Equivalences among five game specifications, including a new specification whose nodes are sets of past choices

The current literature formally links "OR forms" (named after Osborne and Rubinstein 1994) with "KS forms" (named after Kuhn and Selten by Kline and Luckraz 2016). It also formally links "simple forms" with "AR forms" (both from Alós-Ferrer and Ritzberger 2016, with the former less prominent than the latter). This paper makes three contributions. First, it introduces a fifth game form whose nodes are sets of past choices. Second, it formally links these new "choice-set forms" with OR forms. Third, it formally links KS forms with simple forms. The result is a formal five-way equivalence which provides game theorists with a broad spectrum of alternative game specifications.