Lost1
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 Nov 18 comment Does $0$ correlation imply independence for marginally normal distributions? @Henry How did you derive that? Nov 14 accepted standardised random variable least square regression $X$ against $Y$, $Y$ against $X$ Nov 13 reviewed No Action Needed Quadratic equations in $\mathbb{C}$ Nov 12 comment increasing process well, this follows from the Tanaka's formula (trivially), but I am guessing that is not the answer you are looking for. So maybe you want to look into a proof for Tanaka's formula. Oct 24 comment 3 contestants choosing a smallest number to win a car So this just seems like a 3 player prisoner dilemma problem. The only stable point is everyone chooses 1 and nobody win. If two player sample over 1 to N uniformly, i am going to pick 1 every time... Oct 24 comment 3 contestants choosing a smallest number to win a car If the players play this, one of the player should always choose 1 and have greater than 0.5 percent chance of winning Oct 24 comment 3 contestants choosing a smallest number to win a car I got the same numbers, so does this mean this game has no nash equilibrium? Oct 24 comment 3 contestants choosing a smallest number to win a car I am slightly confused. In prisoner's dilemma, both criminal should turn their friend in when they are not colluding. Your last sentence suggestions collusion? While this is in a way, optimal, it is certainly unstable. Oct 24 comment 3 contestants choosing a smallest number to win a car the optimal strategy cannot be over a large number surely? If 2 players do this, i can just choose 1 and 2 with probability 1/2 to beat this strategy. At the top, you said your assumption is the players are not cooperating, but settling for a distribution which make the prob of winning as close to 1/3 as possible is collusion. Oct 24 comment 3 contestants choosing a smallest number to win a car I don't quite know how to write down the max min (?) problem. Oct 24 comment 3 contestants choosing a smallest number to win a car @stochasticboy321 I am vaguely aware of the concept of nash equilibrium concept but I am not sure how we prove it in this case. in a perfectly rational world, the players would probably collude... Oct 24 revised 3 contestants choosing a smallest number to win a car added 18 characters in body Oct 24 comment 3 contestants choosing a smallest number to win a car @stochasticboy321 the person who chooses 2. Basically I think we want a strategy which maximises the individual chance of winning but penalises people from deviating. If the choice was (1,1,1), then nobdy wins. Oct 24 comment 3 contestants choosing a smallest number to win a car @Aretino I assume no. if they are, then they should sign a contract and throw a dice, the person with highest number gets to pick 1, giving each person 1/3 of chance of winning. Oct 24 revised 3 contestants choosing a smallest number to win a car added 9 characters in body Oct 24 comment 3 contestants choosing a smallest number to win a car @Aretino in which case, if the other two play 1 or 2 with probability 1/2. everyone still have 1/4 chance of winning. If everyone think like that, no body wins. Oct 24 comment 3 contestants choosing a smallest number to win a car @JohnDouma i meant you just choose an integer. Oct 24 revised 3 contestants choosing a smallest number to win a car deleted 9 characters in body Oct 24 asked 3 contestants choosing a smallest number to win a car Oct 23 comment Hölder type of inequality? This is what I was in the process of typing out, except I think the top line should be $F(W_t)-F(0)$?