Soft: A game where players use an arbitrary structure as a guideline while trying to play identically. The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Do Symmetric Games with Nash Equilibria always have a symmetric Equilbrium?Static game questionTic-Tac-Toe Game(Infinite hat)-guessing problemWeighted War - Game of Mind and ProbabilityGame theory involving matrix determinantsOptimal stategy in 'asking for pie' game?How can Nash Equilibrium arise in real-life games?On the existence of an equivalent behavioral/mixed strategyCan a game theory strategy go in an endless loop?
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Soft: A game where players use an arbitrary structure as a guideline while trying to play identically.
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Do Symmetric Games with Nash Equilibria always have a symmetric Equilbrium?Static game questionTic-Tac-Toe Game(Infinite hat)-guessing problemWeighted War - Game of Mind and ProbabilityGame theory involving matrix determinantsOptimal stategy in 'asking for pie' game?How can Nash Equilibrium arise in real-life games?On the existence of an equivalent behavioral/mixed strategyCan a game theory strategy go in an endless loop?
$begingroup$
The following two player game is an (inadequate) attempt to capture an idea I am very interested in exploring. If any of the learned folks here recognize the problem I'm playing with and can point me in the right direction for study, I would greatly appreciate it.
We start with a set. This can be anything.
Both players choose an element from the set without showing the other.
After both have picked, they reveal their chosen elements to each
other. If they are not the same element, they repeat the process. If
they are the same element, they have won after $t$ turns.
Players don't communicate beforehand.
They are allowed random choices in their strategies.
Players would like to minimize $E[t]$.
The game is intended to be set up so that players end up following the same
strategy if they don't make any arbitrary choices while selecting
their strategy. E.g. if the elements of the set are just the points
contained by a circle, they can't both arrive at "pick [some arbitrary
point in the circle]" as their strategy, but they may arrive at "pick
the center" as their strategy.
soft-question game-theory symmetry
asked Apr 7 at 21:03
rbrowserbrowse
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
The following two player game is an (inadequate) attempt to capture an idea I am very interested in exploring. If any of the learned folks here recognize the problem I'm playing with and can point me in the right direction for study, I would greatly appreciate it.
We start with a set. This can be anything.
Both players choose an element from the set without showing the other.
After both have picked, they reveal their chosen elements to each
other. If they are not the same element, they repeat the process. If
they are the same element, they have won after $t$ turns.
Players don't communicate beforehand.
They are allowed random choices in their strategies.
Players would like to minimize $E[t]$.
The game is intended to be set up so that players end up following the same
strategy if they don't make any arbitrary choices while selecting
their strategy. E.g. if the elements of the set are just the points
contained by a circle, they can't both arrive at "pick [some arbitrary
point in the circle]" as their strategy, but they may arrive at "pick
the center" as their strategy.
soft-question game-theory symmetry
asked Apr 7 at 21:03
rbrowserbrowse
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
This is basically the coordination game? See this
$endgroup$
– Don Thousand
Apr 7 at 21:09
$begingroup$
Sort of, but I'm thinking of the game as being based on some object (in my question, a set) and interested in characterizing that object by how two players of the corresponding game can find symmetries in the object and play the coordination game optimally, if that makes any sense.
$endgroup$
– rbrowse
Apr 7 at 21:30
add a comment |
$begingroup$
The following two player game is an (inadequate) attempt to capture an idea I am very interested in exploring. If any of the learned folks here recognize the problem I'm playing with and can point me in the right direction for study, I would greatly appreciate it.
We start with a set. This can be anything.
Both players choose an element from the set without showing the other.
After both have picked, they reveal their chosen elements to each
other. If they are not the same element, they repeat the process. If
they are the same element, they have won after $t$ turns.
Players don't communicate beforehand.
They are allowed random choices in their strategies.
Players would like to minimize $E[t]$.
The game is intended to be set up so that players end up following the same
strategy if they don't make any arbitrary choices while selecting
their strategy. E.g. if the elements of the set are just the points
contained by a circle, they can't both arrive at "pick [some arbitrary
point in the circle]" as their strategy, but they may arrive at "pick
the center" as their strategy.
soft-question game-theory symmetry
asked Apr 7 at 21:03
rbrowserbrowse
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
The following two player game is an (inadequate) attempt to capture an idea I am very interested in exploring. If any of the learned folks here recognize the problem I'm playing with and can point me in the right direction for study, I would greatly appreciate it.
We start with a set. This can be anything.
Both players choose an element from the set without showing the other.
After both have picked, they reveal their chosen elements to each
other. If they are not the same element, they repeat the process. If
they are the same element, they have won after $t$ turns.
Players don't communicate beforehand.
They are allowed random choices in their strategies.
Players would like to minimize $E[t]$.
The game is intended to be set up so that players end up following the same
strategy if they don't make any arbitrary choices while selecting
their strategy. E.g. if the elements of the set are just the points
contained by a circle, they can't both arrive at "pick [some arbitrary
point in the circle]" as their strategy, but they may arrive at "pick
the center" as their strategy.
soft-question game-theory symmetry
soft-question game-theory symmetry
asked Apr 7 at 21:03
rbrowserbrowse
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 7 at 21:03
rbrowserbrowse
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 7 at 21:03
rbrowserbrowse
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 7 at 21:03
rbrowserbrowse
82
asked Apr 7 at 21:03
rbrowserbrowse
82
82
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
rbrowse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
This is basically the coordination game? See this
$endgroup$
– Don Thousand
Apr 7 at 21:09
$begingroup$
Sort of, but I'm thinking of the game as being based on some object (in my question, a set) and interested in characterizing that object by how two players of the corresponding game can find symmetries in the object and play the coordination game optimally, if that makes any sense.
$endgroup$
– rbrowse
Apr 7 at 21:30
add a comment |
1
$begingroup$
This is basically the coordination game? See this
$endgroup$
– Don Thousand
Apr 7 at 21:09
$begingroup$
Sort of, but I'm thinking of the game as being based on some object (in my question, a set) and interested in characterizing that object by how two players of the corresponding game can find symmetries in the object and play the coordination game optimally, if that makes any sense.
$endgroup$
– rbrowse
Apr 7 at 21:30
1
1
$begingroup$
This is basically the coordination game? See this
$endgroup$
– Don Thousand
Apr 7 at 21:09
$begingroup$
This is basically the coordination game? See this
$endgroup$
– Don Thousand
Apr 7 at 21:09
$begingroup$
Sort of, but I'm thinking of the game as being based on some object (in my question, a set) and interested in characterizing that object by how two players of the corresponding game can find symmetries in the object and play the coordination game optimally, if that makes any sense.
$endgroup$
– rbrowse
Apr 7 at 21:30
$begingroup$
Sort of, but I'm thinking of the game as being based on some object (in my question, a set) and interested in characterizing that object by how two players of the corresponding game can find symmetries in the object and play the coordination game optimally, if that makes any sense.
$endgroup$
– rbrowse
Apr 7 at 21:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I think there is nothing specifically like this in the game theoretic literature. The reason is that the game you are describing has a trivial Nash equilibrium:
Whatever the set, both pick the same element immediately, thus minimizing $t$.*
What you describe is different from a coordination game where the players have preferences over the elements in the set, not over the time it takes to reach "agreement" as here. In your game, players don't care which element is chosen as long as there is agreement. In the typical coordination games there is usually a twist, say for set $(a,b)$, player 1 would prefer both to select $a$ while player 2 would prefer both to select $b$, inducing a small conflict of interest.
*How can they pick the same element from the set without prior communication you might ask? This is part of a Nash equilibrium, which requires all players to correctly guess the strategy of the opponent and best respond to it.
The most relevant topic for you, therefore, seems not to be what the equilibria are, but which of the many available ones is selected; i.e., the topic of equilibrium selection. Thomas Schelling did some work on that decades ago invoking the notion of "focal points". There is more recent work employing notions of risk dominance etc.
answered Apr 8 at 12:09
NamelessNameless
2,7531333
$endgroup$
add a comment |
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$begingroup$
I think there is nothing specifically like this in the game theoretic literature. The reason is that the game you are describing has a trivial Nash equilibrium:
Whatever the set, both pick the same element immediately, thus minimizing $t$.*
What you describe is different from a coordination game where the players have preferences over the elements in the set, not over the time it takes to reach "agreement" as here. In your game, players don't care which element is chosen as long as there is agreement. In the typical coordination games there is usually a twist, say for set $(a,b)$, player 1 would prefer both to select $a$ while player 2 would prefer both to select $b$, inducing a small conflict of interest.
*How can they pick the same element from the set without prior communication you might ask? This is part of a Nash equilibrium, which requires all players to correctly guess the strategy of the opponent and best respond to it.
The most relevant topic for you, therefore, seems not to be what the equilibria are, but which of the many available ones is selected; i.e., the topic of equilibrium selection. Thomas Schelling did some work on that decades ago invoking the notion of "focal points". There is more recent work employing notions of risk dominance etc.
answered Apr 8 at 12:09
NamelessNameless
2,7531333
$endgroup$
add a comment |
$begingroup$
I think there is nothing specifically like this in the game theoretic literature. The reason is that the game you are describing has a trivial Nash equilibrium:
Whatever the set, both pick the same element immediately, thus minimizing $t$.*
What you describe is different from a coordination game where the players have preferences over the elements in the set, not over the time it takes to reach "agreement" as here. In your game, players don't care which element is chosen as long as there is agreement. In the typical coordination games there is usually a twist, say for set $(a,b)$, player 1 would prefer both to select $a$ while player 2 would prefer both to select $b$, inducing a small conflict of interest.
*How can they pick the same element from the set without prior communication you might ask? This is part of a Nash equilibrium, which requires all players to correctly guess the strategy of the opponent and best respond to it.
The most relevant topic for you, therefore, seems not to be what the equilibria are, but which of the many available ones is selected; i.e., the topic of equilibrium selection. Thomas Schelling did some work on that decades ago invoking the notion of "focal points". There is more recent work employing notions of risk dominance etc.
answered Apr 8 at 12:09
NamelessNameless
2,7531333
$endgroup$
add a comment |
$begingroup$
I think there is nothing specifically like this in the game theoretic literature. The reason is that the game you are describing has a trivial Nash equilibrium:
Whatever the set, both pick the same element immediately, thus minimizing $t$.*
What you describe is different from a coordination game where the players have preferences over the elements in the set, not over the time it takes to reach "agreement" as here. In your game, players don't care which element is chosen as long as there is agreement. In the typical coordination games there is usually a twist, say for set $(a,b)$, player 1 would prefer both to select $a$ while player 2 would prefer both to select $b$, inducing a small conflict of interest.
*How can they pick the same element from the set without prior communication you might ask? This is part of a Nash equilibrium, which requires all players to correctly guess the strategy of the opponent and best respond to it.
The most relevant topic for you, therefore, seems not to be what the equilibria are, but which of the many available ones is selected; i.e., the topic of equilibrium selection. Thomas Schelling did some work on that decades ago invoking the notion of "focal points". There is more recent work employing notions of risk dominance etc.
answered Apr 8 at 12:09
NamelessNameless
2,7531333
$endgroup$
I think there is nothing specifically like this in the game theoretic literature. The reason is that the game you are describing has a trivial Nash equilibrium:
Whatever the set, both pick the same element immediately, thus minimizing $t$.*
What you describe is different from a coordination game where the players have preferences over the elements in the set, not over the time it takes to reach "agreement" as here. In your game, players don't care which element is chosen as long as there is agreement. In the typical coordination games there is usually a twist, say for set $(a,b)$, player 1 would prefer both to select $a$ while player 2 would prefer both to select $b$, inducing a small conflict of interest.
*How can they pick the same element from the set without prior communication you might ask? This is part of a Nash equilibrium, which requires all players to correctly guess the strategy of the opponent and best respond to it.
The most relevant topic for you, therefore, seems not to be what the equilibria are, but which of the many available ones is selected; i.e., the topic of equilibrium selection. Thomas Schelling did some work on that decades ago invoking the notion of "focal points". There is more recent work employing notions of risk dominance etc.
answered Apr 8 at 12:09
NamelessNameless
2,7531333
answered Apr 8 at 12:09
NamelessNameless
2,7531333
answered Apr 8 at 12:09
NamelessNameless
2,7531333
answered Apr 8 at 12:09
NamelessNameless
2,7531333
2,7531333
add a comment |
add a comment |
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rbrowse is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
This is basically the coordination game? See this
$endgroup$
– Don Thousand
Apr 7 at 21:09
$begingroup$
Sort of, but I'm thinking of the game as being based on some object (in my question, a set) and interested in characterizing that object by how two players of the corresponding game can find symmetries in the object and play the coordination game optimally, if that makes any sense.
$endgroup$
– rbrowse
Apr 7 at 21:30