Automated Mechanism Design

1. Automated Mechanism Design Tuomas Sandholm Presented by Dimitri Mostinski November 17, 2004

2. Mechanism Design • Art of designing the rules of thegame (aka. mechanism) so that a desirable outcome (according to a givenobjective) is reached despite the fact that each agent acts in his own selfinterest • Some examples of applications • Auctions • Voting protocols • Divorce settlement procedures • Collaborative rating systems

3. Manual Mechanism Design • Traditional approach to mechanism design • Good design is hypothesized based on designers experience and intuition and then desirable properties are proven formally • Over last 40 years a small number of canonical mechanisms were created, each designed for a class of settings and a specific objective

4. Problems with Manual MD • The most famous and most broadly applicable general mechanisms, VCGand dAGVA, only maximize social welfare • The general mechanisms that do focus on a self-interested designer are onlyapplicable in very restricted settings • The designer mayalso be interested in the outcomeper se • It is often assumed that side payments can be used to tailor the agents' incentives,but this is not always practical • The most common mechanismsassume that the agents have quasilinear preferencesui(o; p1, ..,pN) = vi(o)− pi

5. Impossibility Results • Traditional research has yielded a number of impossibility results of the form “no mechanism works across a class of settings” for different definitions of “works” and different classes of settings. • E.g. Gibbard-Satterthwaite theorem states that for the class of general preferences,no mechanism exists where • an outcome outcome canbe any one of at least three candidates • the mechanism is nondictatorial • truth telling is a dominant strategy for all agents

6. Automatic Mechanism Design (AMD) • A novel approach to mechanism design proposed by Conitzer and Sandholm in 2002 • Mechanismis computationally created for the specic problem instance athand

7. Advantages of AMD • It can be used in settings beyond the classes of problems that have beensuccessfully studied in manual mechanism design to date • It can allow one to circumvent the impossibility results by considering an instance of the class not the class itself • It can yield mechanisms that produce better results and are harder to manipulate by using the information that the mechanism designer has about the agents‘preferences • It shifts the burden of mechanism design from humans to a machine.

8. AMD formalism • Am automatic mechanism design setting is • A finite set of outcomes O • A finite set of N agents • For each agent I • A finite set of types Qi • A probability distribution gi over Qi • A utility function ui : Qi x O  R • An objective function whose expectation the designer wishes to maximizeg(o; p1, ..,pN)

9. More AMD formalism • A mechanism consists of • An outcome selection function o : Q1x .. x QN O if it is deterministic • A distribution selection function p : Q1x .. x QN P(O) if it is randomized • For each agent i a payment selection function pi: Q1x .. x QN R if it involves payments

10. Individual Rationality • An agent must never be worse off by participating in the mechanism • Types of Individual Rationality • Ex antethe agent would participate if it knewnothing at all (not even its own type) • Ex interimthe agent would always participate if it knewonly its own type • Ex postthe agentwould always participate even if it knew everybody's type • In an AMD setting with an IR constraint there exists a fallback outcome o0 such that for every agent iui(qi,o0) = 0

11. Incentive Compatibility • The agents should never have an incentiveto misreport their type • Two most commonsolution conceptsare • implementation in dominant strategies • Truth telling is the optimal strategy even if all other agents’ types are known • implementation in Bayesian Nash equilibrium • Truth telling is the optimal strategy if other agents’ types are not yet known, but they are assumed to be truthful

12. Formally the AMD problem • Given • Automated mechanism design setting • An IR notion (ex interim, ex post, or none) • A solution concept (dominant strategies or Bayesian Nash equilibrium) • Possibility of payments and randomization • A target value G • Determine • If there exists a mechanism of the specified type that satisfies both the IR notion and the solution concept, and gives an expected value of at least G for the objective.

13. Complexity results • Consider a case of only one agent • The two discussed IR options coincide here • The two solution concepts coincide as well • Proving hardness for this case would imply lower bound on the general problem • AMD is NP-hard (by reduction to MINSAT) if • Payments are not allowed • Payments are allowed but the designer is looking for something other than social welfare maximization • AMD can be solved in (expected) polynomial time using randomized algorithm for LP problems • If the input is structured in a way that it can be concisely communicated it can also be faster processed

14. An example

15. Some results of AMD • It reinvented the Myerson auction which maximizes the seller's expected revenue in a 1-object auction • It created expected revenue maximizing combinatorial auctions • It created optimal mechanisms for a public good problem (deciding whether or not to build a bridge) • It created optimal mechanisms for public goods problems with multiple goods

16. Conclusion • Automated mechanism design is a brand new area of research • The problems that were long studied for manual mechanism design can all be applied to AMD