Like Daniel has mentioned, the difference between will and would in the example sentences you provided is based on the level of commitment: "Yes, I will go to the game tomorrow". This means that the person in this sentence has confirmed guaranteed 100% that he will be there at the game. "Yes, I would go to the game tomorrow." means that the person has not made a commitment to go to the game and is still uncertain.
Using would can also express a hypothesis or hypothetical situation (Example: I would go on this trip but my schedule is full)
The key to knowing whether to use will or would in a sentence or to know the difference between the two is to look at the context of the sentence.