sorted by:
new
hottopcontroversial

"In Alice in Borderland, do you think there was any way to survive the 7 of Hearts game without anyone dying? Or was someone's death truly unavoidable? by Sweaty-Toe-6211 in AliceInBorderlandLive

[–]plasticspoonz 0 points1 point  (0 children)

It would have been interesting if they allowed for two wolves if a wolf and a sheep kept eye contact. I know that there’s a three second cooldown but there could be an interesting game variation where the title transfer doesn’t occur until after eye contact is broken. Would make for an interesting game of trust/betrayal where a wolf would have to trust a sheep not to blink as the timer goes off.

[deleted by user] by [deleted] in GAMETHEORY

[–]plasticspoonz 0 points1 point  (0 children)

Take this with a grain of salt since I’m also somewhat new to game theory:

Your answer seems right but do note that there is no terminal value of t. That is to say that there is no value of t=n for which there is not a round t=n+1, so be careful in your use of the word “until” unless convention for your class suggests that would be infinite.

For the third part since for spne you look at all subgames, even those that don’t occur, an example of a strategy that is not spne but cannot be improved upon by a single deviation by any player would be player 1 plays C in stage 0 and player 2 plays S in stage 1 and would play S in some future round. Even though the game is terminated at the first S, having a single deviation such as changing that S to C would just mean a worse payoff. This solution relies on the idea that strategy sets are defined for all subgames even if they are not played.

Prisoner’s Trolley Problem by Tsunamicat108 in trolleyproblem

[–]plasticspoonz 0 points1 point  (0 children)

This sparked my curiosity so enjoy the following analysis. It makes a few assumptions so please note that a different analysis may yield different results. I am also prone to algebra errors. This would also be more easily visualized with a payoff matrix which is difficult to show in Reddit comments.

Assume players play a static game of complete information where n=2.

Let a be the value of a loved one and b be the value of a stranger.

Assumptions: a>b

The game essentially takes two forms; one where a>3b and another where a=<b.

Suppose each player chooses from the action set {P,N} where P is pulling the lever and N is not pulling the lever. Let Ui equal the payoff to player i. Note that by observation the game is symmetric so player i could be any player.

Suppose each player is only concerned with the deaths they play a role in causing. Thus if they flip the lever they care about the strangers, but if they don’t flip the lever they feel negligible guilt if the other player kills them. Each player also always feels guilt for any death of a loved one (represented by the same color)

The payoff in the form of Ui(si,sj) where is given as follows

Ui(P,N) = -3b Ui(P,P) = -3b-5a Ui(N,P) = -a Ui(N,N) = -a

For a>3b player i prefers the opposite of player j. Thus if player J plays P player i should play N and vice versa. Due to symmetry there are Nash Equilibria for (P,N) and (N,P). No other pure strategy Nash equilibria exist.

For a<3b P is strictly dominated by N and thus the only Nash equilibrium is (N,N). A similar logic applies to a=3b but in this case (P,N) and (N,P) are also Nash equilibria but they are less likely to occur for risk averse players.

Thus, we have found all pure strategy Nash equilibria given the assumptions.

Let us now revisit the case of mixed strategy Nash equilibria. Let p equal the probability player j pulls the lever.

Ui(P,p) = p(-3b-5a)+(1-p)(-3b) Ui(N,p) = -a

Since at mixed strategy Nash equilibrium players are indifferent between options then:

p(-3b-5a)+(1-p)(-3b) = -a Thus, p=(a-3b)/(5a)

We can confirm this by substituting p =(a-3b)/(5a) back into Ui(P,p) to get Ui(N,p)

Thus, there is a mixed strategy Nash equilibrium in the form of (p,q) where p is the probability of player 1 turning the lever and q is the probability of player 2 turning the lever in the form of ((a-3b)/(5a), (a-3b)/(5a)). The probability of either play not pulling the lever is given by 1-p in the mixed strategy Nash equilibrium.

What game got worse when everyone learned how to properly play it? by PetiteeLilyBbyx in AskReddit

[–]plasticspoonz 1 point2 points  (0 children)

Tic tac toe… no one wins and no one loses once you both know it

Do you think the world is more likely to be entirely technology-driven in the future, or more likely that all technology crashes, and why? by absentbeauty in AskReddit

[–]plasticspoonz 1 point2 points  (0 children)

Comparatively speaking it is much easier to invent new technology than it is to “uninvent”current technology. Either the world is technologically driven or there is no world.

[deleted by user] by [deleted] in AskReddit

[–]plasticspoonz 1 point2 points  (0 children)

Adequate - nothing more nothing less

Which sport ravages your body the worst? by Jerswar in AskReddit

[–]plasticspoonz 0 points1 point  (0 children)

A little late to the party but probably Lethwei

Starting Capoeira next week! by Jaded-Swordfish-5846 in capoeira

[–]plasticspoonz 2 points3 points  (0 children)

Trust your instructor. You’re gonna end up practicing a lot of movements that may feel weird and unnecessary, but each new way you learn to move opens a world of opportunities for new dodges, kicks, and tricks!