Nash Equilibrium and Sports go hand in hand

Nash Equilibrium – Each firm is doing the best it can, given what its competitors are doing.

It is present in football, it is there in all racquet sports, it is obviously there in a mentally engrossing sport like chess and also present in track events of athletics. The concept of Nash Equilibrium is present in almost all sports in one form or the other.

The Equilibrium was explained by the mathematician John Nash in 1951.Originally an economic concept for the oligopolistic firms to take strategic decision regarding the price; it has a huge relevance in the world of sports. No manager, coach, captain or a player can strategise without considering what their competitor is doing.

So, how does it work? Let’s take an example from football. Assume that the managers of two competing teams have almost the same qualities and are of equal competence. The manager of one team will decide upon a formation which is best to counter the formation of the other team. But the former will know that the same thing must be going through the mind of the manager of the latter team and in turn, will field a formation that is best suited to counter the first team. Then what should the two managers do? It’s natural to assume that both managers will field the best formation they can given what the other is doing and do not have the incentive to deviate from the plan as it may lead to a loss for either team.

Similarly, Nash Equilibrium works for athletes of equal competence running in a long distance race regarding who will speed up when and at what point of the race. In lawn tennis, it exists where the server has to decide on which side to serve the ball to get the best result, while also thinking where will the receiver hit it to get his/her best result. In motorsport, the team manager has to find best ways to increase the speed of the car, while also considering that other team managers are doing the same. In all these cases, once the decision is taken, no team wants to change it because that gives them the best payoff.

Unlike in above sports, where strategies are made at about the same time, cricket, golf and chess require players to make decisions one after the other. A golf player hits a shot from the tee before his competitor does. Here, the natural advantage is with the first person as he knows for sure that the latter will take a shot in reaction to his shot. If the first player’s shot was executed well, then the second player will hit a shot at par with the former, because if the latter becomes too ambitious to hit it farther than the former, then there is a chance that the execution will be poor and the ball might land on the bunker or the rough. In a way, the second player too hits such which is best for him given that the first player didn’t hit a bad shot.

One condition in Nash Equilibrium is that it assumes that the competitors are rational and take wise decisions. One irrational decision by a player can lead to loss in the game. But in sports, irrationality can definitely occur to both competing teams. A recent example can be the Game 6 of the World Chess Championship 2014 between Magnus Carlsen and Viswanathan Anand. In the middle of the game, Carlsen playing with white pieces (a natural advantage) committed a blunder. Here the Equilibrium was disturbed. Given the Nash Equilibrium, Anand was not at all expecting such a move from Carlsen and in turn, within seconds made an irrational move and eventually lost the game. All in all, a bad decision by either of the competitors again restored the Nash Equilibrium.

As competition is increasing, Nash Equilibrium is finding its way in all sports. Players are analysing every match and learning from their opponents’ decisions. Most of the game is being played in the mind. Ultimately, planning is an important part of winning a game in any sport. Thus, Nash Equilibrium is the order for all sports.

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