Research map / Multi-agent systems and games / Human-AI and goal-conditioned
Uncommon Belief in Rationality
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Proposes graph-based RBR (rationality and beliefs in rationality) graphs for uncommon higher-order beliefs about rationality, a doxastic rationalisability solution concept, and a partition-refinement algorithm that minimises RBR graphs to a canonical form.
Problem
Common belief in rationality (RCBR) is too strong for systems with heterogeneous agents (e.g., irrational or doxastic agents), and no existing formalism explicitly models uncommon belief-in-rationality structures for strategic reasoning.
Approach
Encode uncommon rationality-and-belief-in-rationality systems as directed labelled graphs whose paths are belief sequences; define iterated rationalisation over these graphs yielding a doxastic rationalisability solution concept, and show doxastic equivalence of nodes coincides with equal belief hierarchies, enabling Hopcroft-style minimisation.
Key results
- Proves that the rational solution is well-defined, reached after finitely many iterated rationalisations.
- Proves nodes are doxastically equivalent iff their belief hierarchies are equal (Psi*_n = Psi*_n').
- Gives an algorithm minimising an RBR graph to a unique canonical form in O(|A|·|N|^2·log|N|) time.
Limitations
- Simplifies rationalisation to elimination of strongly dominated pure strategies, not full best-response rationalisability.
- No empirical evaluation; results are purely theoretical with a worked 2/3-average game example.
Experimental setup
Builds on: rationalisability iterated strategic thinking cognitive hierarchy model Hopcroft's algorithm
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