Are games tournament increase the income of country?

Not by much I think, it is just that everyone will be in hotels and needs food and stuff, so the places where tournaments are will make more money then usual for a while. For the rest I'm not sure, a lot of money gained at the tournament will go to the organisation or the national tt association I think.

Depends on what kind of game it is. For the real big game, like olympic, usually the host country will lose money due to all those new infrastructure. But it may boost up the income in the surrounding area for short period of time.

Well Dorian, like Dici mentioned above, it really depends on what sort of games you are implying to. For massive competitions like the Olympics or the football World Cup, we are talking about billions spent on just the infras (usually from loans), and that's before the games. Depending on how well they were organized, we are talking about billions in takings from the directly selling of tickets, sponsorships, to kick backs from retails and hotels reservations. And as I am sure you noticed too, your everyday necessities will increase in prices as well.
And after the games are finished and dusted, you are left with under utilized stadiums and infras, plus a huge loan to pay back from the coffers, in this case the country. So in the end, you are worse than you started,at least for growing country..unlike China for instance.
But, on a smaller scale like WTTC, it's good to host coz the benefits outweighs the negative effect. You don't have to spend a bomb on infras, and you still get kick backs from retails and hotels, plus increasing the tourism revenue in the long run. Basically, the risk is lower.

The infras is of course only when the current infra isnt good enough. I think a lot of countries could host big games with their current infra.