I try to get the intuitive understanding of the notion "degenerate two player game".
Definition. A two-player game is called non degenerate if no mixed strategy of support size $k$ has more than $k$ pure best responses.
What's so special about degenerate game, why sometimes we should consider degenerate case and non degenerate case separately?
Whether the definition of degenerate game is applied to non two player game(so far I saw only 2 player version)?
Consider the following two player game in standard form.
$0/0 \space \space \space \space \space 10/10$
$0/0 \space \space \space \space \space 10/10$
When the column player picks pure strategy to play column two. The row player has more than one pure best response: the first row and the second row.
Does it mean that this always happens in degenerate game, that we have few solutions with the same payoffs for each player? On the other hand, in the above example, we can just use mixed strategy for the row player: play the first row with probability 0.5 and play the second row with probability 0.5.
As you see I really confused by the definition of degenerate game and will appreciate any help.