The Mathematics of Attachment, Grief, and Complicated Grief in Psychiatric Care


The APA lecture focused on a model with detail to game theory.

Lawrence Amsel, MD, MPH, Columbia University, delivered a talk at the annual APA meeting in San Diego on the application of game theory for issues experienced by individuals grieving for a lost loved one.

In describing the motivation for work in this area, Amsel said the overall goal for doctors is to reduce the “subjectivity inherent to psychiatry by quantitating descriptive information in order to fit it into mathematical models.”

“The approach taken involves an economic analysis of various behaviors such as grieving by use of tools derived from computational cognitive science,” Amsel said.

Referencing early work on grief by Sigmund Freud, Amsel told the audience that in his 1917 essay, “Mourning and Melancholia,” Freud proposed that grieving involved de-cathecting — or emotionally neutralizing the individual, discrete memories of the deceased.

“Contemporary psychiatry has, perhaps too quickly, abandoned these ideas,” Amsel said.

Drawing on literature for reward learning and game theory that addresses how human agents utilize information on reward or fear in the service of reaching their goals, Amsel provided equations that form the foundation of a model that uses a reward-learning approach for understanding attachment formation. Amsel described the model as a process that sets up a structure of “expected utilities for shared experiences.”

“The mirror image of attachment is the normal grief reaction to loss that can be given by an equation that captures the difference between expected reward and actual reward set up by the loss,” Amsel said. “This model captures elements of both Freudian and contemporary theories of grief and sees the grieving process as looking backward and forward simultaneously.”

In the forward-looking direction, Amsel told the standing-room-only audience that the model serves as a series of exposure and habituation exercises that allow for a reattribution capable of transforming negative expectations of future experiences into something more tolerable. Looking backward, reattribution allows for piecewise detachment from the shared memories that comprise the relationship with the lost partner.

Presenting the normal grieving process as a rational, “utility-maximizing” program involving a continually updating reward-learning process, Amsel said that these features make it possible to eventually reclaim positive utilities from life’s experiences following a major loss.

“Complicated grief may have a similar structure and can result from any of several different failure modes of the process described above, leading to persistence of grief,” Amsel said.

Further describing the tools used and how they relate to game theory — and in particular, the concept of the prisoner’s dilemma — Amsel said the second model was shaped around seeing the individual as divided between 2 internal agents.

“The first agent, the desired future self, seeks to restructure life by becoming an independent agent and abandoning the expectations of the relationship,” Amsel said. “The other agent, the ghost, plays a denial position and attempts to maintain the relationship. We show this model can lead to a classic prisoner’s dilemma-like game that under certain circumstances can manifest as a behavioral trap.”

Amsel said that unlike the classic prisoner’s dilemma, this process is best modeled using 2 agents within a single individual.

Amsel concluded his presentation by telling the assembled psychiatrists that these abstract mathematical models can predict the empirical phenomenology of attachment, grief, and complicated grief.

“Psychiatry benefits from the use of such concepts to model psychopathology,” Amsel said.

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