Are direct mechanisms always truthful?
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I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones.
One thing that is not clear to me is the concept of direct mechanism and its relationship with the revelation principle.
From what I got a direct mechanism is a mechanisms, in which, instead of messages, the agents report their preference/type. Are we assuming this is a truthful report?
I am asking that because the revelation principle is stated as "anything that can be accomplished by any mechanism can actually be accomplished by a direct revelation mechanism that is individual rational and incentive compatible" in this notes but as "a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function), then the same function can be implemented by an incentive-compatible-direct-mechanism (i.e. in which players truthfully report type) with the same equilibrium outcome (payoffs)." on Wikipedia.
So I don't get if truthfulness is implied by the direct mechanism or if it is an additional requirement.
game-theory mechanism-design
asked Dec 7 at 0:11
Alessandro
439421
add a comment |
up vote
3
down vote
favorite
I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones.
One thing that is not clear to me is the concept of direct mechanism and its relationship with the revelation principle.
From what I got a direct mechanism is a mechanisms, in which, instead of messages, the agents report their preference/type. Are we assuming this is a truthful report?
I am asking that because the revelation principle is stated as "anything that can be accomplished by any mechanism can actually be accomplished by a direct revelation mechanism that is individual rational and incentive compatible" in this notes but as "a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function), then the same function can be implemented by an incentive-compatible-direct-mechanism (i.e. in which players truthfully report type) with the same equilibrium outcome (payoffs)." on Wikipedia.
So I don't get if truthfulness is implied by the direct mechanism or if it is an additional requirement.
game-theory mechanism-design
asked Dec 7 at 0:11
Alessandro
439421
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones.
One thing that is not clear to me is the concept of direct mechanism and its relationship with the revelation principle.
From what I got a direct mechanism is a mechanisms, in which, instead of messages, the agents report their preference/type. Are we assuming this is a truthful report?
I am asking that because the revelation principle is stated as "anything that can be accomplished by any mechanism can actually be accomplished by a direct revelation mechanism that is individual rational and incentive compatible" in this notes but as "a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function), then the same function can be implemented by an incentive-compatible-direct-mechanism (i.e. in which players truthfully report type) with the same equilibrium outcome (payoffs)." on Wikipedia.
So I don't get if truthfulness is implied by the direct mechanism or if it is an additional requirement.
game-theory mechanism-design
asked Dec 7 at 0:11
Alessandro
439421
I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones.
One thing that is not clear to me is the concept of direct mechanism and its relationship with the revelation principle.
From what I got a direct mechanism is a mechanisms, in which, instead of messages, the agents report their preference/type. Are we assuming this is a truthful report?
I am asking that because the revelation principle is stated as "anything that can be accomplished by any mechanism can actually be accomplished by a direct revelation mechanism that is individual rational and incentive compatible" in this notes but as "a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function), then the same function can be implemented by an incentive-compatible-direct-mechanism (i.e. in which players truthfully report type) with the same equilibrium outcome (payoffs)." on Wikipedia.
So I don't get if truthfulness is implied by the direct mechanism or if it is an additional requirement.
game-theory mechanism-design
game-theory mechanism-design
asked Dec 7 at 0:11
Alessandro
439421
asked Dec 7 at 0:11
Alessandro
439421
edited Dec 7 at 0:25
asked Dec 7 at 0:11
Alessandro
439421
asked Dec 7 at 0:11
Alessandro
439421
asked Dec 7 at 0:11
Alessandro
439421
439421
add a comment |
add a comment |
1 Answer
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Incentive compatible here means that you have no incentive to lie. A direct mechanism that is not incentive compatible would entice some agents to report a false type.
answered Dec 7 at 1:09
denesp
12.2k32147
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
add a comment |
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1 Answer
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1 Answer
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up vote
3
down vote
Incentive compatible here means that you have no incentive to lie. A direct mechanism that is not incentive compatible would entice some agents to report a false type.
answered Dec 7 at 1:09
denesp
12.2k32147
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
add a comment |
up vote
3
down vote
Incentive compatible here means that you have no incentive to lie. A direct mechanism that is not incentive compatible would entice some agents to report a false type.
answered Dec 7 at 1:09
denesp
12.2k32147
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
add a comment |
up vote
3
down vote
up vote
3
down vote
Incentive compatible here means that you have no incentive to lie. A direct mechanism that is not incentive compatible would entice some agents to report a false type.
answered Dec 7 at 1:09
denesp
12.2k32147
Incentive compatible here means that you have no incentive to lie. A direct mechanism that is not incentive compatible would entice some agents to report a false type.
answered Dec 7 at 1:09
denesp
12.2k32147
answered Dec 7 at 1:09
denesp
12.2k32147
answered Dec 7 at 1:09
denesp
12.2k32147
answered Dec 7 at 1:09
denesp
12.2k32147
12.2k32147
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
add a comment |
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it?
– Alessandro
Dec 7 at 1:24
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy.
– denesp
Dec 7 at 5:44
add a comment |
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