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Game Theory 101 MOOC (#16): Subgame Perfect Equilibrium

admin by admin
July 11, 2020
in Game
43
Game Theory 101  MOOC (#16): Subgame Perfect Equilibrium



Game Theory 101: The Complete Textbook on Amazon:

This lecture begins our adventure through sequential games, in which players take turns moving. Not all Nash equilibria are sensible in this context, so we introduce a new concept: subgame perfect equilibrium. A subgame perfect equilibrium requires all actions to be Nash equilibria in every subgame of the larger game. In essence, this requires all threats players make to be credible.

We consider a game between two firms deciding whether to enter a market and engage in a price war. Can a monopolist’s threat to launch a price war convince a challenger to stay out of the market?

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Comments 43

  1. Zofia M. says:
    1 year ago

    Thank you very much!

    Reply
  2. Myles Allen says:
    1 year ago

    Thanks William! Super helpful mate.

    Reply
  3. PPsmall says:
    1 year ago

    What kind of dog do you have?

    Reply
  4. riaanvb says:
    1 year ago

    Hi William SpAniel!

    Reply
  5. Susan Xiao says:
    1 year ago

    Thank you so much for the book + the website!!! I am so excited that I came up with these videos I learned a lot!

    Reply
  6. Christian Geraud N.B. says:
    1 year ago

    Does each firm know the expected payoff of their choices?!

    Reply
  7. warm blankets says:
    1 year ago

    thank u so much!! i absolutely hate math and economics but somehow u make it interesting to me it's a miracle

    Reply
  8. Ulvi Mustafayev says:
    1 year ago

    Hi.Thank you for this excellent presentation.I have watched all the videos and find them super useful.Unfortunately, there 2 exercises about game theory that I can't solve.Pleaseee could you help me? Pleasee

    Reply
  9. Andrey E. Vedishchev says:
    1 year ago

    2:59, if 2's choice is irrelevant, why is it choosing War and not Accept? In other words: why are the NEs (In, Accept) and (Out, War) instead of (In, Accept) and (Out, Accept)?

    Reply
  10. GOT THAT U says:
    1 year ago

    This concept completely ignored the profit of being a monopoly of the market, which is not true in the real world. However, what I have to agree is that this youtuber (William) explained all the concepts in the game theory much more clearly and effectively than professors in my school. And I am a student in Durham University, which the university suppose to have the best teachers to teach us. AND!!! THE PROFESSOR USED 55 MINS TO EXPLAIN A CONCEPT WHICH WILLIAM FINISHED EXPLAINING CLEARlY IN 8 MINS!!! WHAT A SHAME.

    Reply
  11. BrainForce95 says:
    1 year ago

    Can someone tell me maybe why Firm1-> out, and Firm 2->war is an equilibrium ?
    or how you can get this equilibrium by doing a backward induction

    Reply
  12. Bryan Lim says:
    1 year ago

    Just to clarify that Firm 1 (In) and Firm 2 (Accept) is the SubGame Perfect NE. Firm 1 (Out) would be an NE, right?

    Reply
  13. Shao Yun Zheng says:
    1 year ago

    Firm 2’s strategy is to burn out firm 1 cash then reraise the price after firm 1 exit. You do see that in real life.

    Reply
  14. JCarmen says:
    1 year ago

    What annoys me is the fact that I am paying £9000 a year to go to university, and this guy, my now dear friend William (haha), has taught me a whole module with free videos and an amazing textbook. Thank you so much, without these videos I didnt stand a chance.

    Reply
  15. GOD says:
    1 year ago

    In the real world though, a monopoly will benefit in the long term from declaring a price war, since the new firm will be forced out of the market after a while. The monopoly firm can however absorb the losses until that time and then continue in thier merry way afterwards.

    Reply
  16. carson kearl says:
    1 year ago

    the payout system of the game was poorly chosen, but other than that great video

    Reply
  17. Saksham Agarwal says:
    1 year ago

    Hi, Can this game be converted into a mixed strategy Nash equilibrium where credibility of an action (say, probab of war by Firm1 is 'w')?

    That way, we may be able to chart out the possibility of firm1 going from (2,2) to (3,1) depending upon the weakness of 'w'.

    I am asking this because there are two Nash equilibriums and one is unstable (the (2,2) one, since there the full game doesn't play out as firm1 never got the chance to act)

    Reply
  18. Elvis Boyaci says:
    1 year ago

    "Some people just want to watch the world burn." -Firm 2

    Reply
  19. Boris Köster says:
    1 year ago

    The problem I see here is that humans act irrational or one company has enough money to do a 0,0 game until the other one runs out of money.

    Reply
  20. SurvivalBayArea says:
    1 year ago

    STRAIGHT OUTTA COMPTON

    Reply
  21. enditend says:
    1 year ago

    don't get the difference between a subgame equilibrium and equilibrium

    Reply
  22. Quickburger9000 Deal with it says:
    1 year ago

    Firm 1 out should be 2, 4 because we see from Firm 2 accept that there are 1 + 3 = 4 points in the market and since Firm 2 has a monopoly on the market, it gets all of the point that are in the market.

    Reply
  23. blackdahliamurder100 says:
    1 year ago

    hey, do you know some videos /sites where I can learn more about Moore-Repullo mechanisms

    Reply
  24. ngyx57 says:
    1 year ago

    So how many subgame perfect nash equilibria are there in this entire game? One?

    Reply
  25. SuPeRev94 says:
    1 year ago

    This video was awesome, thank you SO MUCH for posting!

    Reply
  26. truth1901 says:
    1 year ago

    'Countries' are an illusion.

    Greece has nothing to lose, Germany will have to accept.

    Reply
  27. StRaWbeRrYsasha says:
    1 year ago

    So how would you interpret a real life scenario such as the UK supermarkets entering a price war? or is that totally different?

    Reply
  28. Chrystel Sinclair-Guionneau says:
    1 year ago

    I have a question: in my excercie i am asked two things (a) Find the set of (pure-strategy) Nash equilibria of the game (b) Find the set of (pure-strategy) subgame-perfect equilibria of the game. What is the difference? I thought that the subgame-perfect equilibrium WAS the Nash equilibrium 🙁 ( I Know I comment a lot in your vids sorry)

    Reply
  29. D Davis says:
    1 year ago

    Thanks for the great example. Glad I watched

    Reply
  30. William Spaniel says:
    1 year ago

    You could think of the 2 meaning that they get to keep their investment.

    Reply
  31. KeepanOpenMind says:
    1 year ago

    Why would firm 1 get 2 from going out? It is not in the market therefore payoff would be O

    Reply
  32. supersweetie92 says:
    1 year ago

    this is explained incredibly well! thankyou

    Reply
  33. William Spaniel says:
    1 year ago

    That's correct.

    Reply
  34. Patrik Zlatic says:
    1 year ago

    Correct me if I'm wrong, but
    (In, accept) is a perfect equillibrium
    while (out, war) is just an "ordinary" Nash equillibrium.

    Reply
  35. Sid says:
    1 year ago

    William Spaniel, you are a life saver. Thanks a lot.

    Reply
  36. William Spaniel says:
    1 year ago

    It won't. I don't know of anyone else who says that a full game is not considered a subgame, but the point is trivial.

    Reply
  37. Adity Das Gupta says:
    1 year ago

    gibbons book says that a full game is not considered a subgame. if i do consider it a subgame, it shouldnt really change anything?

    Reply
  38. William Spaniel says:
    1 year ago

    Should be the same thing.

    Reply
  39. Adity Das Gupta says:
    1 year ago

    incredible threats? Gibbons book calls it non-credible threats. And I have been reading about subgame perfect outcome. How is that different form this?

    Reply
  40. HeavenForbid7 says:
    1 year ago

    I saw some game theory videos of yours, you are so much better at explaining all of this than my microeconomics lecturer teaching at a prestigious university… they should hire you.

    Reply
  41. John Farish says:
    1 year ago

    Ah, I was looking at the wrong numbers. Thanks for the quick reply! I understand now.

    Reply
  42. William Spaniel says:
    1 year ago

    Not sure what you mean. Firm 1 earns 3 by entering and 2 by staying out. So, it enters.

    Reply
  43. John Farish says:
    1 year ago

    I don't understand, wouldn't it always be more profitable for Firm 1 to opt out? I understand Firm 2's incredible threat, but I don't see why knowing it's incredible should make you want to accept less profit. Thanks for any light you could shed on this.

    Reply

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