| Yhteenveto: | What payoffs are positionally determined for deterministic two-player
antagonistic games on finite directed graphs? In this paper we study this
question for payoffs that are continuous. The main reason why continuous
positionally determined payoffs are interesting is that they include the
multi-discounted payoffs.
We show that for continuous payoffs, positional determinacy is equivalent to
a simple property called prefix-monotonicity. We provide three proofs of it,
using three major techniques of establishing positional determinacy --
inductive technique, fixed point technique and strategy improvement technique.
A combination of these approaches provides us with better understanding of the
structure of continuous positionally determined payoffs as well as with some
algorithmic results.
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