Game Equivalence Note for van Benthem Workshop

The most famous work on game equivalence is Thomson (1952) “Equivalence of Games in Extensive Form.” Two more recent works which serve as inspiration for the present project are Bonanno (1992) “Set-Theoretic Equivalence of ExtensiveForm Games” and van Benthem (2001) “Extensive Games as Process Models.” Thomson frames the debate by considering a large space of games (extensive form games) and a well defined property which can be assigned to each member of that set (the corresponding strategic form game). Thomson then demonstrates first that the space of extensive form games can be partitioned For those who are unfamiliar with them, extensive form games are basically trees, decorated with 1. an assignment of a single player to each node (the player whose turn to act it is at that point in the game) 2. equivalence relations between nodes labeled with the same player (that player’s “information set” at that stage in the game) 3. a function from end nodes and players to payoffs of some form