PIE: A Data-Driven Payoff Inference Engine for Strategic Security Applications

Haipeng Chen, Mohammad T. Hajiaghayi, Sarit Kraus, Anshul Sawant, Edoardo Serra, V. S. Subrahmanian, Yanhai Xiong

Research output: Contribution to journalArticlepeer-review


Although most game theory models assume that payoff matrices are provided as input, getting payoff matrices in strategic games (e.g., corporate negotiations and counter-terrorism operations) has proven difficult. To tackle this challenge, we propose a payoff inference engine (PIE) that finds payoffs assuming that players in a game follow a myopic best response or a regret minimization heuristic. This assumption yields a set of constraints (possibly nonlinear) on the payoffs with a multiplicity of solutions. PIE finds payoffs by considering solutions of these constraints and their variants via three heuristics. First, we approximately compute a centroid of the resulting polytope of the constraints. Second, we use a soft constraint approach that allows violation of constraints by penalizing violations in the objective function. Third, we develop a novel approach to payoff inference based on support vector machines (SVMs). Unlike past work on payoff inference, PIE has the following advantages. PIE supports reasoning about multiplayer games, not just one or two players, it can use short histories, not long ones which may not be available in many real-world situations, it does not require all players to be fully rational, and it is one to two orders of magnitude more scalable than past work. We run experiments on a synthetic data set where we generate payoff functions for the players and see how well our algorithms can learn them, a real-world coarse-grained counter-terrorism data set about a set of different terrorist groups, and a real-world fine-grained data set about a specific terrorist group. As the ground truth about payoffs for the terrorist groups cannot be tested directly, we test PIE by using the payoffs to make predictions about the actions of the groups and corresponding governments (even though this is not the purpose of this article). We show that compared with recent work on payoff inference, PIE has both higher accuracy and much shorter runtime.

Original languageEnglish
Article number8952764
Pages (from-to)42-57
Number of pages16
JournalIEEE Transactions on Computational Social Systems
Issue number1
StatePublished - Feb 2020

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


Manuscript received April 10, 2019; revised November 3, 2019; accepted November 17, 2019. Date of publication January 8, 2020; date of current version February 24, 2020. This work was supported in part by Guggenheim Fellowship, NSF under Grant CCF:SPX 1822738 and Grant IIS:BIGDATA 1546108, in part by DARPA under Grant SI3CMD, in part by the UMD Year of Data Science Program Grant, and in part by the Northrop Grumman Faculty Award. (Corresponding author: V. S. Subrahmanian.) H. Chen, V. S. Subrahmanian, and Y. Xiong are with Dartmouth College, Hanover, NH 03755 USA (e-mail: [email protected]; [email protected]; [email protected]).

FundersFunder number
National Science FoundationBIGDATA 1546108, CCF:SPX 1822738
Defense Advanced Research Projects AgencySI3CMD
Northrop Grumman


    • Counter terrorism
    • game theory
    • payoff inference


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