I recently read this article titled "The Braess Paradox In Soccer – How A Team Can Be Better Without Its Best Scorer"; and thought about the application of game theory to teams.
The Nash equilibrium is a self-enforcing agreement, aligning the self-interests of individuals, and distinguishing between cooperative and non-cooperative games. A common example used to explain the Nash equilibrium is where a traffic light is not working at a crossroads. If you act unilaterally and speed through the junction without considering the strategy of the person coming from the road to your left, you might make it home in record time or die trying. Alternatively, you could consider the other person's strategy, and slow down or stop to come to a mutual understanding. You won’t get home with a new lap record, but you are far more likely to get home. This is a Nash equilibrium. The payoff isn’t massive, but in the longer term it is more mutually beneficial to both parties. Once parties arrive at such an equilibrium, no party can profit by deviating unilaterally from it.
Where the Nash equilibrium is lost in a team, e.g. an individual is changing their strategy unilaterally for their own self-interest; the team could suffer overall. The key is identifying when that tipping point is reached. The Nash equilibrium is stable where individuals refine their strategies based on the response of others. Repeated interactions promote rational strategies. As mathematician John Williams’ strategy showed, “Tit for tat” encourages better outcomes overall. You scratch my back, I scratch yours. It builds trust and mutual cooperation.
Where an individual is acting in their own self-interest and upsetting the equilibrium within the team, the Braess Paradox strategy could be considered; not by removing that individual, but by removing the incentive and/or ability for an individual to act unilaterally through the implementation of various other strategies. It's interesting to think about what those strategies can be.
A really interesting video explaining the Braess Paradox was produced by Veritasium, and is well worth a watch: This mechanism shrinks when pulled
Also a useful explanatory document is located here: Braess's paradox
