Don't think in terms of a single-round game, think in terms of a situation where you have to co-exist with the other party for a relatively long time and have some kind of a relationship with it.

I also had in mind this bit of wisdom from Robin.

The conclusions about a particular specific issue of today are not necessarily all that important compared to sharing a a general framework of approaches to things, a similar way of analyzing them...

As stated, this primarily matters for pundits. Notice that the methods of thinking that he's talking about don't reliably lead to the same conclusions; different values and different facts mean that two people who think very similarly (i.e. structure arguments in the same way) may end up with opposite policy preferences, able to look at each other and say "yes, I get what you think and why you think it, but I think the opposite." And so a particular part of the blogosphere will discuss policies in one way, another part another way, it'll be discussed a third way on television, and so on. But the battle lines will still be drawn in terms of conclusions, because policy conclusions are what actually get implemented, and it doesn't seem sensible to describe the boundaries between the areas where policies are discussed as "battle lines," when what they actually are is an absence of connections.