MHB Proving Independence of Axioms in Game Theory: A Case Study

  • Thread starter Thread starter crobertson0308
  • Start date Start date
  • Tags Tags
    Axioms Independence
crobertson0308
Messages
1
Reaction score
0
I have four axioms and I am stuck trying to prove the independence of these axioms.

Axiom 1: Each game is played by two distinct teams.
Axiom 2: There are at least four teams.
Axiom 3: Exactly six games are played.
Axiom 4: Each distinct team played once against the same team.

I've justified both Ax 4 and 3 are independent but need help justifying the other two axioms
 
Physics news on Phys.org
Hi,
Here is a set of models that prove the independence. I leave it to you to verify that each is actually a model.

2csausi.png
 
Would the undefined terms be elements(teams, game)...relation(is, are)?
 
I need to create three theorems that follow from the four axioms. One theorem I came up with was if there are exactly four teams, then each team plays exactly three games. I'm having trouble coming up with another two. The only path I'm seeing is increasing the number of teams and seeing what happens with the models.
 
msalamon said:
I need to create three theorems that follow from the four axioms. One theorem I came up with was if there are exactly four teams, then each team plays exactly three games. I'm having trouble coming up with another two. The only path I'm seeing is increasing the number of teams and seeing what happens with the models.

What did you get as the undefined terms?
 
For the objects: game(s), team(s)
For the relations: is, are, and I wasn't sure of played should be considered a relation or not

- - - Updated - - -

Pardon my typo; of should be if.
 
Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...

Similar threads

Replies
1
Views
1K
Replies
3
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
Replies
7
Views
11K
Replies
14
Views
2K
Replies
7
Views
2K
Back
Top