Bing inspired by the recent clang between Federer and Djokovic in Wimbledon 2012. we as a group decided to research the game theory kineticss of this famed match-up. Both these participants have faced each other rather frequently at important occasions ensuing in exciting lucifers. There are two facets of this game that we wish to analyse. At first. how the comparative strengths of these participants determine the result of the game. While Federer is the title-holder in the truth and arrangement of serves. Djokovic boasts of the best return game of all time. Second. how do the tribunal conditions affect the scheme of each participant. We evaluate this game as a coincident move game with assorted schemes. This is because of the really little reaction clip available. We model the game in the signifier of a tree and usage chance of winning of each participant to find the final payments. The chances in bend are calculated from the past public presentation of the participants against each other. So who would you wager your money on:
Federer’s surgeon-like preciseness in functioning OR Djokovic’s ultra-aggressive return game Read on to happen out! !
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 august competitions. A match-up between them is non merely interesting. but besides entertaining for the witnesss. Both the participants have their comparative strength and failings. while Federer has more assortment in forehand. return of service is Novak’s forte. Federer is great at tactics but due to the age factor Novak has an border in staying power. Both participants are every bit matched in footings of mental stamina. The Wimbledon semi concluding between the two participants was a grass tribunal lucifer. therefore it was even more interesting to see both of them conflict on such conditions for the first clip. A sum-up of their statistics till day of the month is given.
Figure 1: Head to Head record
Game theory has frequently been found to be rather relevant in the analysis of the game of tennis and we besides aim to aim that. As a game in which the scheme of each participant influences the schemes of the other participant. game theory can be used to analyse the optimal schemes for the participants.
Besides assorted constructs of game theory like imperfect information. uncomplete information and assorted schemes have a direct application in the game. Assorted academic documents have discussed the game of tennis from different positions. One such paper. that we found interesting. nowadayss a treatment on the assorted scheme equilibrium with a focal point on celebrated and experient participants. Before go oning with our analysis of the game we would wish to foreground the key larning from the paper that we found utile. Paper: Minimax Play at Wimbledon-Mark Walker and John Wooders. Department of Economics ( University of Arizona ) November 7. 1998
This paper chiefly helped us in traveling frontward with our involvement in analysing the unstructured game of tennis. It argues that there has been much consistence seen in the game drama predicted by theory for tennis and the existent game drama. Even though participants have deviated from the assorted scheme equilibrium. on the whole it is found to be rather consistent. The writers besides argue that the theoretical model is excessively simplistic to explicate the complex game of tennis. Hence we have tried to outdo theoretical account the existent state of affairs. taking realistic premises wheresoever necessary.
Game Details. Payoffs and Schemes:
Against the above background. we decided to analyze a fluctuation of the Best -Response Analysis of the tennis point by looking at the modern twenty-four hours matchup of Roger Federer and Novak Djokovic. Federer’s strength lies in the fluctuation and arrangement of his service while Djokovic has the best return game amongst current participants. So it’s logical that the result of a lucifer depends mostly on how each of these participants optimizes their scheme for their several countries of strength.
Here we consider a coincident zero-sum game in which Djokovic has merely two pure schemes on the return ( he can either support or travel on full-scale onslaught ) . whereas Federer has three pure schemes on the service ( travel broad. travel down the T. or topographic point it in the center of the box ) . Typically. in such games we find that the participant who has three ( or more ) pure strategies uses merely two of them in equilibrium. The others do non calculate in the mix for such a participant. We must therefore determine which 1s are used and which 1s are non. Another point to be noted is that the schemes adopted by both the participants vary with T he playing conditions. chiefly the type of tribunal. In this paper we analyze the consequence of two types of tribunals – clay and hard.