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I've been reading about mechanism design and the field seems a little abstract, in that I cannot ascertain whether a certain approach towards solving games falls under mechanism design.

Let me clarify with the help of a specific example of an evolutionary game.

I have a population within which agents are either mutants or incumbents. The parameters to be decided are:

  1. the fraction of the mutants ($\epsilon$)
  2. the fitness $F$ of the agents

Now, if I came up with algorithms to define/calculate the above in such a way that the population ends up being evolutionarily stable, would my solution be called a mechanism?

Thanks

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Mechanism design is basically just algorithm design, where you don't control the inputs: instead, you assume that the inputs are controlled by different agents, who each have their own set of feasible actions, and their own utility function over outcomes, and are acting to maximize their own utility (and not yours, as the mechanism designer). So you are constrained in how you can design your algorithm, because you have to design it in such a way so as to manage the incentives of the agents so that they will want to share their data with you. The classic example is designing an auction for a good in such a way so that the bidders will reveal to you how much they really value the good.

So the fundamental characteristic in mechanism design is that you have agents who will act independently of the mechanism to further their own goals. Its hard to tell from your description, but it sounds like you simply have an algorithms problem. Possibly your problem is to design an algorithm to compute an equilibrium of some sort, but this would not typically be thought of as mechanism design.

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  • $\begingroup$ I see. So mechanism design formally comes into the picture only when the algorithm has the following features: 1. It must respond to a wide class of inputs. 2. The users must have some private information that they won't be better off hiding, and the algorithm must encourage them to reveal. Of course, there might be many more features, but this is what I have gathered. Am I right? Also, is it necessary that agents share data with the designer? $\endgroup$
    – Jaidev Deshpande
    Commented Aug 14, 2012 at 3:37
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Great answer. I just want to add that the problem you posed seems to require a solution like Nash equilibrium or a Evolutionary stable strategy. That does not typically come under mechanism design. Its more basic game theory where everything (the game) is well defined and you find the equilibrium outcome. Mechanism design moves in the other way. Given you want a desirable outcome (like bidders revealing information in an auction or world peace:)), how would you design the game itself (given inputs like agents preferences, utility etc) The field of mechanism design is definitely more abstract, interesting but powerful application of game theory. (I'm an amateur student trying to learn economics, so please correct me if I'm wrong).

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