Game Theory 101 (#26): Forward Induction

[@CarolJeanLouis]

YOU ARE THE GREATEST ONLINE PROFESSOR EVER!!!!!!! YOU ARE AWSOME!! THANK YOU!!

[@Gametheory101]

(Pub, hare) and (stag, stag) are the game's PSNE. (There are more in mixed strategies.) Player 1 cannot hunt a hare in any equilibrium because choosing pub strictly dominates it.

[@PunmasterSTP]

I’m so glad that these videos and your textbook are pub-licly available. Perhaps I’ll read you book at a…restaurant…

[@Gametheory101]

Not really. Player 2's moves were not limited. Player 2 could have still chosen rabbit. It's just that player 1 has conveyed information to player 2 by not going to the pub. That information makes choosing rabbit a bad move for player 2.

[@potaytopotawto8704]

Insightful! All Nashes are not created equal! Forward induction is a neat concept but about implied forward induction? For game theory, the assumptions are that both players want to maximize their individual EV and both KNOW THAT THE OTHER PLAYER WANTS TO DO SO AS WELL. Isn't this enough information to remove the pub option while keep stag, stag the only unique solution? I mean I think there's two independent concepts at work here. One is the formal definition of the nash equilibrium.

[@Gametheory101]

At the risk of sounding slightly like your lecturer, I do applied research into bargaining and war. Game theory is really useful to keep the logic of your argument straight and prove the existence of agreements that two states prefer to war. I also do research on baseball while I am bored. Check my website.

[@adamhilmi761]

Suppose me and my mate went fishing but we had to chose between a net or a pole and we were supposed to meet at the pub. He lets me know that he wants to spend the time fishing but before telling me what to bring, his phone dies. Guess using this logic I can safely assume to bring the net instead of the pole.

[@niemand262]

I can't help but see social/political conflicts in this model. Imagine the political stag hunt. Two political parties can pursue their individual goals (rabbits), or jointly pursue communal goals (stags). In politically banal periods, many people can freely choose to ignore political discourse by ignoring it (going to the pub). But, covid has amplified the demand that people choose a side (i.e., play their demanded subgame) by eliminating the availability of the pub option. Political actors have also added a punishment game subsequent to this game, to drive down the utility of the pub option. The political machine is trying to win it's war by increasing the cost of you choosing not to play.

[@Gametheory101]

Further in the series, there is a unit on the repeated prisoner’s dilemma. Although I don’t frame it like this (both regarding politics and like a stag hunt), that’s basically what happens in there. And it’s also similar to how political scientists model those scenarios.

[@potaytopotawto8704]

(continued from above) That is stability, individual deviations do not results in higher EV. The 2nd, more importantly, is that they both assume the other is rational (the basis for strong dominance). Thus, even if the pub option were not there, we can still use its implication just the same and conclude that stag, stag is the only logic result. Note that rabbit, rabbit is still a nash equilibrium by definition, but stag, stag is the unique rational solution for both players even without pub.

[@Existence_Predicate]

Whwn do you use forward induction?

[@SJ23982398]

I don't get it, if you assume your opponent is rational you always pick stag. And you always get paid 3 anyway? Doing otherwise would be irrational so you don't really need the information of the seeing player 2 in the pub? And if you don't know player 2 is rational, he still could have chosen the rabbit.

[@yourdeadmother]

hey william ive been watchign your entire series on game theory 101 and i must say you are doing a great job. but im hoping you can convince that what were doing here is not just theoratical and can actually be applied meaningfully in real life situations. and by real life situations i mean something that is of significance because when i asked this question to my lecturer he always comes up with dumb shit like oh you can use it figure out whats gonna happen in a war.

[@adamhilmi761]

I wrote an amateur comment about this using this video as an example.

[@TheMadFoxes]

Hmm, I’m not very convinced honestly; is player one assuming player 2 is thinking at k-level 2 and expecting him to have acted as a rational K-level 1 player? Because if player one is either an idiot or a k-level two thinker, he could pass up the pub to hunt a rabbit either out of irrationality or malice respectively. Idk what do you make of that thought? It’s probably beyond the scope of the game, but I think K-level expectations would play a large part in this since the new nash equilibrium would assume my be to always choose the pub since it guarantees 2.5 no matter if player two would have arrived at the definite-stag or play it safe rabbit conclusion; how is the pub not the clear nash equilibrium

[@martinchristensen5918]

Is going to the pub a nash equilibrium? And is hunting the rabit still a nash equilibrium after the game change? I understand the game and I understand it's not a subgame perfect equilibrium, but I'm wondering if the other two outcomes would be nash equilibriums as the critia for nash equilibriums are less strict.

[@murtazahamid6141]

for curiousity s' sake what would happen if the pub payoff was 2 instead of 2.5, would the weak dominance be enough to come to this same conclusion?

[@VinWeiLee27171]

so in a way, player 1 limited player 2's moves by presenting something he's not going to do?

[@russellfernandez57]

Sounds like nuclear weapons

[@glozone-718]

If player 1's utility for SPE (Go the pub, Rabbit Rabbit) was 2.7, how would this affect the process of forward induction?

[@IBMua]

Awesome! =)

[@ryder848]

While we wouldn't get 3 pleasure points for picking rabbit as player 2 based on the Pub Hunt, we would get 2, and a leg up on player 1 (if this example was more monetary, less emotional), how do we start to account for inherent evil, or greed?

[@sharathkumar8422]

I think you'd still have to reflect those qualities in terms of payoffs. Player 2's payoff wouldn't be 2 if she also derived pleasure from getting a leg up on player 1. It would have to be greater than 3 cause she'd have choose to go for that over hunting a stag together where her payoff is 3. If this were the case and player 1 knew player 2's dislike of him, then he'd probably have chosen to hunt the rabbit as well (backward induction) or go to the pub alone. If he didn't know her intentions then he'd be fooled.

[@williamkibler592]

This is a form of tick for tat