James Zou1 , Sujit Gujar2, David Parkes1 Tolerable Manipulability in Dynamic Allocation Without Money James Zou1 , Sujit Gujar2, David Parkes1 1School of Engineering and Applied Sciences, Harvard University 2Indian Institute of Science Definition Greedy mechanism: First Come First Pick Proposition 2. If the score difference between successive items is less than one, a strategic agent has a dominant strategy that achieves its most preferred available item. 1. Introduction Theorem 3. If the score difference is less than one and all agents are strategic, Scoring Rule makes Identical allocations as Greedy would on truthful reports. Definition strategyproof mechanism: for all agents truthful reporting is a dominant strategy equilibrium. For any type of agent, and for any reports that other agents may make, it can do no better than reporting its true preference.. T=1 T=2 T=3 A better allocation: Simulation 1. Scoring Rule significantly outperforms Greedy if all agents are truthful. T=1 T=2 T=3 Theorem 1. A deterministic online mechanism is strategyproof, neutral and non-bossy if and only if it is the Greedy mechanism. Definition Neutral : Mechanism does not depend on item labelings [3]. Definition Non-bossy: An agent can not affect the allocation of another agent through misreporting without changing its own allocation [3]. Pro: robust, avoid agent speculation. Con: poor performance in many settings. Definition: Manipulation Tolerant Mechanism. 1) If all agents are strategic, then the performance is equivalent to a strategyproof mechanism. 2) The mechanism outperforms any strategyproof mechanism if any number of agents are strategic and the rest truthful. Weaker than manipulation optimal proposed in [1]. Simulation 2. Strategic agents do better than truthful agents. Measuring Performance. Rank efficiency = average true rank of agents for allocated items. = average utility (ex-ante efficiency) if the same utility drop off between successive items. Greedy is ex-post Pareto Optimal but has poor rank efficiency. 2. Dynamic Allocation Without Money: A Case Study 3. Manipulation Tolerant Scoring Rule Probabilistic Model of Agent Types. Model Setup: N agents and N items. Each agent has a strict preference ranking over all items. May report any preference. Agent has arrival/departure times A and D. May report A' >= A and D' <= D. Each agent must be allocated one item in [A', D']. Online. Agent only cares about its own allocation. Simulation 3. Scoring Rule is robust to agent mistakes. Popularity: 0.5 0.3 0.2 Given the popularity, the score of an item is the expected rank a random agent would have for it. (1+1+1+2+2)/5 = 1.4 (1+2+2+2+3)/5 = 2 (1+3+3+3+3)/5 = 2.6 4. Discussion 1) In many settings, some agents will be truthful because they are altruistic, naive, not well informed, or too lazy to manipulate. 2) Manipulation tolerant mechanism offers a promising new avenue of research in domains where SP mechanisms are difficult to construct or compromises performance. [1] Othman, A and Sandholm, T. Better with Byzantine: Manipulation Optimal Mechanisms. SAGT 09. [2] Feigenbaum, J and Shenker, S. Distributed algorithmic mechanism Design. DAMMCC 02. [3] Svenssen, L. Strategy-proof allocation of indivisible goods. SCW 99. Scoring Rule Allocation Algorithm Assign to each agent the available item that minimizes its rank(item)-score(item) 2-2.6 1-1.4 3-2 T=1 T=2 T=3 1-1.4 2-2