Probability

[IlanSherer]

Hello

Can you help me please with the following question (the question is about cooperation):

In the game 2 rounds and N players.
Every player wants to maximize his profits.
If there is a player who doesn't understand the game and will play like another player, then the player who doesn't understand the game imitates another player because a player who doesn't understand the game believes that another player understands the game.
The probability that a certain player who doesn't understand the game will play in the second round like another player who played in the first round is P (for example, if a certain player who donated 7 Dollars in the first round, then the player who doesn't understand the game will donate 7 Dollars in the second round).
The payment that each player receives for 1 Dollar that he donates is (0.6 + P*0.6) Dollars (for example, if a certain player donates 4 Dollars then the same player receives 4*(0.6 + P*0.6) Dollars).
Find P as a function of N when there are N players who each receive 10 Dollars (to donate or keep for themselves) in each round, and each player receives 0.6 Dollars for every 1 Dollar that one of the players donates (for example, if a certain player donates 3 Dollars then each player including the donor receives 3*0.6 Dollars).

- Players can't use in a certain round the money they received from another round, for example, if the players received 10 Dollars in the first round then they can only use it in the first round.
- We know nothing about the players, we don't know which of them understand the game and which of them don't understand the game (maybe everyone understands the game and maybe no one understands the game), we don't know who imitates whom, we don't know which players will donate (and how much will donate) and which of the players will not donate, we know nothing about them except the information presented above.

If you didn't understand something or have questions then feel free to ask! I will be happy to answer any of your questions

Thank you so much and have a great week everyone!

 

[BigBeachBanana]

Every player wants to maximize his profits.

What is the rule of the game? How do you gain or lose?

If there is a player who doesn't understand the game and will play like another player, then the player who doesn't understand the game imitates another player because a player who doesn't understand the game believes that another player understands the game.

There's a chance that multiple players know the game well and make the same optimal donation. How can you differentiate between those who are imitating and those who are just making optimal bets?

The probability that a certain player who doesn't understand the game will play in the second round like another player who played in the first round is P (for example, if a certain player who donated 7 Dollars in the first round, then the player who doesn't understand the game will donate 7 Dollars in the second round).

Is P the amount a person donated i.e. a random variable or the probability of someone who doesn't understand the game will donate the same amount in the second round i.e. Pr(P=p)? You're confusing here.

The payment that each player receives for 1 Dollar that he donates is (0.6 + P*0.6) Dollars (for example, if a certain player donates 4 Dollars then the same player receives 4*(0.6 + P*0.6) Dollars).

You said the donated amount previously is P, now it becomes 4, then what is the P in this equation?

in each round, and each player receives 0.6 Dollars for every 1 Dollar that one of the players donates (for example, if a certain player donates 3 Dollars then each player including the donor receives 3*0.6 Dollars).

The money is coming out of who's pocket? Who's paying the players?

Is this a school assignment or a personal curiosity? Where did this question come from? Depending on your answer, you'll receive different kinds of responses. Most importantly, tell us what your thoughts are.