Author: Aviral Verma

Game Theory is dependent on the idea of Nash equilibrium. Nash equilibrium, the situation when neither of the players can choose any other strategy than the one in Nash equilibrium in order to get a better payoff. We can apply the same in the sport of basketball. Imagine a game coming to a winning shot. There are certain scenarios in order to win the game and to lose the game. Considering one of the situations where the loosing team is down by two points, has ball possession and say 20 seconds on the shot clock and the game as well. The team takes a shot. The shot can be either a two-pointer or a three-pointer, two-pointer having higher possibility. With a two-pointer the game would go into an overtime, but instead having a three-point shot, although with less probability, would help win them the game. The paper assumes having a 50% chances of winning upon going into overtime. On the other hand, the current winning team also has two choices. One is to defend the three-pointer, while risking an open two-point shot. The other is to defend the two-pointer shot, but risk the three-pointer shot from the opposite team.

Based on the data collected in the paper, there is no dominant strategy for either team. They have to play a mixed strategy in order to be unpredictable for the other side. After some calculations, the mixed strategy equilibrium comes out to be (p , q) = (0.670 , 0.207), p being the chances of offensive team taking two-point shot and q being the chances of defending team saving the two-point. For the leading team to win, they should defend the three-point shot and not worry about the overtime as in that they would have a 50% chance to win as previously seen. The decision is a tough one for both sides and this relates to many real life interesting situations such as this Finals game.

Reference:

Game theory applied to basketball by Shawn Ruminski

Rail network is a crucial network which has to be made efficient. The increasing density of population needs to be considered as a key factor in the entire railways network. The train timetable scheduling can have defects because of large number of trains and passengers which cause real time traffic delays. Such delays can be prevented with a better evaluation and identification of the rail system performance. This can be done by considering a Train State Graph (TSG).


A train state graph is a directed graph with horizontal axis as time stamp and vertical axis as train index. The time stamp shows an occurrence of an event such as arrival, departure, delay, braking. Each nodes represents a unique state of a train. The vertices in the graph shows the transition of train.
As suggested in the paper, we can set a constant time step (e.g. 50 s), so that the longest time interval between two discrete events is the constant time step. This would help to analyze events but will not be effective if the time constant is too small or too big. A solution to this problem is to mark the delays caused by major events and then remove them and decrease the delay for future. In other words, simply identify and try to eliminate the root causes of the delay.

Source:
https://doi.org/10.1080/0305215X.2017.1284832