1. Shengen Zhai

2.  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.  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.  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.  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.  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.  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.  Levels in the all-pay auction are separable by Strategic Reasoning, and Recursive Depth.

9.  Levels in the all-pay auction are not separable by Bayesian Maturities and Backward Induction.

10.  By combined cognitive requirements

11.  Levels in the second-price auction are separable by Bayesian Maturities and Backward Induction

12.  Levels in the second-price auction are NOT separable by Strategic Reasoning, and Recursive Depth.

13.  By combined cognitive requirements

14.  Levels in the first-price auction are not separable

16.  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.  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.  L0 strategies are noisy in complicated games ◦ Economic justification: L0 players do not behave uniformly due to no obvious basic strategy.

19.  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.