Navigating the Complexities of Healthcare: A Game Theory Approach to Optimizing Patient Outcomes

One of my favorite ways to really think through a complex problem like the misalignment of incentives is to apply a game theory framework to it and I’ve used this for over a decade. We can move through these decision frameworks a lot faster if just stay high level for now. Before we get started let’s make sure we set up the ground rules properly. Keep in mind this will be a high level meant to start discussions. The actual real world complexities are more nuanced.?

1. Basics of Game Theory:?

• Players: The decision-makers in the game.
• Strategies: The possible actions each player can take.
• Payoffs: The rewards or outcomes players receive based on the combination of strategies chosen.
• Games: Can be cooperative (players can form binding commitments) or non-cooperative (no binding commitments).

Now let’s explain the games to be played and the key concepts including my brilliant mathematician advisor the late Dr. Nash and the “Nash Equilibrium” which we will be using for this example.?

1. Types of Games:?

• Static Games: Players make decisions simultaneously without knowledge of the others' choices.
• Dynamic Games: Players make decisions sequentially with some information about previous actions.

????3. Key Concepts:

• Nash Equilibrium: A situation where no player can benefit by unilaterally changing their strategy, assuming other players keep their strategies unchanged.
• Dominant Strategy: A strategy that provides a higher payoff regardless of what the other players do.
• Pareto Efficiency: An outcome where no player can be made better off without making at least one player worse off.
• Zero-Sum Game: A situation where one player's gain is exactly another player's loss.
• Non-Zero-Sum Game: Outcomes where the total payoff to all players can vary; cooperation can lead to better outcomes for all.

4. Examples of Games

• Prisoner's Dilemma: Two criminals must decide whether to betray each other or remain silent. The Nash equilibrium leads to both betraying, which is suboptimal for both.
• Battle of the Sexes: A couple must decide on an activity to do together, each preferring a different activity but wanting to be together.
• Hawk-Dove Game: Models conflict and cooperation, where players choose between aggressive (hawk) or peaceful (dove) strategies.

5. Applications of Game Theory

• Economics: Market competition, auctions, pricing strategies.
• Political Science: Voting systems, international relations, war strategies.
• Biology: Evolutionary strategies, animal behavior.
• Business: Negotiation tactics, corporate strategy, competitive bidding.

6. Advanced Topics

• Repeated Games: Games that are played multiple times, where strategy can evolve based on past outcomes.
• Bayesian Games: Games involving incomplete information, where players have beliefs about the unknown factors.
• Mechanism Design: Creating systems or mechanisms that lead to desired outcomes, considering the strategic behavior of participants.

Things to know before we get started…?

Game theory provides a framework for understanding strategic interactions in various fields. By analyzing the choices and payoffs, players can identify optimal strategies and predict outcomes in competitive and cooperative scenarios. So let’s see what this looks like…?

To integrate these real-world considerations into the Nash Equilibrium framework without muddying the waters too much, let us explicitly incorporate the incentives of C-level executives, government officials, and private equity owners. We'll distill these factors into the strategies and payoffs, maintaining a clear and structured approach. Here's how we can structure the framework:

Players and Strategies

Players:

1. Hospital CFO
2. Chief Medical Officer (CMO)
3. Hospital CEO
4. Insurance Company
5. Government (HHS/CMS)
6. Patients
7. Private Equity (PE) Fund

Strategies:

1. Hospital CFO:
2. CMO:
3. Hospital CEO:
4. Insurance Company:
5. Government (HHS/CMS):
6. Patients:
7. Private Equity (PE) Fund:

Payoff Matrix Considerations

We'll integrate the motivations for high compensation, profit maximization, and political considerations into the payoff matrix. Here’s an example focusing on key interactions:

Enhanced Payoff Matrix (Hospital CFO, CMO, CEO, Insurance Company, Government, Patients, PE Fund)

CFO \ CMO \ CEO \ Insurance \ Govt \ Patients \ PE Fund

PR (F), Control Costs (K), Lower Rates (I), Advocate (N), Maximize Profits (P)

PR (F), Control Costs (K), Maintain Rates (J), Advocate (N), Maximize Profits (P)

PR (F), Increase Funding (L), Lower Rates (I), Advocate (N), Maximize Profits (P)

PR (F), Increase Funding (L), Maintain Rates (J), Advocate (N), Maximize Profits (P)

Feedback (G), Control Costs (K), Lower Rates (I), Advocate (N), Maximize Profits (P)

Feedback (G), Control Costs (K), Maintain Rates (J), Advocate (N), Maximize Profits (P)

High Negotiation (A), Best Equip.?

(D)

Link with the clean look in google sheets at the payoff matrixes as I realize this is hard to follow: https://docs.google.com/spreadsheets/d/1QeumfFUgflHw9veIjya4APsf1l7G1u1sW8r_mCeNaxU/edit?usp=sharing

(-5, 5, 2, 5, 4, 5, 5)

(3, 5, 2, 1, 2, 3, 5)

(-4, 5, 2, 5, 6, 5, 5)

(4, 5, 2, 1, 4, 4, 5)

(-4, 6, 3, 5, 4, 5, 5)

(4, 6, 3, 1, 2, 3, 5)

High Negotiation (A), Optimize (E)

(-5, 4, 2, 5, 3, 5, 5)

(3, 4, 2, 1, 2, 3, 5)

(-4, 4, 2, 5, 5, 5, 5)

(4, 4, 2, 1, 4, 4, 5)

(-4, 5, 3, 5, 3, 5, 5)

(4, 5, 3, 1, 2, 3, 5)

Accept Lower Rates (B), Best Equip. (D)

(1, 5, 2, 2, 4, 4, 4)

(2, 5, 2, 3, 3, 4, 4)

(1, 5, 2, 2, 5, 5, 4)

(2, 5, 2, 3, 4, 5, 4)

(1, 6, 3, 2, 4, 5, 4)

(2, 6, 3, 3, 3, 4, 4)

Accept Lower Rates (B), Optimize (E)

(1, 4, 2, 2, 3, 4, 4)

(2, 4, 2, 3, 2, 3, 4)

(1, 4, 2, 2, 4, 5, 4)

(2, 4, 2, 3, 3, 4, 4)

(1, 5, 3, 2, 3, 5, 4)

(2, 5, 3, 3, 2, 3, 4)

Balance Budget (C), Best Equip. (D)

(2, 5, 1, 2, 4, 5, 4)

(3, 5, 1, 3, 3, 4, 4)

(2, 5, 1, 2, 5, 5, 4)

(3, 5, 1, 3, 4, 5, 4)

(2, 6, 2, 2, 4, 5, 4)

(3, 6, 2, 3, 3, 4, 4)

Balance Budget (C), Optimize (E)

(2, 4, 1, 2, 3, 5, 4)

(3, 4, 1, 3, 2, 3, 4)

(2, 4, 1, 2, 4, 5, 4)

(3, 4, 1, 3, 3, 4, 4)

(2, 5, 2, 2, 3, 5, 4)

(3, 5, 2, 3, 2, 3, 4)

Incorporating Real-World Incentives

1. Hospital CEO’s Focus on Compensation:
2. Government’s Political Influences:
3. Private Equity’s Profit Maximization:

Nash Equilibrium Analysis with Real-World Incentives

1. Hospital CFO’s Best Responses:
2. CMO’s Best Responses:
3. Hospital CEO’s Best Responses:
4. Insurance Company’s Best Responses:
5. Government (HHS/CMS)’s Best Responses:
6. Patients’ Best Responses:
7. Private Equity Fund’s Best Responses:

Nash Equilibrium Identification with Real-World Incentives

Based on the above best responses, the Nash Equilibrium is:

• Hospital CFO: Balance Budget (C)
• CMO: Advocate for Best Equipment (D)
• Hospital CEO: Maximize Executive Compensation (H)
• Insurance Company: Lower Reimbursement Rates (I)
• Government (HHS/CMS): Favor Large Employers/Contributors (M)
• Patients: Advocate for Better Care (N)
• Private Equity Fund: Maximize Short-Term Profits (P)

This equilibrium is represented by (C, D, H, I, M, N, P) with payoffs (3, 5, 5, 5, 8, 5, 5).

Conclusion

Incorporating real-world incentives such as executive compensation, political influences, and profit maximization into the Nash Equilibrium framework could perhaps give us a more realistic view of the healthcare system. This equilibrium reflects the complexities and competing interests of various stakeholders.

By understanding these dynamics, policymakers and stakeholders can design interventions that better align incentives with patient outcomes, such as:

• Transparent Reporting: Mandating transparent reporting of executive compensation and linking it to patient outcomes.
• Policy Adjustments: Enacting policies that balance the interests of large employers and public health needs.
• Incentive Realignment: Creating financial incentives for long-term value creation over short-term profits.

Perhaps this approach could drive a healthcare system that moves toward a more sustainable and patient-centered model. Hopefully it at least gets a conversation going.