Applying Bayesian Games to the Life Sciences

Applying Bayesian Games to the Life Sciences

May 11, 2022 Comments Off on Applying Bayesian Games to the Life Sciences Blog Post Snowfish

In an industry as competitive as life sciences, companies have to make decisions in the face of uncertainty and incomplete information. In our previous post on game theory, we outlined a simple example for how this technique can be used in a research and development situation where two companies decide to develop or not develop a product when faced with the choices of a competitor.  Although that simple “game” provided a good outline to think about strategy, it is evident that the situation lacks nuance. In the real world, companies are often unaware of their competitors’ potential profits and costs. With such incomplete information, it can be difficult to discern how your competitors will behave. While no one has perfect foresight, it is helpful to analyze how your competitors may act depending on their private information. Enter Bayesian Games. 

A Bayesian Game is a set of players, with each player having a set of player types. Each player type has a set of possible actions. In this game, the players do not know their opponents’ type but the players, based on prior experience and knowledge, have a common belief about the types that each player could have. Like every other situation in Game Theory, each player has a payoff function. However, in this game, the players’ payoff depends on: their own type, the actions of other players, and the type of their opponents. 

An Example of Bayesian Games in the LIfe Sciences Business

Ok, I realize that this may appear esoteric, to let me apply this to a well-known area within life sciences. Gene therapy presents a revolutionary method to treat disease. According to companiesmarketcap, there are 14 companies in the gene therapy space. However, CRISPR Therapeutics and Intellia Therapeutics dominate the market, with each having a market cap (share price * shares outstanding) of over $3 billion. 

In a situation where CRISPR and Intellia are both deciding whether to develop a therapy, they must make decisions within a great deal of uncertainty. If they both decide to develop and market the therapy, they risk making negative duopoly profits. If they both decide to not develop, neither makes any profits and society is worse off because no one receives the treatment. The most profitable situation for either CRISPR or Intellia would be for one of them to develop the treatment while the other does not. 

Because CRISPR and Intellia do not know the potential profits and costs of each others’ strategies (that information is private), they must formulate a strategy based on what type of player they believe they are facing. In other words, if CRISPR believes Intellia is a high cost type, it will develop a strategy that maximizes its payoff given this belief. Likewise, if CRISPR believes that Intellia is a low cost type, it will formulate a strategy that maximizes its payoff given the opponent is low cost. 

In the table below, I depict the situation in the strategic form. I had a similar chart in our previous post on Game Theory, but this chart now includes private information. The c’s in the private information for CRISPR and Intellia. For example, if CRISPR knows it is low cost (c=0.5), it has a weakly dominant strategy to develop (0.5>0; 1.5>0).

However, if CRISPR has a high cost to develop its strategy depends on what type (high or low cost) it believes Intellia to be. If CRISPR believes Intellia is low cost, it will not develop because Intellia will be able to price CRISPR out of the market. If CRISPR believes Intellia is high cost, CRISPR will develop with a certain probability p because Intellia could decide not to develop. 

  Intellia 
  DevelopDo not Develop
CRISPRDevelop1-c, 1-c2-c,0
 Do not Develop0, 2-c0,0

Private information prevents CRISPR from knowing what type of opponent Intellia is. The only thing CRISPR is certain of is its own type. Thus to have any chance of success, the key is that it must develop strategies for facing either type. 

Conclusion


In the life sciences, companies have to make decisions under uncertainty. Mapping the possible types and decisions of your opponents’ competitors can pay dividends. Snowfish leverages a variety of methods including Game Theory to help inform your strategies. Please reach out to us at info@snowfish.net for help with profiling your competitor and developing a winning strategy. 

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