Difference between equilibrium and k-rationalizability I'm reading a Structural Models of Nonequilibrium Strategic Thinking: Theory,
Evidence, and Applications by Crawford, Costa-Gomes and Iriberri. They write the following:


  In two-person games, a player can find his set
  of k-rationalizable strategies via k rounds of
  iterated strict dominance, without the need
  for fixed-point reasoning. Thus, k-rationalizability is cognitively less taxing than equilibrium, especially for small k.


K rationalizable strategies are those that survive k-rounds of iterated strict dominace (for n=2 player games). For n >2, k-rationalizable strategies are those that survive k-rounds of iterative never best response elimination. 

What is meant by fixed point reasoning here? Is there a difference between fixed point reasoning and iterative never-best-response elimination? 

Relevant section is Section 2.2 found on page 12.
What is meant by fixed point reasoning here? 


Specifically, Nash equilibria. One way to define a Nash equilibrium in words is "a strategy profile from which no player can be made better-off by unilaterally deviating to a different action".  In other words, a Nash equilibrium is a "fixed point" because if the game ends up there, play stops because there are no more optimal moves.


  Is there a difference between fixed point reasoning and iterative never-best-response elimination?


Yes, they are different solution concepts.  The key is the last paragraph on page 12 of the article - basically, think of k-rationalizability as half-assing the game while still keeping the assumptions of full info, rationality, belief in mutual rationality, and so on.  Instead of stopping play when there are no optimal moves, play stops when some kind of decision-making resource is exhausted. It is interesting precisely to the extent that it may or may not model how real people, who face real information costs and processing time limitations, might approach games.