Game Theory 101 (#16): Subgame Perfect Equilibrium

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?

[JassyB]

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.

[elvisboyaci]

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

[HeavenForbid]

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.

[susanxiao]

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

[yannickingermany]

Hi William, I am an engineering student who borrowed the course; electronics marketing from another department. Your explanations are going to help me pass my exams. Thank you so much.

[SuPeRev]

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

[DubsCat_]

Will you are a lifesaver for my Game Theory class, thank you for making all these videos

[supersweetie]

this is explained incredibly well! thankyou

[ddavis]

Thanks for the great example. Glad I watched

[absidd]

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

[Gametheory]

Two. The full game is always considered a subgame. The other subgame is Firm 2's move.

[niemand]

A firm one in and out. These games are getting spicy. Great stuff.

[Wmabcdef]

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

[saksham_agarwal]

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)

[ulvumustafayev]

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

[phatnoir]

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

[StRaWbeRrYsasha]

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

[RandomGaming-the-OG]

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.

[SuitedBunny]

Can you do Nash Bargaining Theory and Rubinstein's Bargaining Model?

[ARPwefightforyou]

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.