Game Theory in the Life Sciences: Research and Development

Game Theory in the Life Sciences: Research and Development

April 25, 2022 Comments Off on Game Theory in the Life Sciences: Research and Development Blog Post Snowfish

A study of the mathematical models of conflict and cooperation between intelligent rationale decision makers, Game Theory provides a useful lens to analyze any industry. When applied to the life sciences, an analysis using Game Theory can yield superior insights in the field of research and development.  

Snowfish regularly completes Market Landscape Analysis for clients. In the course of our assessment, we consider a variety of factors impacting the market for a treatment including regulatory environment, market size and price, setting of the treatment, clinical data, benefits of the existing treatment, and competition.

A thorough competitive analysis means highlighting potential competitors in addition to existing ones. Existing competitors can be relatively easy to uncover. Just Google companies with an FDA approved treatment for the disease you are interested in treating and you are in business. However, potential competition can be more challenging. This is where Game Theory can be quite useful.

A Quick Primer on Game Theory

Game Theory is the study of strategic behavior through mathematical models. A “game” is a set of: players, actions for each player, and payoff functions for each player that depend on the actions of their opponents.

The classic Prisoner’s Dilemma provides a good example of a game. In the Prisoner’s Dilemma, two burglars get caught. As dexterous criminals, these burglars have been careful not to tell their co-conspirator their names. In the interrogation room, the district attorney tells them that if both remain silent, he has enough evidence to convict both of them and send them to jail for two years.

However, if one of the burglars confesses and the other one does not, the attorney will give the confessor a lighter sentence (1 year in prison) and a harsher sentence to the one that remained silent (5 years in prison). In the last case, if both of the burglars confess, they each get three years in prison.  

I have mapped the situation out below

 SilentConfess
Silent-2,-2-5,-1
Confess-1,-5-3,-3

In this game, each player has to consider which strategy (silent or confess) will give them the best payoff based on the other player’s choice. For the row player, if the column player chooses silent, the row player is best off choosing confess. If the column player chooses confess, the row player is best off choosing silent as well.

For the column player, the analysis is the same. No matter what the row player does, the column player is best off choosing confess. This situation yields an equilibrium of [confess, confess].

This equilibrium is what is what is called Nash equilibrium. Nash equilibrium is a situation where no player can change what he is doing and get a strictly higher payoff. For the row player, if he changes from confess to silent, he gets a worse payoff (-5 instead of -3). For the column player the same situation occurs where switching to silent would achieve a payoff of -5.

Game Theory: Research and Development

In the life sciences, a similar situation can play out when two companies are deciding whether to develop and market a treatment. As we have written about previously, drug development is costly; the average out-of-pocket costs to develop a novel prescription is $1.4 billion. With such a cost at stake, deciding whether to develop or not (go-no-go decision) requires careful analysis. 

Game Theory can help you and your team make these decisions. Take the COVID-19 vaccine race with Pfizer and Moderna for example. Pfizer and Moderna both had to decide whether to develop a vaccine or not. If both companies decided against developing a vaccine, they would have achieved a payoff of zero. 

If one company decided to develop a vaccine and the other company did not, the developing company would receive a payoff of M-c where M is the monopoly profits and c is the cost of R&D. When both companies chose to move ahead with development (what actually occurred), they each got a payoff of D-c where D is the duopoly profits and c is the cost.

The situation looks like this.

  Pfizer 
  DevelopDo not Develop
ModernaDevelopD-c, D-cM-c,0
 Do not Develop0, M-c0,0

Equilibria in this situation depends on the profitability of each action. For Moderna, if D-c >0 (duopoly profits are greater than R&D costs), it will choose to develop when Pfizer chooses to develop. If Pfizer chooses to not develop, Moderna will choose to develop if M-c>0 (the monopoly profits are greater than zero).

For Pfizer, the analysis is the same. If Moderna chooses to develop, Pfizer will develop if D-c>0. If Moderna chooses to not develop, Pfizer will develop if M-c>0.

To perform this analysis,

  1. Estimate the revenues that your treatment will generate depending on the structure of the market. 
  2. Estimate the revenues that your competitor will generate depending on the structure of the market. 
  3. Estimate the cost of your products R&D and the cost of your competitors’ R&D
  4. Map out the various situations in a strategic form (pictured above) and determine the best course of action by finding your best responses

While this model is an oversimplification of what occurs in industry, it does encourage critical thinking about the moves of your competitors. 

Conclusion

Profitability is critical to determine what path your company should take when looking at potential research and development. Applying Game Theory to your research and development decisions will yield valuable insights into how a company should behave when faced with the choices of its opponents.  

To help with your analysis of competitors, please contact us at info@snowfish.net 

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