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

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

  3. 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

  4. 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)?

  5. 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.

  6. 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

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

  8. 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.

  9. 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.

  10. 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.

  11. 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)

  12. 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.

  13. 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.

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

  15. 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)


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