Abstract
In this paper we discuss how causal models can be used for modeling multi-agent interaction in complex organizational settings, where agents’ decisions may depend on other agents’ decisions as well as the environment. We demonstrate how to reason about the dynamics of such models using concurrent game structures where agents can change the organisational setting and thereby their decision dependencies. In such concurrent game structure, agents can choose to modify their reactions on other agents’ decisions and on the environment by intervening on their part of a causal model. We propose a generalized notion of interventions in causal models that allow us to model and reason about the dynamics of agents’ dependencies in a multi-agent system. Finally, we discuss how to model uncertainty and reason about agents’ responsibility concerning their dependencies and thereby their choices.
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Notes
- 1.
Although we use this example due to its simplicity and its extensive analysis in the literature, we can also use new interpretation of this example to illustrate the dependencies of agents’ decisions in multi-agent organisations. Let Suzy and Billy be two loan officers working in a bank, who decide to accept or reject a mortgage application. Then \(ST=1\) (and \(BT=1\)) can indicate that Suzy (and Billy respectively) rejects an application. Then \(SH=1\) (and \(BH=1\)) mean that Suzy’s (and Billy’s) rejection is registered in the administration database. We also assume that Suzy has a priority, so Billy’s rejection is registered (\(BH=1\)) only if Suzy’s is not (\(SH=0\)). Then, the mortgage is rejected (\(BS=1\)) if \(SH=1\) or \(BH=1\).
- 2.
The detailed overview can be found in [13].
- 3.
Please note that for notational convenience we use \(\mathcal {L}(\textsf{C})\) instead of \(\mathcal {L}(\textsf{C}(\mathcal {S}))\).
- 4.
Here we assume for simplicity that each agent in \(\mathbb{A}\mathbb{G}\) controls only one variable in \(\mathcal {V}_a\), so \(|\mathbb{A}\mathbb{G}|=|\mathcal {V}_a|\). But without loss of generality one can assume that \(\mathcal {V}_a\) is partitioned into disjoint subsets controlled by agents in \(\mathbb{A}\mathbb{G}\). In this case \(|\mathbb{A}\mathbb{G}|\le |\mathcal {V}_a|\).
- 5.
We note that such an intervention (updates) make the agents in \(\vec {X}\) independent of other agents as their decision-making functional specifications are now reduced to a constant function. Later in Sect. 4 we will introduce more general interventions (updates) that can create arbitrary dependencies between agents.
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Gladyshev, M., Alechina, N., Dastani, M., Doder, D. (2023). Dynamics of Causal Dependencies in Multi-agent Settings. In: Ciortea, A., Dastani, M., Luo, J. (eds) Engineering Multi-Agent Systems. EMAS 2023. Lecture Notes in Computer Science(), vol 14378. Springer, Cham. https://doi.org/10.1007/978-3-031-48539-8_7
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