INTEL 726

Military Strategy Paper: Integrating Game Theory in Decision-Making for “No Man Left Behind” vs. “Dead Weight Left Behind”

1. Introduction

Military operations are defined by high-risk environments where decisions made in the heat of battle can significantly impact the success or failure of a mission. One of the fundamental dilemmas in warfare revolves around the principle of “No Man Left Behind” (NMLB), where soldiers risk their lives to rescue comrades, versus a more utilitarian approach of “Dead Weight Left Behind” (DWLB), where wounded or incapacitated personnel are abandoned to ensure operational efficiency and survival of the rest.

In this paper, game theory—a mathematical framework for analyzing strategic interactions among rational actors—is used to evaluate these two principles. By applying game theory to this ethical and tactical debate, we can model different military scenarios, calculate potential outcomes, and determine the optimal strategies based on varying conditions and priorities.

2. Theoretical Framework: Understanding the Principles

2.1. No Man Left Behind (NMLB)

NMLB represents a deeply ingrained ethos in many militaries worldwide. It is based on a strong sense of duty, unity, and moral responsibility. From a tactical perspective, NMLB aims to maintain morale and cohesion within the unit, ensuring that every soldier trusts the organization to prioritize their lives.

2.2. Dead Weight Left Behind (DWLB)

The DWLB principle, while more controversial, focuses on operational efficiency, mission success, and the overall survival of the group. In situations where a soldier is incapacitated beyond recovery or too wounded to continue the mission, DWLB advocates for leaving them behind to preserve resources and minimize risk to the rest of the unit.

3. Game Theory Concepts in Military Decision-Making

Game theory provides a useful lens to analyze these two principles, especially in terms of payoffs, risks, and strategic choices that must be made in high-stress environments. The following game theory concepts are particularly relevant:

• Prisoner’s Dilemma: A situation where individual rational choices lead to a suboptimal group outcome, reflecting the tension between group loyalty and self-preservation.
• Zero-Sum vs. Non-Zero-Sum Games: In military operations, choices may either lead to a zero-sum game (where one side’s loss is the other’s gain) or a non-zero-sum game (where cooperation or mutual aid can improve overall outcomes).
• Nash Equilibrium: A strategic point where no actor has an incentive to deviate from their strategy, given the strategies of others. In the context of military strategy, this reflects a stable decision where both personal and group survival are balanced.

4. Game Theoretical Models for NMLB vs. DWLB

4.1. Scenario 1: Combat Patrol with Casualty (2-Person Game)

Players: Unit Leader (Player A) and Casualty (Player B)

Choices:

• Player A: Rescue the casualty (NMLB) or abandon them (DWLB)
• Player B: Hope for rescue or prepare for being abandoned

Payoffs:

• Rescue (NMLB): Increased risk to Player A, higher survival chance for Player B, morale boost for unit, potential mission compromise.
• Abandon (DWLB): Reduced risk for Player A, guaranteed loss of Player B, mission continuation, possible morale damage.

This can be modeled as a Prisoner’s Dilemma. If the leader chooses DWLB, they minimize personal risk, but the unit as a whole could suffer due to decreased morale and trust. If they choose NMLB, the immediate risk is higher, but long-term cohesion and trust remain intact. However, the optimal choice depends on external factors like the mission’s criticality and the enemy’s proximity.

Nash Equilibrium in this case can lean towards DWLB in extreme survival scenarios, but generally tends to favor NMLB to maintain unit integrity.

4.2. Scenario 2: Large Unit with Limited Resources (Multi-Player Game)

Players: Entire Unit

Choices:

• Majority of the Unit: Continue with the mission (DWLB) or slow down for the wounded (NMLB).
• Wounded Soldier: Stay and wait for help or encourage the unit to continue (self-sacrifice).

This scenario reflects a Non-Zero-Sum Game where both the unit and the wounded soldier benefit more if the group reaches a collective decision that maximizes survival. If the majority opts for DWLB, the group could move faster, but morale and future trust could decline. If they opt for NMLB, resource drain could increase, but long-term unit cohesion is protected.

In a non-zero-sum context, cooperation and understanding between all players can lead to better outcomes for the entire unit, making NMLB the favored strategy when long-term benefits like morale and cohesion outweigh short-term gains.

4.3. Scenario 3: High-Stakes Mission with External Threats (3-Person Game)

Players: Unit Leader (Player A), Team (Player B), Enemy Forces (Player C)

Choices:

• Player A (Leader): Rescue the casualty (NMLB) or prioritize mission objectives (DWLB).
• Player B (Team): Support rescue (NMLB) or focus on mission (DWLB).
• Player C (Enemy): Attack or retreat.

This scenario introduces an external force that could exploit the unit’s decision. If Player A and Player B prioritize NMLB, they risk exposure to the enemy (Player C), but maintain team morale. If they choose DWLB, they minimize exposure but suffer internal fractures. The enemy’s decision can further complicate the game, as they may strike harder if they detect weakness.

The Nash Equilibrium emerges when both the team and leader coordinate actions that minimize the risk of enemy exploitation, which could favor DWLB in short-term, high-stakes operations but push for NMLB in less urgent or less risky environments.

5. Strategic Insights from Game Theory

1. Unit Cohesion vs. Operational Efficiency: Game theory highlights the inherent trade-off between preserving unit cohesion and ensuring operational efficiency. In most games, the long-term benefits of NMLB, such as maintaining morale and trust, outweigh the immediate gains of DWLB in small units. However, in high-stakes scenarios, DWLB can temporarily provide strategic advantage if unit leaders believe the casualty is unsalvageable.
2. Dynamic Decision-Making: Decisions made under fire require dynamic adaptation. Game theory shows that no single strategy is optimal in all situations; rather, the environment, enemy threat, and available resources will dictate the best approach.
3. Psychological and Moral Dimensions: Game theory analysis brings out the psychological impact of decisions. Soldiers are more likely to engage in DWLB if the perception of survival probability is low, whereas NMLB is likely to be chosen when team morale and trust are already high.

6. Conclusion

Game theory provides a structured approach to analyzing the difficult choice between “No Man Left Behind” and “Dead Weight Left Behind.” By modeling different military scenarios, we see that the optimal strategy is context-dependent, and leaders must weigh short-term risks against long-term unit health. While NMLB offers significant advantages in terms of trust, morale, and cohesion, DWLB may sometimes be necessary in extreme survival situations where the mission’s success or the survival of the majority is paramount.

Ultimately, military leaders must make these decisions with an understanding of both the strategic and human elements, balancing the immediate operational requirements with the long-term implications for unit unity and trust.