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Delay-Predictability Tradeoffs in Reaching a Secret Goal

19 Pages Posted: 26 May 2016 Last revised: 14 Aug 2017

John Tsitsiklis

Massachusetts Institute of Technology (MIT)

Kuang Xu

Stanford Graduate School of Business

Date Written: August 13, 2017

Abstract

We formulate a model of sequential decision-making, dubbed the Goal Prediction game, to study the extent to which an overseeing adversary can predict the final goal of an agent who tries to reach that goal quickly, through a sequence of intermediate actions. Our formulation is motivated by the increasing ubiquity of large-scale surveillance and data collection infrastructures, which can be used to predict an agent's intentions and future actions, despite the agent's desire for privacy.

Our main result shows that with a carefully chosen agent strategy, the probability that the agent’s goal is correctly predicted by an adversary can be made inversely proportional to the time that the agent is willing to spend in reaching the goal, but cannot be made any smaller than that. Moreover, this characterization depends on the topology of the agent's state space only through its diameter.

Keywords: privacy, secrecy, goal reaching

Suggested Citation

Tsitsiklis, John and Xu, Kuang, Delay-Predictability Tradeoffs in Reaching a Secret Goal (August 13, 2017). Stanford University Graduate School of Business Research Paper No. 16-25. Available at SSRN: https://ssrn.com/abstract=2784502 or http://dx.doi.org/10.2139/ssrn.2784502

John Tsitsiklis

Massachusetts Institute of Technology (MIT) ( email )

Cambridge, MA 02139
United States
617-253-6175 (Phone)

Kuang Xu (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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