Classical game theory is descriptive. It takes the “rules of the game” as given and tries to predict how self-interested agents will behave within those rules. The typical outcome of such analysis is the identification of an equilibrium.

Mechanism design inverts the problem. Instead of asking what behavior will result from a given set of rules, it asks what set of rules (mechanism) will induce a behavior that will lead to a desired outcome. The Mechanism Designer begins with a social outcome that should be implemented based on the players’ private information. The task is to define the mechanism such that when rational agents play this game, their self-interested equilibrium behavior precisely implements the designer’s desired outcome. An auction is an example of a mechanism. The design of an auction depends on the desired goal (e.g., economic efficiency or revenue maximization). The players’ private information is their valuation of the good being auctioned.

Mechanism design exists because of information asymmetry: agents have private information, that the designer cannot directly observe. The designer wants to implement the desired outcome, but must first get agents to reveal the true private information. Since agents act strategically, they may lie if it benefits them. The mechanism must solve two problems (1) getting agents to truthfully reveal information. (2) using the reported information to choose an outcome.

Constrasting with standard algorithmic design. In standard algorithmic design, the input $x$ is assumed to be given and passive. The goal is to design an algorithm $f$ that efficiently computes the desired output f(x). In mechanism design, the inputs themselves are strategic. The agent with its true private information is a rational entity. The mechanism designer proposes a function f(•) that maps the reported private information (input) to outcomes. The agent observes f(•) and strategically chooses which input to provide. Therefore, the “engineering” challenge is not just to design a function that computes the correct output given the true inputs, but to design a function that is robust to input manipulation.