RyanCarey
commented
2 years ago Yes, we do have one that treats single and multi agent cases, just it's named "sufficient recall https://github.com/causalincentives/pycid/blob/master/pycid/core/macid_base.py#L257". We should definitely mention in the docstring that sufficient recall is also known as solubility.
I believe a MACID should be soluble if for each agent, its decision nodes are soluble with respect to its own utility nodes, while presuming all other control nodes are turned into chance nodes by a fixed decision strategy. Yes, absolutely, and this is how it's defined in the literature, for instance definition 5.2 of "Ignorable Information in Multi-Agent Scenarios" by Milch & Koller.
The stronger definition sounds plausible.
On Fri, 20 May 2022 at 23:06, Sebastian Benthall @.***> wrote:
Is your feature request related to a problem? Please describe. For a given CID, it's of interest to know whether or not it is soluble, as defined by Nilsson and Lauritzen (2000). It is also useful to know what in order of decision nodes a soluble model can be solved via backwards induction.
Describe the solution you'd like Maybe a method on the CID class that tests for solubility, returning an ordering of decision nodes if it's soluble and None otherwise?
Describe alternatives you've considered I wonder if this capability is already in the library.
Additional context I've been wondering if solubility has been defined for MACIDs. I believe a MACID should be soluble if for each agent, its decision nodes are soluble with respect to its own utility nodes, while presuming all other control nodes are turned into chance nodes by a fixed decision strategy. While that does not afford backwards induction to solve the entire model, it would allow the backwards induction of each agent given the strategy of others, which could then be iterated until equilibrium.
Or, a strong version of multi-agent solubility would be the original condition, but considering all utility and decision nodes regardless of the agent that owns them. This would identify a much smaller class of CIDs as soluble, but it might be possible to solve these for all agents with a single backwards induction pass.
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-- Ryan Carey FHI Research Fellow & Statistics DPhil Student, Oxford University
Jamesfox1
sbenthall
Is your feature request related to a problem? Please describe. For a given CID, it's of interest to know whether or not it is soluble, as defined by Nilsson and Lauritzen (2000). It is also useful to know what in order of decision nodes a soluble model can be solved via backwards induction.
Describe the solution you'd like Maybe a method on the CID class that tests for solubility, returning an ordering of decision nodes if it's soluble and None otherwise?
Describe alternatives you've considered I wonder if this capability is already in the library.
Additional context I've been wondering if solubility has been defined for MACIDs. I believe a MACID should be soluble if for each agent, its decision nodes are soluble with respect to its own utility nodes, while presuming all other control nodes are turned into chance nodes by a fixed decision strategy. While that does not afford backwards induction to solve the entire model, it would allow the backwards induction of each agent given the strategy of others, which could then be iterated until equilibrium.
Or, a strong version of multi-agent solubility would be the original condition, but considering all utility and decision nodes regardless of the agent that owns them. This would identify a much smaller class of CIDs as soluble, but it might be possible to solve these for all agents with a single backwards induction pass.