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Measuring Responsibility in Multi-Agent Systems

Chunyan Mu, Nir Oren

TL;DR

This work introduces a family of quantitative measures of responsibility in multi-agent planning, building upon the concepts of causal responsibility proposed by Parker et al.~[ParkerGL23], and is the first to capture the causal responsibility properties of outcomes over time.

Abstract

We introduce a family of quantitative measures of responsibility in multi-agent planning, building upon the concepts of causal responsibility proposed by Parker et al.~[ParkerGL23]. These concepts are formalised within a variant of probabilistic alternating-time temporal logic. Unlike existing approaches, our framework ascribes responsibility to agents for a given outcome by linking probabilities between behaviours and responsibility through three metrics, including an entropy-based measurement of responsibility. This latter measure is the first to capture the causal responsibility properties of outcomes over time, offering an asymptotic measurement that reflects the difficulty of achieving these outcomes. Our approach provides a fresh understanding of responsibility in multi-agent systems, illuminating both the qualitative and quantitative aspects of agents' roles in achieving or preventing outcomes.

Measuring Responsibility in Multi-Agent Systems

TL;DR

This work introduces a family of quantitative measures of responsibility in multi-agent planning, building upon the concepts of causal responsibility proposed by Parker et al.~[ParkerGL23], and is the first to capture the causal responsibility properties of outcomes over time.

Abstract

We introduce a family of quantitative measures of responsibility in multi-agent planning, building upon the concepts of causal responsibility proposed by Parker et al.~[ParkerGL23]. These concepts are formalised within a variant of probabilistic alternating-time temporal logic. Unlike existing approaches, our framework ascribes responsibility to agents for a given outcome by linking probabilities between behaviours and responsibility through three metrics, including an entropy-based measurement of responsibility. This latter measure is the first to capture the causal responsibility properties of outcomes over time, offering an asymptotic measurement that reflects the difficulty of achieving these outcomes. Our approach provides a fresh understanding of responsibility in multi-agent systems, illuminating both the qualitative and quantitative aspects of agents' roles in achieving or preventing outcomes.

Paper Structure

This paper contains 14 sections, 3 theorems, 26 equations, 4 figures, 9 algorithms.

Table of Contents

  1. Introduction
  2. Related work and our contributions.
  3. Model
  4. The Stochastic Model of MASs
  5. Probabilistic ATL
  6. Formalising Responsibility
  7. Measuring Causal Responsibility
  8. Metrics
  9. Proportional measure.
  10. Probabilistic measure.
  11. Entropy measure.
  12. Measuring causal responsibilities
  13. Complexity.
  14. Conclusions and Future Work

Key Result

theorem 1

The complexity of checking CAR and CPR is $M \cdot P^{NP \cap co-NP}$, and $M \cdot 2^{|Ag|} \cdot P^{NP \cap co-NP}$ for CCR. Here, $M$ is the number of histories and $|Ag|$ is the number of agents in the system.

Figures (4)

  • Figure 1: The transition system representing CPD.
  • Figure 2: $\mathsf{CAR}$ for the measures over time for Example \ref{['eg:dcar']} (b)
  • Figure 3: $\mathsf{CPR}$ over time for Example \ref{['eg:dcpr']}
  • Figure 4: $\mathsf{CCR}$ over time for Example \ref{['eg:dccr']}

Theorems & Definitions (22)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • definition 5
  • definition 6
  • definition 7
  • definition 8: Syntax
  • definition 9: semantics
  • definition 10: Causal Active Responsibility (CAR)
  • ...and 12 more