2. Reshef Meir, Ariel D. Procaccia, and Jeffrey S. Rosenschein

3.  A very simple example of mechanism design in a decision making setting  8 slides  An investigation of incentives in a general machine learning setting  2 slides

4.  ECB makes Yes/no decisions at European level  Decisions based on reports from national banks  National bankers gather positive/negative data from local institutions  Bankers might misreport their data in order to sway the central decision

5.  Set of n agents  Agent i controls points X i = {x i1,x i2,...}  X  For each x ik  X i agent i has a label y ik  { ,  }  Agent i reports labels y’ i1,y’ i2,...  Mechanism receives reported labels and outputs c + (constant  ) or c  (constant  )  Risk of i: R i (c) = |{k: c(x ik )  y ik }|  Global risk: R(c) = |{i,k: c(x ik )  y ik }| =  i R i (c)

6. Agent 1Agent 2   + + – – – – – – + + + +

7.  If all agents report truthfully, choose concept that minimizes global risk  Risk Minimization is not strategyproof: agents can benefit by lying

8. Agent 1Agent 2   + + – – – – – – + + + + – – + +

9.  VCG works (but is not interesting).  Mechanism gives  -approximation if returns concept with risk at most  times optimal  Mechanism 1: 1. Define i as positive if has majority of + labels, negative otherwise 2. If at least half the points belong to positive agents return c +, otherwise return c -  Theorem: Mechanism 1 is a 3-approx group strategyproof mechanism  Theorem: No (deterministic) SP mechanism achieves an approx ratio better than 3

10. Agent 1 Agent 2 + + + + + + + + + + – – – – – – + + + + Agent 1 Agent 2 + + + + + + + + + + – – – – – – – – – – Agent 1 Agent 2 + + + + + + – – – – – – – – – – – – – – – – – – + + + +         + + + + + +

11.  Theorem: There is a randomized group SP 2- approximation mechanism  Theorem: No randomized SP mechanism achieves an approx ratio better than 2

12.  A very simple example of mechanism design in a decision making setting  8 slides  An investigation of incentives in a general machine learning setting  2 slides

13.  Each agent assigns a label to every point of X.  Each agent holds a distribution over X  R i (c) = prob. of point being mislabeled according to agent’s distribution  R(c) = average individual risk  Each agent’s distribution is sampled, sample labeled by the agent  Theorem: Possible to achieve almost 2- approximation in expectation under rationality assumption

14.  Classification:  Richer concept classes  Currently have strong results for linear threshold functions over the real line  Other machine learning models  Regression learning [Dekel, Fischer, and Procaccia, in SODA 2008]