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Amsterdam Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. The jury is still out concerning the epistemic conditions for backward induction, the " oldest idea in game theory " (Aumann, 1995, p. 635). Aumann (1995) and Stal-naker… (More)

We consider two simple variants of a framework for reasoning about knowledge amongst communicating groups of players. Our goal is to clarify the resulting epistemic issues. In particular, we investigate what is the impact of common knowledge of the underlying hypergraph connecting the players, and under what conditions common knowledge distributes over… (More)

It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to… (More)

We analyze the Brandenburger-Keisler paradox in epistemic game theory, which is a 'two-person version of Russell's paradox'. Our aim is to understand how it relates to standard one-person arguments, and why the 'believes-assumes' modality used in the argument arises. We recast it as a fixpoint result, which can be carried out in any regular category, and… (More)

The main aim of this paper is to raise awareness of higher-order knowledge (knowledge about someone else's knowledge) as an issue for computer game AI. We argue that a number of existing game genres, especially those involving social interaction, are natural fields of application for an approach we call explicit knowledge programming. We motivate the use of… (More)

We provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. We first establish a generic result that links true common beliefs (and, respectively, common knowledge) of players' rationality defined by means of 'monotonic' properties, with the iterated elimination of strategies that do not satisfy these properties. It… (More)

In the context of strategic games, we provide an axiomatic proof of the statement (Imp) Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. Rationality here means playing only strategies one believes to be best responses. This involves looking at two… (More)

Motivated by the distributed implementation of game-theoretical algorithms , this paper proposes an explicit form of knowledge-based programming. Abstracting from the game-theoretical details, we describe a general scenario where a group of agents each have some initially private bits of information which they can then communicate to each other. We draw on… (More)