Why a country is conducting sports competition like commonwealth games etc..

I think such sports are good because they encourage others to take up some form of exercise and win games locally. Without such events, we would not have anybody to defeat and therefore no motivation to take up sports. However, I do not approve of sports such as car racing, motor racing, boxing, etc. Not only are races such as these dangerous for participants, they use up a lot of fuel for unnecessary purposes. Moreover, special race tracks have to be built for them, and special cars too. People need to look at better avenues to enjoy their adrenalin rush.

I think with the sport as it is in addition to adding a better relationship between the state and its citizens, it is quite reasonable, and the prize would be No. 2.

Well it is for many reasons - As you say - relationships and money are the important ones. The other one which I see as good and positive is - such games boost the confidence of many sportsmen - if you look at the world championships - only top and best 3 get recognition globally. Others are not even considered - but when competing in smaller segments (with lesser no. of participating countries) there are more who can win here - competition is a little less tougher and also recognition boosts the sportsman.