As the holiday season approaches, my independent study on Game Theory is also coming to an end. In my last post, I would like to take the opportunity to reflect on my work with Game Theory this past semester, some lessons I’ve learnt, and my plan for the coming weeks.
Since the start of September, I’ve been watching Game Theory courses on Yale Open Courseware and doing weekly problem sets accompanying the lectures. Unlike Tom who watched these lectures last year, I found myself naturally drawn to the real world examples Professor Polak used to illustrate complex concepts. As I mentioned in my first post, Game Theory is not a purely theoretical subject separated from the real world but develops models based on our needs to find the best way to organize a party, pay our taxes, or choose a route to go to school. This deep connection means that Game Theory not only teaches us the best response(s) to a specific situation but also teaches us ways to approach life problems.
One of the most important life lessons I learnt is to put myself in others’ shoes and consider their preferences, options, and reactions to my moves. When analyzing a multi-player game, one of the first things to do is to find out other players’ options and payoffs they have in each situation. The information helps a player better predict the move of the others since each of us essentially are trying to get the best payoff in our individual situations. Because people’s actions are interconnected in the game and in the society, knowing others’ situation helps me have a better sense of my role in the bigger picture. This way I can be a leader that helps all players work together towards a better Nash Equilibrium as I described in the Community Weekend Event example. Also, when we think about other people’s situations, we must take note of their individuality. One must acknowledge that while everyone tries to maximize his/her payoffs, not everyone’s payoff is the same in every situation. For example, when we are creating a duty schedule, it is important to note the difference of a “morning person” and a “night owl” because some people might gain higher payoff taking a morning or a night shift and it can work in everyone’s favor to accommodate that. Still one more thing to consider when we put ourselves in others’ shoes is how our actions and reputation change other people’s decision and our long-term options. Especially in sequential games like getting a bank loan, our credit history plays a huge part in whether the bank is willing to lend us a huge sum of money. Often in life, we are not playing a one-time game. Our actions today influence our options in the next step. If I want to get a big loan from the bank for a start-up when I graduate from college, I will need to start building a good credit history by repaying my bills even though not paying bills might give me a higher payoff in the short term. Studying Game Theory pushes me to think more about other people’s hopes and strength when working with them in group projects and to consider both short-term and long-term consequence before I act.
On the other hand, comparing models in Game Theory to real life shows me the limits of current mathematics models to take into account all the complexity of human experience. Arguably, we can model randomness with possibility and mixed strategy and different preferences with different payoffs. Yet, as I try to navigate the real world in Game Theory’s perspective, I’ve found that in many situations personal variables like irrationality are not given or are simply inaccessible. The two posts that touched me the most are “How Hannibal defeated Game Theory” and “Game Theory in the Norman Conquest”. In both posts, I told stories about how barbarians defeated the well-thought out military strategies of famous generals with their “irrationality”. Furthermore, in both cases, it was luck that helped the Romans and William the Conquer to win the battle. In hindsight, there might be new ways to perfect my models that I have yet to learn about. These “failures” of Game Theory nonetheless remind me constantly that no matter how close my model is to the reality, it is never perfect. Imperfections make me humble in front of humanity, nature, and knowledge and push me to go deeper.
One last thing Game Theory has taught me is to have a plan for the future. Thus, here, I would like to propose some goals for the final month of my independent project. First of all, I want to finish the remaining 5 lectures and 3 problem sets in the Open Course. I want to continue to push myself to connect new concepts in the lecture to real world problems and go back to perfect the models I developed previously. As I currently planned, my independent study will either culminate in a final exam or a presentation to a small group during the exam period. There’re still a lot of new ideas to learn and concepts to familiarize myself with, so the next month would be really busy and rewarding for me.