Beyond admissibility: Dominance between chains of strategies

TL;DR

This paper explores a new rationality concept based on dominance chains in finite graph games with quantitative objectives, addressing limitations of admissibility in such settings.

Contribution

It introduces the notion of maximal uniform chains as a new dominance-based rationality concept and establishes decidability results for these chains in specific game classes.

Findings

Established criteria for dominance chains in game strategies.

Proposed maximal uniform chains as a rationality notion.

Proved decidability of key questions about uniform chains.

Abstract

Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by an admissible strategy. However, in games played on finite graphs with quantitative objectives (as used for reactive synthesis), this is not the case. We consider increasing chains of strategies instead to recover a satisfactory rationality notion based on dominance in such games. We start with some order-theoretic considerations establishing sufficient criteria for this to work. We then turn our attention to generalised safety/reachability games as a particular application. We propose the notion of maximal uniform chain as the desired dominance-based rationality concept in these games. Decidability of some fundamental questions about uniform chains is established.