Does anyone know whether any work has been done in the field of game theory to model adjustive or dynamic strategies? "Adjustive" and "dynamic" are words I chose (since they fit well with what I mean by them), so a different term might actually be used, but let me explain what I mean by them.

Consider, for example, the 2 person zero-sum game with payoff matrix for the row player as follows:

[ 1 -1 ]
[ -1 1 ]

A simple example of an adjustive/dynamic strategy would be to initially play GTO (choose each row with probability 50%) but whenever the opponent's past actions exit a 75% confidence interval for GTO play, switch to the maximally exploitive strategy (choose the appropriate row with probability 100%).

Here's another example. Let x1 and x2 be the number of times our opponent has played columns 1 and 2, respectively. On the first round, play each row with probability 50%. On each subsequent round, play row 1 with probability x1/(x1+x2) and row 2 with probability x2/(x1+x2).

Has a way to formalize these kinds of strategies been developed? What about computing which of these kinds of strategies would win against each other on average when played for a certain number of iterations?

yes, work has been done in this field. "Tit for Tat" is a well known example for prisoner's dilemma. In poker and some other games, the research in this field is often listed under the keywords "opponent modeling".

There are many many many papers on game theory approaches to evolutionary and behavioral ecology dynamics.