Abstract
Disaster response is a major challenge given the social and economic impact on the communities affected by disaster incidents. We investigate how coalition formation can be used for the problem of forming a hierarchy of resources (e.g., personnel responding to the incident). As a case study, we consider the roaring river flood scenario and model the Incident Command System (ICS) framework—providing guidelines on cooperatively responding to disaster incidents. Our approach is based on sequential characteristic-function games induced by size-based valuation structures. We show that this approach can deliver a hierarchy as required by the Operations Section of the ICS and provides a promising way to generate practical solutions for some realistic disaster scenarios.
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The datasets generated during and/or analysed during the current study are available in the SCFG repository, https://github.com/smart-pucrs/SCFG
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Open Access funding enabled and organized by Projekt DEAL. The first author acknowledges partial funding by CAPES—Brasil—Finance Code 001. The second author gratefully acknowledges partial funding from CNPq and CAPES
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A Glossary
A Glossary
Acronym | Var | Meaning |
---|---|---|
— | A | a set of agents |
— | C | a subset of agents (coalition) |
CS | CS | a partition of A (coalition structure) |
— | \(\varvec{CS}^A\) | the set of all coalition structures over A |
— | v(C) | a function: \(2^A \rightarrow \mathbb {R}\) |
CFG | \(\Gamma \) | a characteristic-function game |
— | G | an interaction graph |
— | \(S^{piv}\) | a set of pivotal agents |
— | Z | a set of allowed coalition sizes |
SVS | \(\pi \) | a tuple \(\langle G,S^{piv}, Z\rangle \) |
— | \(\varvec{C}^\pi \) | the set of all coalitions induced by an SVS \(\pi \) |
— | \(\varvec{CS}^\pi \) | the set of all CSs induced by an SVS \(\pi \) |
— | \(\Gamma ^{\pi }\) | a CFG game induced by an SVS \(\pi \) |
— | \(\mathcal {H}\) | a totally ordered sequence of CFGs |
— | \(\Pi \) | a totally ordered set of SVSs |
— | h | the length of both \(\mathcal {H}\) and \(\Pi \) |
— | \(\mathcal {R}\) | a relation \(\subseteq (\varvec{CS}A \cup \{\varnothing \}) \times \varvec{CS}A \) |
FCSS | \(\varvec{CS}\) | a feasible sequence of CSs |
— | \(\mathcal {V}(\varvec{CS})\) | \(\sum ^h_{i=1} \sum _{C \in CS_i} v_i(C) : CS_i \in \varvec{CS}\) |
— | \(\varvec{\Gamma }\) | a sequence of CFGs induced by SVSs |
SEQSVS | \(\mathcal {G}\) | a tuple \(\langle A, \mathcal {H},\Pi ,\mathcal {R}\rangle \) |
— | \(\bar{b}\) | the degree UCT-Seq simulation param. |
— | \(\bar{d}\) | the depth UCT-Seq simulation param. |
— | \(\gamma \) | the exploration factor UCT-Seq param. |
— | \(A^{piv}\) | a set \(\bigcup _{i=1}^h S^{piv}_i\) of pivotal agents |
— | \(\lambda \) | a span of control |
— | R | a set of roles |
— | IO | a set of incident objectives |
— | demand(.) a function mapping \(IO \rightarrow 2^R\) | |
— | response(.) | a function mapping \(S^{piv} \rightarrow 2^IO\) |
— | \(a_i\) | the ith agent |
— | \(adopted\_by(a_i)\) | a subset of R |
— | \(expect(a_i)\) a set \(\{r \in R \mid o \in response(a_i)\), | |
\(r \in demand(o)\}\) | ||
— | \(e^r\) | the number of agents that should adopt role r |
— | \(related(a,a')\) | a function \(A \times A \rightarrow [0, 1]\) |
— | relationship(C) | a function \(2^A \rightarrow [0, 1]\) |
— | disturbed(C) | a function \(2^A \rightarrow [0, 1]\) |
— | m(.) | a multiplicity function of a multiset |
— | X(C) | a set of required roles \(\bigcup _{a\in C\cap S^{piv}_1} expect(a)\) |
— | \(\mathcal {X}(C)\) | a multiset of required roles \(\langle X(C), m_{X(C)} \rangle \) |
— | Y(C) | a set of available roles \(\bigcup _{a\in C\backslash A} adopted\_by(a)\) |
— | \(\mathcal {Y}(C)\) | a multiset of available roles \(\langle Y(C), m_{Y(C)} \rangle \) |
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Krausburg, T., Bordini, R.H. & Dix, J. Modelling a chain of command in the incident command system using sequential characteristic function games. Ann Math Artif Intell (2023). https://doi.org/10.1007/s10472-023-09878-7
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DOI: https://doi.org/10.1007/s10472-023-09878-7