Responsibility Attribution in Parameterized Markovian Models


  • Christel Baier Technische Universität Dresden
  • Florian Funke Technische Universität Dresden
  • Rupak Majumdar Max Planck Institute for Software Systems


Planning with Markov Models (MDPs, POMDPs), Action, Change, and Causality, Cooperative Game Theory


We consider the problem of responsibility attribution in the setting of parametric Markov chains. Given a family of Markov chains over a set of parameters, and a property, responsibility attribution asks how the difference in the value of the property should be attributed to the parameters when they change from one point in the parameter space to another. We formalize responsibility as path-based attribution schemes studied in cooperative game theory. An attribution scheme in a game determines how a value (a surplus or a cost) is distributed among a set of participants. Path-based attribution schemes include the well-studied Aumann-Shapley and the Shapley-Shubik schemes. In our context, an attribution scheme measures the responsibility of each parameter on the value function of the parametric Markov chain. We study the decision problem for path-based attribution schemes. Our main technical result is an algorithm for deciding if a path-based attribution scheme for a rational (ratios of polynomials) cost function is over a rational threshold. In particular, it is decidable if the Aumann-Shapley value for a player is at least a given rational number. As a consequence, we show that responsibility attribution is decidable for parametric Markov chains and for a general class of properties that include expectation and variance of discounted sum and long-run average rewards, as well as specifications in temporal logic.




How to Cite

Baier, C., Funke, F., & Majumdar, R. (2021). Responsibility Attribution in Parameterized Markovian Models. Proceedings of the AAAI Conference on Artificial Intelligence, 35(13), 11734-11743. Retrieved from



AAAI Technical Track on Planning, Routing, and Scheduling