A New Approach to Treating Cancer With Game Theory
http://fortune.com/2018/08/10/beating-cancer-game-theory/
Last month, a team comprised of a data scientist, a mathematician, a biologist, a physician published a paper on “Optimizing Cancer Treatmeng Using Game Theory”. Clifton Leaf of Fortune News helps break down this team’s findings and remarkable application of game theory to cancer treatment. The formulation of cancer treatment using game theory begins with the players who in this case are the oncologist, whose responsibility is to distribute treatment; and the cancer cells, which aim to defend themselves and spread through the body. This setup is an attacker versus defender game, similar to problem 4 in the current homework set. Leaf notes that one common strategy used by oncologists is to prescribe very high doses of “cytotoxic drugs” in an effort to destroy the cancer cells and prevent them from spreading. While one would expect this strategy to be effective, in actuality it could induce metastasis in any surviving cells. This means the cells that resist the oncologist’s attack could repopulate and spread at a fatal rate. It is only after the metastasis kicks in that physicians recognize the cancerous cells did not respond and try to switch treatments. Unfortunately, at this point it is often too late to win the game.
There is an evident problem here that Leaf extracted from the research paper: the doctors seem to be a step behind; the cancer is acting as the leader and the doctors are following. The team of researchers propose a new strategy that relies on game theory in an effort to reverse these leader/follower roles between the cancer and the doctors. The team suggests, instead of administering one forceful attack of cytotoxic drugs, why not reveal the cancer cells’ strategies and respond according to these resistance tactics? But how can you reveal the opponent’s strategies? The idea is to give a patient smaller doses of a few types of medicines and examine (i) which group of cells resist a certain type of medicine and (ii) how they resist it. Then, by knowing and understanding the cancer cells’ strategies, the doctors can determine what their best-response is.
The researchers discuss how they can exploit this asymmetry of the game to defeat cancer cells. Predicting the cancer’s “moves” gives the doctor a clearer path to defeating cancer. Mathematically, the researchers model both players’ best responses as curves. In a regular game, the players play simultaneously and the Nash Equilibrium is the outcome (the intersection of the best response curves). But in this new game, since the doctor will already know the cancer’s strategy, a “Stackelberg solution” will result. A Stackelberg solution allows the doctor to choose the optimal outcome that lies anywhere on the cancer’s best response curve. The Stackelberg solution is often much better than the Nash Equilibrium—and that is the advantage of understanding the cancer’s behaviour.
In reading this article, I learned the amazing breadth of applications of game theory and the models we learn in class. Although while learning the concepts of game theory, we are exposed to very simple games, it is motivating to know that the formulation of the same concepts to large-scale, real-world, interdisciplinary problems can be life-changing. I will be eager to know the success of this treatment strategy in the coming years.
Works Cited:
Leaf, C. (2018, August 10). Ready Player One: Beating Cancer With Game Theory. Retrieved September 08, 2018, from http://fortune.com/2018/08/10/beating-cancer-game-theory/
Stanková, K., Brown, J. S., Dalton, W. S., & Gatenby, R. A. (2018). Optimizing Cancer Treatment Using Game Theory. JAMA Oncology. doi:10.1001/jamaoncol.2018.3395
this is really cool!