GTO-7-04: The Core

[@julianocamargo6674]

The core is just the feasible set of a system of inequalities. I find this representation much easier to understand. If some equations contradict each other, the set may be empty. Same as in linear algebra. If the feasible set is not empty, most likely it will not be 'unique', that is, it will not consist of a single point, it will define a polytope in space.

[@julianocamargo6674]

The core is the feasible set of a system of inequalities, as many people have seen in linear algebra. We must also add the equality xA + xB + xC + xD = 100 and all the subset constraints : xA + xB >= 100, xA + xC >= 100 and so on. With this representation, it is clear why the core can be empty: conflicting constraints may cause the system not to be solvable. If not empty, typically it will be a region in space (a polytope). The feasible set will consist of a single point only in degenerate cases.

[@cralix85]

Jackson explains better ... hope he can do all the serie !!

[@yaakovbendovid3253]

I don't understand how B, C and D (a winning coalition) could receive less than $100 million when a winning coalition either gets $100 million or nothing, according to the definition of a simple game. Am I wrong somewhere? Please help.

[@mitanim3519]

don't understand the Shapley value calculation !!!

[@julianocamargo6674]

Watch the other video about it

[@yaakovbendovid3253]

Disregarding the payoff vector x, which could be the real world reason for B receiving the same payoff as C and D? You say this payoff is fair. Is B maybe realising his full potential only in the sub coalition?

[@SG-lj8uu]

Great video

[@knguyen1294]

this makes no sense. Why is the second player shapley value is equal to third and fourth player. That would make the coalition unfair and second player's value actually got smaller in a coalition In addition, I'm not sure about this but if player 1's shapely value is 50 out of 100 and 51 is required to win. Does that make the player 1 a veto player. But a coalition between 2, 3 and 4 still work

[@harveyspecter3361]

The game is a simple game so only when 51 is reached, the coalition will be worth something. That is the case for when A with any other party or all minority parties join. Hence, they all have the same contribution for when v(S)=100.

[@HH-ut2du]

Harvey Specter the way i calculated it is as following. We have actually 24 Grand coaltions of ABCD. 6 starting with A, 6 starting with B. Etc. That gives you N! = 24 To calculate shapley v. You follow each combination taking votes from the first (in the case of calition ABCD :45 from A, then 6 only from B and zero from C and zero from D)enough votes from the second, as you have reached the 51 percent votes. Or, if the combination is DCBA 15 out of 15 from D, Then 15 out of 15 from C and the remaining 21 from B and nothing from A,... After doing this, you add the votes in each column A, B, C, and D. You calculate the average over coalitions by dividing the sum of each column by 24. You devide by 51 and you multiply by 100. I’ve gotten following this (45; 24.8; 15.03; 15.03) Can someone tell me how am i wrong? Thank you

[@julianocamargo6674]

You don't add the number of votes. If A is alone, it makes nothing. If it receives B in sequence, B is critical for winning and B should score fully the 100 in that permutation. Of course when you consider all 24 permutations, in most of them A was determinant for winning. This is why A makes 50%. The others get 16.67%. Notice it does not matter if you have 15 votes or 25 votes in this scenario, either would do for reaching the necessary number of votes (they are interchangeable).

[@gonzerlax3696]

Actually, i don't understand why shapley value's 50,16.67,16.67,16.67 because I got 23,12.67,7.67,7.67 .

[@fz91425]

+Eint Sandi gonzerlax Aung i got the same results because the grand coalition is 51, but for the results in the video he assumed that the grand coalition is 100 i don't understand why !!!?

[@limessuperior3066]

Guys, easy... because the value of the coalition is the gain of 100 billion dollars. the 51 percent is just for giving you information about which coalitions assume a payout. once they are over the 51%, the payout of the coalition is 100, so v({S})=100. those coalitions that have less then 51 votes, have payout v({S})=0. at the end all the shaplay values have to sum up to 100, so even in the case of 51, your payout vector (23,12.67,7.67,7.67) is wrong, because its sum is not 51.

[@lauramarianella]

Hard to understand...

[@groovyrabbits3122]

you are like a robot. I can not listen to the robot. You are not a robot.

[@alenpavlovic]

If you ask me, bad explanation .