## Search found 136 matches

Fri Jul 10, 2009 8:28 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Only in the cases where the rational player knows that they can play 99 to gain a better outcome then if they play 100. If a player knows they will receive a worse outcome by playing 99 over 100 then they should play 100. This does not exist. Playing 99 gives equal or better outcome than 100 in eve...
Mon Jul 06, 2009 9:18 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

99 may seem a better number, but the reason I keep 100 as the "high number" is the same reason that we need to keep a high number in the first place. if it weren't 100 it couldn't be 99 ect. Yes, I understand why you would put the limit here, but that's just not how I see it : 100 is domi...
Sun Jul 05, 2009 8:18 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Right then, sorry about that. I hadn't missed that point, but I just didn't have a good way to make a function that kept 100 as an option while choosing the option that is most "rational". I figured it out though. I made a new program which starts by giving a weight to 100, that is you de...
Sat Jul 04, 2009 1:19 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Also as far as your 102 to 200 scenario goes, it does not yield a different result if you account for the fact that you had to pay 100. If you do not account for that fact then the strategy and the situation is indeed completely different. Absolutely not. The fact that you have or haven't had to pa...
Fri Jul 03, 2009 7:57 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

don't say my results are wrong if you don't know how I arrived at them, especially if I posted how I arrived at them. Well, first of all, don't say I don't know how you arrived at your results, since I obviously know exactly what you did, and got them long before you. It just was obvious that they ...
Fri Jul 03, 2009 10:36 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

then I devided each payout by the sum of all the payouts and multiplied by 100 to get the new percent. weighting each number by the amount it would get using the last strategy. Ok, that's where the method fails. This was the first thing I tried, but you can notice it is wrong because in a stable st...
Thu Jul 02, 2009 8:36 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

well I can't quite figure out how to post the graph, but I can describe it to you. Well, I am really curious to know what exactly you did here. I actually did this kind of thing at the beggining of this thread. Changing the strategy at each step to maximize profit against the strategy of the previo...
Fri Jun 26, 2009 2:03 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Re:

If your know your opponent can only play some thing in the set [2,97]U{100} then 100 is a suboptimal play for you because 99 is at least as good and sometimes better than 100 for every choice in that set. That is true if 99 is still in our range. Chen said If our set was, for some reason [2, 97] U ...
Fri Jun 26, 2009 8:40 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

"Restricted to [2,n]" simply means that any option other than those between (and including) 2 and n have been eliminated. It does not imply that every option between 2 and n is definitely valid. In other words, the definition of "restricted" means that, if in fact Q can only pla...
Thu Jun 25, 2009 6:20 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

"Restricted to [2,n]" simply means that any option other than those between (and including) 2 and n have been eliminated. It does not imply that every option between 2 and n is definitely valid. In other words, the definition of "restricted" means that, if in fact Q can only pla...
Thu Jun 25, 2009 2:45 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Those of you who think there is no solution to this problem: please show me your proofs that rational players will not play 2. I have graciously provided proofs that they cannot play anything else for you, but I don't know for what reasons they would not play this either. I do know that our definit...
Thu Jun 25, 2009 10:31 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Jedaz wrote:How about a game of 2 players who chose either 1 or 2 and if they get nothing if they pick the same, but win if they pick differently. Ie: with the payoff table of

Code: Select all

     1      21  {0,0}  {1,1}2  {1,1}  {0,0}
Playing 1 or 2 with equal probability is a Nash equilibrium in this game.
Thu Jun 25, 2009 6:28 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

(...)two players pick three non negative numbers that sum to 1, one of those three is randomly picked for each player, and the person with the higher number wins. So, for instance, if you pick (1/3, 1/3, 1/3) and I pick (1/4, 1/4, 1/2) then you win 2/3rds of the time, but if I went with (1/5, 2/5, ...
Wed Jun 24, 2009 4:07 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Not when the game can only be played in a finite number of possible ways. However, there are games where there isn't a nash equilibrium. Is there a way to prove that this is not possible in a game with a finite number of options ? One that (probably) doesn't, which has a lot more interesting struct...
Wed Jun 24, 2009 1:58 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Yat: Here is the new payoff matrix. As you can see, there are two deterministic Nash equilibria ({2,3} and {3,2}) and 1 mixed equilibrium (50/50 on the deterministic equilibria). Thus, we don't have enough information to determine what they will play (and neither do they). I believe the reasoning c...
Tue Jun 23, 2009 1:55 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

AvalonXQ, it would help me to know how your detailed argument would end in a slightly different problem (I mean, the rules are slightly different. The problem itself may lead to totally different conclusions). The only difference would be that in the particular case where both players play 2, they b...
Sun Jun 21, 2009 10:32 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Jedaz: Changing the question doesn't change the answer to the original problem. A person that says "I'll play the strategy that does best against an average human being" will fail miserably when they are playing a rational person who knows that they will play this strategy. Wait... what ?...
Sun Jun 21, 2009 10:15 am UTC
Forum: Logic Puzzles
Topic: Spider
Replies: 23
Views: 7433

### Re: Spider

I see you are stuck on this one... If you give me a clue about the bear, I give you a clue about the spider !

Just kidding

Spoiler:
Unfold the room, everything will become straight forward.
Thu Jun 18, 2009 2:06 pm UTC
Forum: Logic Puzzles
Topic: Tournament problem
Replies: 7
Views: 1379

### Re: Tournament problem

This is simply a sorting problem. Any sorting algorithm using comparisons must make at least N*log2(N) comparisons in the worst case. Use mergesort to achieve this lower bound. This figure is high in the case of N=4. Consider that you can sort them in 5 comparisons, (first sort three with three com...
Thu Jun 18, 2009 2:00 pm UTC
Forum: Logic Puzzles
Topic: Tournament problem
Replies: 7
Views: 1379

### Re: Tournament problem

This is simply a sorting problem. Any sorting algorithm using comparisons must make at least N*log2(N) comparisons in the worst case. Use mergesort to achieve this lower bound. That's true, merge gives same worst case scenario as the algorithm I proposed. However, Nlog2(N) gives an idea of the comp...
Thu Jun 18, 2009 11:17 am UTC
Forum: Logic Puzzles
Topic: Tournament problem
Replies: 7
Views: 1379

### Re: Tournament problem

It seems like it should just be the number of losers in a single-elimination tournament, that is, n-1. (The same can be seen if you look at a tournament like a single pass of bubble sort.) This would be enough to determine the winner, but I don't think that's the question. If we need to get the who...
Wed Jun 17, 2009 10:52 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Well, I see this thread is still going. Yakk, I certainly would not want to start arguing with you again, but I would just like you to set things strait for me, as I am still trying to understand what you are trying to explain here. In your post, you say that : if "game G" with "playe...
Thu Jun 04, 2009 5:14 pm UTC
Forum: Logic Puzzles
Topic: Crossing the desert
Replies: 22
Views: 6412

### Re: Crossing the desert

Nice...
Cutting in quarters was actually more efficient than cutting in thirds. Puck, you screwed up big time !
Thu Jun 04, 2009 5:05 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Ooooops ! I missed something quite important in your post ! It is quite possible that the answer to the question is "there is no way to answer this question, you need to specify more information". There we go... not only it is quite possible, but it is actually the case. I am surprised you...
Thu Jun 04, 2009 4:51 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

If you ask two perfectly rational players what is their favorite color, would the situation be symetrical ? Would they have to answer the same thing ? No, assuming the colours are symmetric with respect to the question asked and the properties of the players described. Everything is said in the que...
Thu Jun 04, 2009 4:07 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Yakk, please present your proof that any two players who are "perfectly rational" (standard English definition) will use identical choice algorithms. Well, as he seems to be a perfectly rational player, his strategy seems to imply never answering this question, except with a "I have ...
Thu Jun 04, 2009 3:41 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Yakk, you can assume the problem is symetrical all you want, it stays an assumtion. There is no symetry to be broken. Both players re perfectly rational, but this does not imply symetry. Or you would have to prove it. If you ask two perfectly rational players what is their favorite color, would the ...
Thu Jun 04, 2009 3:22 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

One such assumption might be "My playing 99 has no logical implication on my opponent playing 100 with 100% probability". Or even "what strategy I generate has no logical implication on my opponent's strategy." That is not an assumption, that is a fact. The only thing which has ...
Thu Jun 04, 2009 2:59 pm UTC
Forum: Logic Puzzles
Topic: Crossing the desert
Replies: 22
Views: 6412

### Re: Crossing the desert

I got a solution with 4 planes. Let's call A, B, C and D. The airport is at longitude 0 on the equator, planes stay on the equator at all times. a plane can travel 1/6 of the equator length in one time unit. A(60,1/3) means plane A is at longitude 60 with 1/3 its maximum fuel load. t=0 :...
Thu Jun 04, 2009 9:01 am UTC
Forum: Logic Puzzles
Topic: Crossing the desert
Replies: 22
Views: 6412

### Re: Crossing the desert

It's like taking the bananas problem backwards. Here the goal is to cross the desert with the less fuel possible, so instead of starting by moving all the bananas from the starting point, we start by determining how the truck will end its journey : the last 500 miles can be done with one load, so th...
Wed Jun 03, 2009 9:51 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

As stated before, I certainly won't bother answering to everything, but that does not mean what you say makes sense. Let me just stress this once again ... Any two players playing a one-shot game with identical strategy choice algorithms will produce the same strategy up to symmetry. Is that a false...
Wed Jun 03, 2009 8:49 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Yakk, you obviously confused Puck and me somewhere, but it does not matter, the reasonning which leads to both players playing 2 makes sense (which does not mean I agree with it), whereas yours don't. So, as a reminder, Puck says the answer is 2, I say logic cannot provide us with another answer tha...
Wed Jun 03, 2009 10:34 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Of the above, 99$gives an expected return of$10.1. Given a more complex model of the other player's expected choices, you can get different results. Well, I am aware of the way to evaluate the expected return of any given strategy against any other strategy or itself, but thank you. What's your p...
Tue Jun 02, 2009 5:15 pm UTC
Forum: Logic Puzzles
Topic: Camels and Bananas
Replies: 27
Views: 5904

### Re: Camels and Bananas

Yes I suspected both solutions were the same, only in a different order. Now, for 1000, if I apply the same method... First, the camel brings 1000 999 bananas cargos at kilometer 1, using each time one banana to go and one to come back, except the last time where it does not come back. That leaves i...
Tue Jun 02, 2009 10:44 am UTC
Forum: Logic Puzzles
Topic: Camels and Bananas
Replies: 27
Views: 5904

### Re: Camels and Bananas

I was too lazy to verify your day count or to look for the differences between your method and mine, but I get a better ratio. First, you take 15/4 days to bring 8 load of 4 bananas at distance 1. The camel is then at distance 1 with 17 bananas. Leave one there, and now take 7/4 days to bring 4 load...
Tue Jun 02, 2009 9:06 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

A Nash equilibrium is a strategy in which other players will be worse off if they deviated from the strategy. Or more precisely, won't be better. Whatever. An auto-strategy does not allow deviation of one player from the other. Yes, but this is an assumption based on super rationality, which is her...
Fri May 15, 2009 9:49 am UTC
Forum: Logic Puzzles
Topic: Irrational Function
Replies: 78
Views: 8262

### Re: Irrational Function

$\pi=4\int_{0}^{1}\sqrt{1-x²}dx$
Tue May 12, 2009 5:15 pm UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

No, I proved that S(k)>0 was non-optimal. Read again how I define S k '. If E(k-1)>E(k), S k (k) does not need to be 1 to make it a bad choice. The meaning of my demonstration is that, if you know your opponent uses a strategy when k is the maximum value he can play (he can play, not he will play, t...
Tue May 12, 2009 8:47 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

Yakk, I would go further than AvalonXQ : not only S(2)=1 is an optimal auto strategy, (or a Nash equilibrium if you want to use proper terms) but it is the only one too. So, the "ideal auto-strategy' you are talking about is S(2)=1. You just put in other words the problem which is here since th...
Mon May 11, 2009 8:21 am UTC
Forum: Logic Puzzles
Topic: Traveler's Dilemma
Replies: 833
Views: 88613

### Re: Traveler's Dilemma

GMontag, you obviously did not read the whole thread, but let me point out the obvious flaw in your logic : the only way you can assume that two perfectly rational players will have to come up with the same strategy is to assume first that there actually exist an objectively optimal strategy. As thi...