Game Theory, Mechanism Design, Differential Privacy (and you). . Aaron Roth DIMACS Workshop on Differential Privacy October 24. Algorithms vs. Games. If we control the whole system, we can just design an algorithm. . Algorithms vs. Games.
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Game Theory, Mechanism Design, Differential Privacy (and you).
DIMACS Workshop on Differential Privacy
A game is specified by:
for a joint strategy profile.
for the joint strategy profile excluding agent .
Agents “Behave so as to Maximize Their Utility”
An action is an (-approximate) dominant strategy if for every and for every deviation :
A joint action profile is a(n) (-approximate) dominant strategy equilibrium if for every player , is an (-approximate) dominant strategy.
Good ol’ rock. Nuthin beats that!
A joint strategy profile is a(n) (-approximate) Nash Equilibrium if for every player and for every deviation :
33% 33% 33%
which elicits reports from agents and chooses some outcome based on the reports.
Definition: A mechanism is (-approximately) dominant strategy truthful if for every agent, reporting her true valuation function is an (-approximate) dominant strategy.
Any -differentially private mechanism is also -approximately dominant strategy truthful [McSherry + Talwar 07]
(Naturally resistant to collusion!)
(no payments required!)
(Good guarantees even for complex settings!)
Who wants $1 for their STD Status?
The wrong price leads to response bias
What is the right price?
Design a truthful direct revelation mechanism.
How much for your STD Status?
Problem: Values for privacy are themselves correlated with private data!
Upshot: No truthful direct revelation mechanism can guarantee non-trivial accuracy and finite payments. [GR11]
There are ways around this by changing the cost model and abandoning direct revelation mechanisms [FL12,LR12]