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







share|improve this question




























    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







    share|improve this question


























      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







      share|improve this question















      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






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 5 hours ago

























      asked 6 hours ago









      Alessandro

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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.






          share|improve this answer





















          • 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
            4 hours ago










          • 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
            31 mins ago













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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.






          share|improve this answer





















          • 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
            4 hours ago










          • 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
            31 mins ago

















          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.






          share|improve this answer





















          • 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
            4 hours ago










          • 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
            31 mins ago















          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.






          share|improve this answer












          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.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 5 hours ago









          denesp

          12.1k32047




          12.1k32047












          • 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
            4 hours ago










          • 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
            31 mins ago




















          • 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
            4 hours ago










          • 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
            31 mins ago


















          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
          4 hours ago




          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
          4 hours ago












          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
          31 mins ago






          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
          31 mins ago




















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