Sentence examples for given common knowledge from inspiring English sources

Given common knowledge of this equilibrium, either pure strategy is a best reply for each agent, in the sense that either pure strategy maximizes expected utility.

If μ* is a strict equilibrium, then one can predict which pure strategy profile the agents in a game will follow given common knowledge of the game, rationality and μ*.

As we have seen, given common knowledge of the game and of rationality, forward induction reasoning can lead the agents to an apparent contradiction: The classical argument for backwards induction is predicated on what agents predict they would do at nodes in the tree that are never reached.

So even if agents have "almost" common knowledge, in the sense that the number of levels of knowledge in "Joanna knows that Lizzi knows that … that Joanna knows that ω2 occurred" is very large, their behavior is quite different from their behavior given common knowledge that ω2 has occurred.

Given this common knowledge, Joanna and Lizzi indeed have decisive reason to follow the Aumann correlated equilibrium f.

The spouses coordinate successfully given their common knowledge, while the pedestrian and the motorists miscoordinate as the result of a breakdown in common knowledge.

Indeed, as Rubinstein points out, given merely "almost" common knowledge, the agents choose as if no communication had occurred at all! Rubinstein also notes that this result violates our intuitions about what we would expect the agents to do in this case.

Given the importance of common knowledge in social interactions, it is remarkable that only quite recently have philosophers and social scientists attempted to analyze the concept.

The overall level of dental knowledge was not high in this study population, with a mean knowledge score of 4.64 ± 1.34 (range, 0 10), although the information in the survey is thought to be common knowledge, given public exposure to mass media.

This balancing process involved encouraging or challenging individual learners while at the same time guiding the team as a whole to consolidate a firmly reflected body of common knowledge, giving the team a relevant direction for their work.

Indeed, while Barwise (1988 , 1989 proves a result showing that the fixed point account implies the hierarchical account and gives examples that satisfy the common knowledge hierarchy but fail to be fixed points, a number of authors who have written after Barwise have given various proofs of the equivalence of the two definitions, as was shown in Proposition 2.18.