Chapter 9: Imperfect Recall and Aggregation of Strategies
We recall that Kuhn (CGT, pp. 193–216) extended and refined the treatment of games in extensive form, including games of “imperfect recall,” that is, games in which a player may not be aware of some of its own earlier moves. (Ch. 3). For non-cooperative analysis, Selten (CGT, pp. 312–54) argues, this multiplicity of agents should be excluded. However, any nontrivial coalition is a compound of two or more agents, so that imperfect recall arises naturally in coalitions. Nevertheless, coalitions seem never to have been discussed for games with imperfect recall. In this chapter we consider two implications of imperfect recall. 9.1 SUPERADDITIVITY In their founding paper of the literature on cooperative solutions for games with given coalition structure, Aumann and Dreze (1974) question the assumption of superadditivity in games in coalition function form.1 The argument for superadditivity is essentially that any vector of strategies available to the two coalitions separately is also available to the merged coalition, so that they can do no worse than to adopt the strategies adopted by the two coalitions separately. Let us call that argument “argument A.” Aumann and Dreze (1974, p. 233) question the argument, although they concede that “superadditivity is intuitively rather compelling.” Nevertheless, they go on to write “. . . ‘acting together’ and sharing the proceeds may change the nature of the game. For example, if two independent farmers were to merge their activities and share the proceeds, both of them might work with less care and energy; the resulting output might...
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