Evolutionary game theory studies the dynamics of how players change their strategies in response to the strategies currently used by other players.
The strategies that offer the biggest payoff against the current population of players gain in popularity, and the evolving distribution of strategies continuously changes the payoffs for each of them. The “replicator equation” is a popular dynamical model, which has applications in economics and biology. Assuming that we want to achieve some target distribution of strategies among the players, we can often achieve this by changing the rules of the underlying game. (E.g., subsidizing certain behavior or penalizing a particular type of players.) Our intervention comes with a cumulative price, integrated over the entire path from the initial strategy distribution to the desired target distribution. A reasonable question is how to structure our intervention to minimize this cumulative price. We will try answering this question for two systems of replicator equations: a Rock-Paper-Scissors game and a model of evolution of cancer cells.

Based on joint ongoing work with Alex Vladimirsky.