# Game Theoretic Analysis of Federer vs Djokovic

Topics: Game theory, Nash equilibrium, Tennis Pages: 11 (2069 words) Published: February 18, 2013
FedEx versus Djoker:
Through the Lens of Game Theory

Term Paper | IIMK | PGP 15

Submitted By: Group 13
Ranjith P

(PGP/015/041)

Ankur Pandit

(PGP/015/206)

Anurag Butoliya (PGP/015/207)
Paran Gupta

(PGP/015/240)

FedEx versus Djoker: Through the Lens of game Theory

Executive Summary:
Being inspired by the recent clash between Federer and Djokovic in Wimbledon 2012, we as a group decided to explore the game theory dynamics of this celebrated matchup. Both these players have faced each other quite often at crucial junctures resulting in exciting matches. There are two aspects of this game that we wish to analyze. At first, how the relative strengths of these players determine the outcome of the game. While Federer is the champion in the accuracy and placement of serves, Djokovic boasts of the best return game ever. Secondly, how do the court conditions affect the strategy of each player. We evaluate this game as a simultaneous move game with mixed strategies. This is because of the very small reaction time available. We model the game in the form of a tree and use probability of winning of each player to determine the payoffs. The probabilities in turn are calculated from the past performance of the players against each other. So who would you bet your money on:

Federer’s surgeon-like precision in serving OR Djokovic’s ultra-aggressive return game Read on to find out!!

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FedEx versus Djoker: Through the Lens of game Theory

Game Setting: Background of the Situation
Roger Fedrer Vs Novak Djokovic is considered to be one of the Tennis’ most revered rivalries. A matchup between them is not only interesting, but also entertaining for the spectators. Both the players have their relative strength and weaknesses, while Federer has more variety in forehand, return of serve is Novak’s specialty. Federer is great at tactics but due to the age factor Novak has an edge in stamina. Both players are equally matched in terms of mental toughness. The Wimbledon semi final between the two players was a grass court match, thus it was even more interesting to see both of them battle on such conditions for the first time. A summary of their statistics till date is given.

Game theory has often been found to be quite relevant in the analysis of the game of tennis and we also aim to target that. As a game in which the strategy of each player influences the strategies of the other player, game theory can be used to analyze the optimum strategies 3|Page

FedEx versus Djoker: Through the Lens of game Theory
for the players.

Also various concepts of game theory like imperfect information,

incomplete information and mixed strategies have a direct application in the game. Various academic papers have discussed the game of tennis from different perspectives. One such paper, that we found interesting, presents a discussion on the mixed strategy equilibrium with a focus on celebrated and experienced players. Before continuing with our analysis of the game we would like to highlight the key learning from the paper that we found useful. Paper: Minimax Play at Wimbledon-Mark Walker and John Wooders, Department of Economics (University of Arizona) November 7, 1998

This paper primarily helped us in going forward with our interest in analyzing the unstructured game of tennis. It argues that there has been much consistency seen in the game play predicted by theory for tennis and the actual game play. Even though players have deviated from the mixed strategy equilibrium, on the whole it is found to be quite consistent. The authors also argue that the theoretical framework is too simplistic to explain the complex game of tennis. Hence we have tried to best model the actual situation, taking realistic assumptions wherever necessary.

Game Details, Payoffs and Strategies:
Against the above background, we decided to examine a variation of the Best -Response Analysis of the...