Paradoxes of Belief and Strategic Rationality. (book reviews)

These two books consider a number of foundational issues in game theory having to do with common knowledge and rationality. Robert Koons is concerned with these issues primarily in relation to equilibrium concepts--such as subgame perfection--that rely on the notion of backward induction. His running example is the chain-store game, although his analysis is just as transparent in the following version of the centipede game:

Here, (j) refers to a decision node for player j; and player 1's payoffs are atop player 2's at the end nodes. It is easily seen that there is a unique subgame ...

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