Focal points. Previous title: without "subject"

[Fioravante Patrone1]

Consider the following game in strategic form:


$(( I \ \\ \ II \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \vdots,\text{Crevari},\text{Coronata},\text{S. Ilario},\text{Sapello}),(\ldots,\ldots,\ldots,\ldots,\ldots),(\ \ \ \text{Cornigliano} \ \ \ \vdots,0 \ 0,0 \ 0,1 \ 1,0 \ 0),(\ \ \ \text{Nervi} \ \ \ \ \ \ \ \ \ \ \ \vdots,1 \ 1,0 \ 0,0 \ 0,0 \ 0),(\ \ \ \ \text{Pra'} \ \ \ \ \ \ \ \ \ \ \ \ \ \vdots,0 \ 0,0 \ 0,0 \ 0,1 \ 1),(\ \ \ \text{Voltri} \ \ \ \ \ \ \ \ \ \ \ \vdots,0 \ 0,1 \ 1,0 \ 0,0 \ 0))$


I have the role of player $I$, and I have already chosen my strategy among the four that I can use.
Of course, you will eventually know my choice, but not before you choose. And we cannot communicate!

You are player $II$. Your choice?

As usual, s'il vous plait, use the spoiler to write down your choice and (which is more interesting, I guess...) the reason(s) for your choice.

Enjoy!



PS: I will give a meaningful name to the "subject" of this thread later. No clues!

[Kroldar]

You guessed the reason for what I asked about pure coordination games. In this kind of games the players have to find a common key to make their own choices without communicating. I remember some of the names of the strategies and, if I am right, the strategies of player $I$ are the names of some boroughs of Genova.
Maybe the strategies of player $II$ are the names of some sub-boroughs and among the four couples of strategies with payoff $(1,1)$ there is an only couple with the right combination of a borough and its own sub-borough. I said "maybe" because I don't know Genova (I've never been there ) but in my opinion that would be a logic explanation of the game.

[Fioravante Patrone1]

good guess...
Question: the payoff that you are going to earn, if you give the "correct" answer, is not enough to pay the effort to find it?

[Kroldar]

What?? I'm sorry... I didn't understand the question.

[Cheguevilla]

Maybe I'm feeling not so glad looking that the powerful Staglieno is missing.
Sincerely, I don't understand your question, Fioravante, about the game's payoff.
Without knowing anything about the game, we also don't know anything about the payoff, I mean, what does this "1" represent for us?
Obviously, it should be related to the game, but it could be read in two different ways:
- measurable payoff, i.e. 1 dollar.
- dichotomic payof, i.e. all or nothing.
If the payoff is one dollar, you can do it just for your fun.
If you're playing for life or death...

[marco vicari]

This is a tipical coordination game, we have multiple equilibria.
My choise is Sapello because this is the only relation i have found.
This question was considered by Schelling, he said that in a game with multiple equilibria, anything that tends to focus the players' attention on one equilibrium may make them all expect it and hence fulfill it.
Schelling called this phenomenon the focal-point effect.
The focal equilibrium is an equilibrium that has some property distinguishes it from all the other equilibria.
So you can read F. Patrone "Decisori Razionali Interagenti" pag. 52-54.

[Fioravante Patrone1]

answer to Kroldar

What I wanted to say is the following.
We have a coordination game.
From your first answer I understood that you knew how to give the "correct" answer. At least, you had a quite precise idea of the kind of information that you needed (in your opinion) for the answer.
But you did not choose your strategy.
So, I interpreted this fact as I said: the "payoff" that you get from the game (a "moral" payoff... ?) is not big enough to convince you to make the effort which is needed to collect the information that would allow you to say your ("correct") choice.

I hope I was clearer, now. If not, I will try again!

[Fioravante Patrone1]

answer to marco vicari

easy: you are correct (and thanks for the advertising!)

[Fioravante Patrone1]

answer to Cheguevilla

"Sincerely, I don't understand your question, Fioravante, about the game's payoff.
Without knowing anything about the game, we also don't know anything about the payoff, I mean, what does this "1" represent for us?
Obviously, it should be related to the game, but it could be read in two different ways:
- measurable payoff, i.e. 1 dollar.
- dichotomic payof, i.e. all or nothing.
If the payoff is one dollar, you can do it just for your fun.
If you're playing for life or death..."

This is a game, not a game form.
So, the payoffs "1" and "0" are just values of your (and mine) utility function.
As usual, I assume that they are vNM utility functions. I would say that in this case they could be just be ordinal utility functions (I mean, the only relevant information is that you p$efer outcomes whose utility value is $1$ to outcomes whose utility value is $0$).

[Kroldar]

You have been very clear, thanks. And you also guessed right: I think it would be impossible for me to make a good choice... I know few things about the boroughs of Genova and I don't know an easy way to get enough informations.

[Fioravante Patrone1]

The given game is in strategic form.
$X=${Cornigliano, Nervi, Pra', Voltri}
$Y=${Crevari, Coronata, S. Ilario, Sapello}
The payoff functions are described via the matrix, which is a quite good way of doing it...

Of course the given game has 4 Nash equilibria.

But a Nash equilibrium is a couple of strategies.
So, knowing which are the Nash equilibria for this game is clueless for "you", the player $II$.

Why is it so easy for me and Cheguevilla to land safely on a Nash equilibrium, while for Kroldar it is something not easy at all?

Is it something that has nothing to do with Game Theory?
The standard model of a game in strategic form is, so, missing something relevant? What?
Instead of describing a game, in strategic form, as $(X,Y,f,g)$, should we add something? We need $(X,Y,f,g,...)$? If yes, for what dots stand for???

[Kroldar]

"Fioravante Patrone":
Why is it so easy for me and Cheguevilla to land safely on a Nash equilibrium, while for Kroldar it is something not easy at all?

You live in Genova and I don't.

"Fioravante Patrone":
Is it something that has nothing to do with Game Theory?
The standard model of a game in strategic form is, so, missing something relevant? What?
Instead of describing a game, in strategic form, as $(X,Y,f,g)$, should we add something? We need $(X,Y,f,g,...)$? If yes, for what dots stand for???

I can't formalize what I mean, but the thing that's missing is the knowledge of some information about the context where players really play the game. I also think that gathering information is the first step to describe a game.

[Cheguevilla]

I fear that now, also for me and Fioravante, it's impossible to reach a Nash equilibrium.
Mainly because the game is missing in the target of players choice. I mean, if I was player X, what should make me choice a neighbor instead of another?
Furthermore, the longer I see the matrix, the less I'm understanding...
The only idea I have is that

the couple Sapello - Pra is the only one where the two neighbors are themselves related.

But, I'm not sure that this is the point of Fioravante's game...

[Fioravante Patrone1]

Great!
Things are worsening, getting foggy, we feel lost in the dark.

This means that a wonderful dawn will come,
maybe tomorrow, or another day, but it will come.


We are desperately (:lol:) looking for a clue,
but the formal definition of a game and of a Nash equilibrium is completely dumb.

Shall we re-start from scratch?
Or we just need to add details to the formal model?
As I use to say, making a model more complicated is an easy exercise, always. Maybe not so fruitful, often.

[Chevtchenko]

"Fioravante Patrone":Great!
Things are worsening, getting foggy, we feel lost in the dark.

Midway upon the journey of our life
I found myself within a forest dark,
For the straightforward pathway had been lost...

[Fioravante Patrone1]

"Sandokan.": For the straightforward pathway had been lost...

I hope you share with me the opinion that it is exactly here, at this point, that a researcher's life becomes exciting, worth of all drops "produced" before

[Chevtchenko]

"Fioravante Patrone":[quote="Sandokan."] For the straightforward pathway had been lost...

I hope you share with me the opinion that it is exactly here, at this point, that a researcher's life becomes exciting, worth of all drops "produced" before[/quote]

Most certainly I do!