How we also model interaction in any kind of interaction. Adversarial or Collaborative
Level-K Thinking in Auctions (Page 11) By David Banks, Duke University ...
From Talk notes.
" ... A fourth solution concept is level-k thinking. If Daphne is a level-0 thinker, she bids non-strategically. If she is a level-1 thinker, she believes Apollo is a level-0 thinker, and makes her best response given her subjective assessment of the probabilities. If she is a level-2 thinker, she believes Apollo is a level-1 thinker, and so forth.
The “I think that you think that I think ...” reasoning becomes intricate. (Recall Vizzini’s analysis of the iocaine powder in The Princess Bride). An example will be more clear: Suppose Daphne is a level-2 thinker. She believes Apollo is a level-1 thinker who thus believes that she is non-strategic.... "
From talk described here.
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