Key Takeaways

  1. Physician as arbiter: Silent bargaining between compassion and the Hippocratic Oath
  2. Nash Solution: Mathematical compromise in end-of-life decisions
  3. Patient strategies: Enhancing bargaining position through advance directives
  4. Static justice: Fair compromise between competing interests

The Moral Fork in the Road

The moral life of the physician is often defined by the tension between duty and mercy. Consider Dr. Smith, standing at the bedside of a terminally ill patient who desperately asks to be allowed to die. One side of Dr. Smith is governed by compassion, a deep feeling of sharing the patient’s suffering coupled with an active desire to relieve that misery. The other side is governed by the Hippocratic Oath, which has been internalized as an absolute commitment: “I will neither give a deadly drug to anybody who asked for it, nor will I make a suggestion to this effect”. This creates an emotional and ethical conflict, forcing Dr. Smith—the “two-headed physician”—to determine not just the manner, but the very timing of the patient’s death.

This dilemma is universal to end-of-life care: How does one reconcile a physician’s moral obligation to preserve life (duty) with the ethical imperative to relieve suffering (mercy)? The standard solution is not typically found through explicit conversation, as studies show that patients and physicians often fail to communicate effectively or ignore each other’s wishes. Instead, the conflict is often resolved when the physician acts as an arbiter. The method used to achieve this resolution is rooted in static justice, which prevails when parties are free to bargain, and is best encapsulated by the Nash Solution.

The Nash Solution as a Moral Compass

The story of the physician as arbiter reveals that end-of-life decisions are frequently governed by a silent bargaining process, formalized not by clinical guidelines but by a pursuit of compromise and fairness. This solution, derived from game theory, is simple and intuitive: it dictates that the compromise must produce the most net total benefit to the parties and then divide that benefit equally between them, using their respective “bargaining positions” as baselines.

Mapping Utility and Duty

To understand this silent bargain, we must quantify the two utilities at stake.

  1. Patient Utility (U): This measures the patient’s total well-being, which includes physical health, dignity, and absence of pain. Upon terminal diagnosis, the patient sees their total utility decline, eventually hitting zero (time t’) when life is no longer worth living. The patient’s wish, t’, is the point where they seek assistance in dying.
  2. Hippocratic Utility (V): This represents the physician’s commitment to preserving life, reflecting the Oath’s mandate. It rises continuously, meaning the physician’s duty favors a longer life. The physician’s wish, t *, is the point in time they choose for the patient to die, which is later than the patient’s wish t’.

The physician is burdened by both compassion (which aligns with reducing the negative utility of the patient’s suffering) and the Oath (which aligns with maximizing V). They resolve this internal conflict by finding the point of static justice, t *, which represents the Nash Solution.

Defining Bargaining Positions

The Nash Solution depends critically on the bargaining position of each party.

  • The Patient’s Bargaining Position: This is defined by the patient’s expected utility if the physician offers no assistance. A patient who has secured alternatives, such as access to excellent palliative care or the capability to end their own life, has a strong bargaining position. This independence reduces their reliance on Dr. Smith.
  • The Physician’s Bargaining Position: This is the Hippocratic Utility (V) that Dr. Smith expects if the patient refuses her help. Since Dr. Smith is bound by both the Oath and her compassion, she is negotiating against her own sense of duty and pity.

The resulting compromise, t *, is therefore later than the patient’s ideal time t’, reflecting the weight of the Oath (V). However, because compassion is a desire to relieve suffering, the compromise is also reached before life is prolonged indefinitely. The Nash Solution, therefore, establishes a fair, albeit reluctant, consensus on the time of death.

The Patient’s Strategy in a Static Game

If patients understand that the physician operates as a reluctant arbiter guided by the Nash Solution, they gain insight into how to influence the decision. The primary strategies involve enhancing their own bargaining strength relative to the physician’s duty, thereby shifting the compromise time t *.

Elevating the Bargaining Floor

The patient can strengthen their position by reducing dependency on the physician. This means executing an advance directive that is comprehensive and actionable: signing a no-resuscitation order, drafting a detailed living will, appointing a health-care proxy, and, critically, arranging for palliative care and hospice. When the patient secures excellent palliative care, the worst-case scenario (uncontrolled suffering) is mitigated, raising their baseline utility and strengthening their bargaining position. This contrasts with the reality described in the Oregon Paradox, where the sheer option of legally hastening death—the ability to cut loss—is what provides the greatest surge in well-being and the desire to live longer, acting as a crucial psychological floor. The power of the Death with Dignity Act (DWDA) is that it enables the patient to seize control over suffering and end life’s negative utility, which is a powerful negotiating tool even if never used.

The Behavioral Profile of the Physician

Patients can also strategically choose a physician whose personal “utility function” (V) is weighted differently.

  1. Compassion Bias: Seeking a physician known to possess a high degree of compassion for patients. While the Oath sets a floor, the strength of compassion influences the speed with which the physician acts to alleviate suffering.
  2. Specialist vs. Generalist: Opting for an experienced general practitioner rather than a specialist, as specialists often “tend to feel especially duty-bound by the Hippocratic Oath”. A generalist may possess a more balanced view of life extension versus overall quality of life.

These steps demonstrate that the patient, far from being a passive recipient of care, can strategically employ instruments of planning and behavioral leverage to secure a desired outcome, shifting the equilibrium point t *.

Moving Beyond the Binary of Life and Death

The conflict between compassion and the Oath reveals a broader truth: when faced with complexity and intense moral gravity, humans often default to a mechanism that guarantees fairness, even if imperfect. The physician’s role as the two-headed arbiter is necessitated by the breakdown of communication and the gravity of the decision itself. The reality is that few dying patients engage in deep, explicit negotiations with their doctors; they are passive because they trust the physician’s inherent “moral compass” to find a just resolution.

The Nash Solution, as a proxy for static justice, provides a mathematically fair compromise between two competing interests, whether those interests reside in two distinct people or within the divided conscience of a single doctor. It is the formalized expression of meeting in the middle after entitlements have been accounted for. By exposing this hidden logic, behavioral bioethics liberates the patient from the expectation of absolute autonomy and empowers them to shape the outcome through strategic leverage. It is a recognition that the governance of death, much like the governance of a corporation, relies on a complex mix of formal rules (the Oath) and managerial decision-making (the physician’s arbitration), culminating in a compromise between “my wish” and “their wish”.