Representing Strategies

Abstract: Quite some work in the ATL-tradition uses the differences between various types of strategies (positional, uniform, perfect recall) to give alternative semantics to the same logical language. This paper contributes to another perspective on strategy types, one where we characterise the differences between them on the syntactic (object language) level. This is important for a more traditional knowledge representation view on strategic content. Leaving differences between strategy types implicit in the semantics is a sensible idea if the goal is to use the strategic formalism for model checking. But, for traditional knowledge representation in terms of object language level formulas, we need to extent the language. This paper introduces a strategic STIT syntax with explicit operators for knowledge that allows us to charaterise strategy types. This more expressive strategic language is interpreted on standard ATL-type concurrent epistemic game structures. We introduce rule-based strategies in our language and fruitfully apply them to the representation and characterisation of positional and uniform strategies. Our representations highlight crucial conditions to be met for strategy types. We demonstrate the usefulness of our work by showing that it leads to a critical reexamination of coalitional uniform strategies.