Game Theory 101 (#18): How NOT to Write a Subgame Perfect Equilibrium

[@PunmasterSTP]

Subgame perfect equilibrium? More like "Some videos are perfectly educational!" Thanks for making all of these (in addition to writing your book) and sharing them on KZbin!

[@supersweetie92]

i was just wondering in the previous video why u didnt just write accept, and this viedo explains it perfectly! so stoked i find your videos

[@JJ-fb2lp]

I find it is better to explain the sub game perfect equilibrium by simply saying that it is a strategy profile for players that represent nash equilbrium for every subgame. That being said, keep up the good work. I really found your videos useful in solving problems.

[@Milkisklim]

Without you I would not have understood game theory. On my course evaluation I am going to strongly recommend your work to be the textbook and not the paperweight of a book i have yet to open.

[@Gametheory101]

Cheers!

[@dv9434]

Thank you very much for the video. My final is today and your videos were extremely helpful. Thank you again for doing this.

[@PunmasterSTP]

I know this was long ago, but how did your final go?

[@Gametheory101]

hehe...

[@ulvumustafayev1823]

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 This is the exercise: A). Consider a duopoly with differentiated products. The two firms are denoted 1 and 2, and their products q1 and q2 with prices p1 and p2, respectively. There is a representative consumer whose net utility from purchasing the two goods is U=q1+q2-1/2(q1 ^2 + q2^2)-yq1q2-p1q1-p2q2 The parameter y, which ranges in between 0 and 1, is the degree of product differentiation (products are perfect substitutes when y= 1, while they are independent when y= 0. Firms have symmetric and constant marginal cost c 1. 1. Derive the direct and indirect demand functions (i.e., quantities as function of prices, and prices as function of quantities) 2. Consider then the case of quantity competition (Cournot). Derive the best response functions and the Nash equilibrium, as a function of the parameters y and c. 3. Do the same for the case of price competition (Bertrand). 4. Compare the two equilibria. Which one is preferred by the firms? And by the consumer? B. Consider a sealed‐bid first‐price auction. There are two bidders, 1 and 2, with valuations for the good of v1 and v2, respectively. Each buyer’s valuation is his/her own private information. v1 is uniformly distributed on include (0,1) and v2 is uniformly distributed on include (0,2). So player 1, for instance, knows v1 exactly but regarding v2 he/she knows only that it is uniformly distributed between 0 and 2. 1. Define the Bayesian equilibrium for this game. 2. Find a Bayesian equilibrium. 3. Discuss uniqueness.

[@Harry-kq9nt]

Does backward induction always lead to a subgame perfect equilibrium?

[@Gametheory101]

Yes

[@PraEstaNs]

wouldn't the SPNE be (accept, do nothing), and (war, escalate) is just NE?

[@qafirang]

Fake identity. He is actually Howard Wolowitz from The Big Bang Theory.

[@papaxsmurf7678]

not even taking a course just watching lol

[@NAunimusofECC]

how come escalation is worth 2 points..

[@KarotteImBeet]

The 2 denotes the player not the utility. So in this game player 2 has the choices to _Escalate_ or _Concede_ .

[@xmajx29]

why isn't threaten included if that's what state 1 does before state 2 can escalate? thanks

[@Gametheory101]

+Marissa J I'm not sure I understand your question. Escalate is part of the SPE.

[@anuragmukherjee1014]

@@Gametheory101 She is talking about you writing ;. She is aking why we dont write ;. I also have the same question. Could you please answer this. By the way this course is really useful and informative.

[@Gametheory101]

@@anuragmukherjee1014 Player 1 never chooses threaten, so you wouldn't write it as an equilibrium strategy.

[@anuragmukherjee1014]

@@Gametheory101 Ok now I get it. Thanks