1 / 21

A Generalized Stackelberg Model

A Generalized Stackelberg Model. Teng, Jimmy The University of Nottingham Malaysia Campus. Incomplete Information Noisy Observation Sequential Games. Noisy inaccurate observations: in between perfect and imperfect information Need to Make Statistical Decision

masao
Download Presentation

A Generalized Stackelberg Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Generalized Stackelberg Model Teng, Jimmy The University of Nottingham Malaysia Campus

  2. Incomplete Information Noisy Observation Sequential Games • Noisy inaccurate observations: in between perfect and imperfect information • Need to Make Statistical Decision • Solving by Bayesian iterative conjectures approach: starts with first order uninformative priors, later priors generated by the game itself • Convergence of conjectures: equilibrium consistent conjectures

  3. Generalized Stackelberg Cournot Model • Currently, Stackelberg and Cournot are two distinct models. • This paper challenges this view • Key issue: value of strategic pre commitment by the Stackelberg leader • Raises question: what is perfect and complete information? Bayesian: the world is essentially uncertain and certainty is special, extreme case.

  4. Noisy Stackelberg Model • Nature decides the type (production cost) of firm 1 • Firm 1 sets production level • Firm 2 inaccurately observes the production level of firm 1, makes inference and decides and own production level

  5. Profits Functions • Firm 1 • Firm 2

  6. Type Prior & Noise Distribution

  7. Prior & Likelihood • Prior • Likelihood • Conjugate Prior: Normal-Normal-Normal

  8. 1st Round • Firm 2 solves • With uninformative first order prior, Posterior=Likelihood

  9. 1st Round • Firm 2’s FOC: • Firm 2’s Optimal Solution:

  10. 1st Round • Firm 1 solves • Optimal q1:

  11. 2nd Round • Firm 2’s Prior: • Posterior:

  12. 2nd Round • Firm 2’s optimal production level: • Firm 1 solves • Firm 1’s optimal production level:

  13. 3rd Round

  14. 3rd Round • Firm 2’s optimal production level: • Firm 1 solves • Firm 1’s optimal production level:

  15. Convergence • 2nd round Firm 1’ production = 3rd round Firm 1’s production • 4th round prior = 3rd round prior • 4th round posterior = 3rd round posterior • 4th round Firm 2’s production = 3rd round Firm 2’s production • And so on

  16. BEIC

  17. Comparative Statics I

  18. Comparative Statics II • Greater Noise Variance leads to lesser reliance on observed data and greater reliance on rational prior. • Lesser variations in q2 in response to observed q1. q1 varies less to affect q2 and P. • Rational prior has smaller variance.

  19. Limits • Cournot solution for complete and imperfect information (or simultaneous) game • Stackelberg Solution for Complete and Perfect Information Game • But,

  20. Indeterminacy of Complete & Perfect Information

  21. Value of Strategic Pre-commitment • Proposition 1: • As the follower relies less on the noisy inaccurate observation and relies more on the prior information and conjectures for making statistical inference and decision, the profit of the leader decreases and the profit of the follower increases.

More Related