities • Strategic Reasoning Abilities • Recursive Reasoning Depths • Auction Mechanisms: • First-Price Auction • Second-Price Auction • All-Pay Auction

  8. Experiment Results I • Levels in the all-pay auction are separable by Strategic Reasoning, and Recursive Depth.

  9. Experiment Results I • Levels in the all-pay auction are not separable by Bayesian Maturities and Backward Induction.

  10. Experiment Results I • By combined cognitive requirements

  11. Experiment Results II • Levels in the second-price auction are separable by Bayesian Maturities and Backward Induction

  12. Experiment Results II • Levels in the second-price auction are NOT separable by Strategic Reasoning, and Recursive Depth.

  13. Experiment Results II • By combined cognitive requirements

  14. Experiment Results III • Levels in the first-price auction are not separable

  15. Experiment Results III • Levels in the first-price auction are not separable

  16. The First Hypothesis • Multidimensional Predictive Model • Unlikely to have a univariate cognitive type • Plausible to have a multidimensional invariant type • Each dimension is independent and measurable as a combination of cognitive abilities • Exhibited level=F(related dimensions of type, game) • Levels of strategic sophistication predictable based on types and the results from the games of the same characteristics and comparable difficulties

  17. The Second Hypothesis • Relationship between cognitive abilities and levels will be lost during the learning process. • Economic justification: • Players with less cognitive abilities acquire the knowledge of sophisticated strategies without independently deriving the strategies

  18. The Third Hypothesis • L0 strategies are noisy in complicated games • Economic justification: L0 players do not behave uniformly due to no obvious basic strategy.

  19. The Fourth Hypothesis • L1 are not optimally responding to L0 in complicated games • Economic justification: in complicated games, L0’s behaviors are ambiguous; it is not possible for L1 develop optimal strategies.

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