# Qatar Fifa 2020 Impact - Game Theory

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 MANAGERIAL ECONOMICS ASSIGNMENT – DUBAI 14-16 Impact of having Doha World Cup 2022 during winter Dhruv Malhotra D14006

 Game Theory: Nash equilibrium of club football vs. international games - impact of having Doha World Cup 2022 during winter

Contents

Introduction

Nash Equilibrium

Analysis

Conclusion

References

## Introduction

On 2nd December, 2010, Qatar won the prestigious bid to host the 2022 FIFA world cup. With the matches generally being played during the off season for the European leagues – June/July, the temperature during the day reaches up to 50 degrees centigrade where as the low temperatures during night time is around 30 degrees in Qatar.

Such temperatures make it impossible for the games to be held during daytime in open stadium which is generally the norm. Even in the last world cup of 2014, the high temperatures of 30 degrees in Brazil was too much for the teams to handle and more often than not, players faced extreme exhaustion. FIFA had to introduce mandatory time outs for the players to refill their lost fluids from their body – an unheard thing for the usual game of football.

At a certain point, there was a discussion regarding a possibility to shift the world cup during winter months of December/January. This notion was unanimously opposed by all major leagues in Europe due to the club matches being affected.

To understand this impact, we take a look at Nash Equilibrium to see the dominant strategy regarding holding the matches during winter months.

## Nash Equilibrium

Nash Equilibrium: Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy. To see what this means, imagine that each player is told the strategies of the others. Suppose then that each player asks himself or herself: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"

If any player would answer "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the set of strategies is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium.

The following game doesn't have payoffs defined:

 L R T a,b c,d B e,f g,h

In order for (T,L) to be an equilibrium in dominant strategies (which is also a Nash Equilibrium), the following must be true:  a > e | c > g | b > d | f > h

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