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
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For this we used primary data collected by observing matches between the two players and secondary data available in the form of serve statistics.
In total we collected data for 300 points played over 8 matches. The rationale behind these pay-offs is the success rate associated with each player’s strategy as shown below.
Data for Clay Court Matches
Points Played on Federer's Serve
Total Points Won by each
(Federer's Strategy, Djokovic's Strategy)
Wide Serve, Defensive Return
Wide Serve, Attacking Return
Serve down the T, Defensive Return
Serve down the T, Attacking Return
Serve in the Middle of Box, Defensive
Return
Serve in the Middle of Box, Attacking Return
300
Federer
Wins
206
Djokovic
Wins
94
8
74
22
27
4
19
8
18
12
63
8
37
We begin looking for a mixed strategy by verifying that there is no pure strategy equilibrium. When we examine the above payoff table, we find that strategy M for Federer is a dominated strategy. So the payoff table is modified as below. This is an extension of the point stated above that for a mixed strategy equilibrium a player uses only two of his pure strategies. Clay Court
Federer
W
T
p-mix
Djokovic
D
67,33
75,25
33p+25(1-p)
Where p = probability that Federer plays W q = probability that Djokovic plays D
6|Page
A
80,20
58,42
20p+42(1-p)
q-mix
67q+80(1-q)
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