“…4 All of our results remain true if we adopt instead the solution concept of interim independent rationalizability studied in Morris and Skiadas (2000), Battigalli and Siniscalchi (2003), and Ely and Pȩ ski (2006). 5 In this paper, we follow , Ely and Pȩ ski (2011), Chen et al (2010Chen et al ( , 2012 to consider a class of games associated with a fixed set of payoff-relevant states Θ. More precisely, for different n-critical types, we demonstrate the strategic discontinuity by suitably varying the payoffs defined on the n × n × |Θ| profiles of actions and Θ.…”