In the lecture, the professor elaborated on the notion of the Nash equilibrium and introduced us to a novel idea called randomization. All the games I have shown in my previous blogs were categorized as pure strategy games, which means people always play the same strategy every time when there is a Nash equilibrium. For example, if you realize obeying school rules is a Nash equilibrium, you will keep following the rules every time because you are better off when you do so.
This time, the professor explained that randomization can sometimes be a Nash equilibrium strategy and can be exemplified in mixed strategy games, which means people assign a probability to all strategies they might play when they are in a Nash equilibrium. For example, when people are playing rock-paper-scissors game, a pure strategy is to play rock every time, while a mixed strategy is to play rock one third of the time, to play paper one third of the time and to play scissor one third of the time.
The idea of randomization and mixed strategy is widely applied in today’s society. When we are separating people into different groups, we tend to use randomization to achieve the fairest and the most ideal result. Next, I am going explain why randomization is a good strategy under certain circumstances.
- The following example serves as an example only.
During a dinner, there are two tables in the dining room—the West table and the East table. There are ten Asians and ten Americans waiting to dine. We can analyze their incentives of sitting on the East or the West table by thinking about the notion of payoff. If there is only an American sitting at the East table while the remaining people are all Asians, his/her payoff is zero, because he/she might not feel as included or as comfortable as sitting with a group of Americans. If ten Americans are sitting at the East table, they will earn payoffs of 0.5: even though they might have a good time and enjoy themselves, it is not an optimal situation. They lose the opportunity to communicate with people from a different culture. If there are five Asians and five American at the East table, they will earn payoffs of 1, which is the most ideal situation.
The following picture is a graph of a person’s payoff according to the information above:
What are Nash equilibria in this game?
A Nash equilibrium is reached when segregation exists. When ten Asians sit at the West table and ten Americans sit at the East table, neither Americans nor Asians have any incentive to switch to another table.
A Nash equilibrium occurs at the optimal situation. When there are five Asians and Americans sitting at each table. However, this equilibrium is extremely tenuous. Once the number of Asians or Americans exceeds five at any table, this equilibrium will tip over to the segregation situation I mentioned above.
One interesting thing to note is that the result of segregation in the dining room does not mean people prefer segregation: They are simply reacting based on their best strategies. When there are more than 50% people of an ethnic group sitting together, the best response for the people from another ethnic group is to move away and to sit with the people who share their same ethnic heritage. However, this situation does not mean they prefer sitting with their own ethnic group.
One strategy that can also be a Nash equilibrium that you might not notice is randomization. When each person is being sent to a table randomly, he/she is playing his/her best response. As there is a 50% percent chance of being assigned to any table, there is no incentive for him/her to change his/her strategy based on his/her active choice. If everyone is being assigned randomly, we are going to achieve a result that will be close to the optimal Nash equilibrium result that every table has approximately the same number of people from each ethnic background. Therefore, randomization provides a solution to this complex situation, for it prevents a segregation situation from happening. Randomization can help people achieve the fairest result in schools, organizations or companies. If there is any form of segregation exists such as the example I demonstrated above, randomization is a solution!
Joe. “Keep Calm and Stop Segregation.” The Keep Calm-o-matic. Keep Calm Network,
n.d. Web. 9 Oct. 2014. <http://www.keepcalm-o-matic.co.uk/p/
“Rock-Paper-Scissors.” NowIKnow. Dan Lewis, n.d. Web. 9 Oct. 2014.