Tolerable Manipulability in Dynamic Allocation Without Money James Zou1 , Sujit Gujar2, David Parkes1 July 13, 2010. AAAI Presentation. 1School of Engineering and Applied Sciences, Harvard University 2Indian Institute of Science 1

Strategyproof Mechanism A mechanism is strategyproof if truthful reporting is a dominant-strategy equilibrium. Pro: robust, avoid agent speculation. Con: poor performance in many settings. 2

Manipulation Tolerant Mechanism Some agents may be truthful. A mechanism is manipulation tolerant: 1) if all agents are strategic, then equivalent to best strategyproof mechanism. 2) outperforms any strategyproof mechanism if any number of agents are strategic and the rest truthful. Given some domain specific performance metric.

Related Ideas Tolerably manipulable: the effects of strategic agents on system performance tolerable. [Feigenbaum, Shenker 02] Manipulation Optimal [Othman, Sandholm 09]: 1. mechanism is undominated by a truthful mechanism when agents are strategic. 2. do better than any truthful mechanism if any agent fails to be rational in any way. 3. Negative results.

Outline 1. Case Study: dynamic allocation without money. 2. Strategyproof mechanisms are severely limited. Poor performance. 3. Score Allocation Mechanism is manipulation tolerant. 4. What if agents make mistakes?

Dynamic Allocation Without Money N agents and N items. Agent has a strict preference ranking over all items. May misreport. Agent has arrival/departure times A and D. May report A' ≥ A and D' ≤ D. Online. Agent must be allocated one item in [A', D']. Agent only cares about its own allocation. 6

Example: Dynamic Allocation Without Money Tue Wed [1,1] [2,3] [3,3] 7

Greedy Allocation Greedy: first come first pick (strategyproof). T=1 [1,1] [2,3] [3,3]

A Better Allocation T=1 T=2 T=3 [1,1] [2,3] [3,3]

Limitations of Strategyproofness. Theorem 1. A deterministic online allocation mechanism is strategyproof, neutral and non-bossy if and only if it is the Greedy mechanism. Neutral : Mechanism does not depend on item labeling. Non-bossy: An agent can not affect the allocation to others through misreporting without changing its own allocation.

Measuring Performance Rank efficiency = average true rank for allocated items. = average utility if the same utility drop off between successive items. Expected Rank Efficiency = ex ante efficiency. Greedy is ex-post Pareto Optimal but has poor expected rank efficiency.

Example: Rank Efficiency Rank Efficiency(Greedy) = (1 + 2 + 3)/3 = 2 Rank Efficiency(Best allocation) = (1 + 2 + 2)/3 = 1.67 [1,1] [2,3] [3,3]

Item Score Given distribution of agent preferences. Score(Item) = Expected True Rank(Agent, Item) Agent ~ Distribution. Lower the score, the more desirable the item.

Example: Score Calculation. Scores: (1+1+1+2+2)/5 = 1.4 (1+2+2+2+3)/5 = 2 (1+3+3+3+3)/5 = 2.6 14

Scoring Rule Allocation Mechanism For each agent, assign it the available item that minimizes rank(item)-score(item). 1-1.4 2-2.6 3-2 [1,1] 1-1.4 2-2 [2,3] [3,3] 15

If All Agents Are Truthful ... Scoring Rule significantly outperforms Greedy. CONSENSUS: heuristic stochastic optimization. 16

Manipulation Tolerant No Gap: sort items by score score difference between successive items < 1. Theorem 2. If No Gap then: 1. a strategic agent has a dominant strategy that achieves its best available item. 2. if all agents are strategic, SR makes identical allocations as Greedy would on truthful reports.

If Some Agents Are Strategic 18

If Some Agents Are Strategic Strategic agents do better than truthful agents. Assumes that strategic agents can correctly construct the dominant strategy preference report. 19

Robust to Mistakes Scoring Rule is robust to mistakes by strategic agents. Mistaken beliefs → underlying preference distribution. 20

Discussion i) identical to SP if all agents are strategic 1. In many settings, some agents will be truthful. 2. Manipulation tolerant mechanism i) identical to SP if all agents are strategic ii) better when some agents are truthful. 3. Case study: dynamic allocation without money. 4. Promising research direction: domains where SP difficult to construct or compromises performance. 21