 Besides variations in preferences and beliefs, a third crucial aspect of players is their styles of information processing, decision making, and reasoning. Real cognitive agents are bounded in their information processing, as both their memory and reasoning capacities are limited. In particular, players may not be able to represent the entire game they are in, nor reason until the end of the game. This phenomenon of short sight has been studied in Grossi and Turrini (2012) and Turrini (2016). Moreover, in real-life iterated social interaction, payoffs are generated along the game, and may not be clear beforehand, (Axelrod &amp; Hamilton 1981). In such contexts, the best strategy in terms of short-term payoffs need not be optimal in the long run, but bounded agents may miss this longer horizon, (Klein, Marx, &amp; Scheller 2021).