Research map / Multi-agent systems and games / Games and equilibria
Responsibility in Extensive Form Games
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Proposes a seeing-to-it responsibility notion for extensive form games combining backwards-strategic seeing-to-it with achievement seeing-to-it, proves it is mutually undefinable with counterfactual responsibility, and studies responsibility gaps and their higher-order hierarchy.
Problem
Seeing-to-it responsibility lacks a proper definition for multi-agent settings where agents act in sequence (extensive form games); existing notions (strategic and achievement seeing-to-it) fail to capture responsibility intuitions, and responsibility gaps are not formally understood there.
Approach
Combine backwards-strategic seeing-to-it (an upfront ability to guarantee the outcome maintained along the play path) with achievement seeing-to-it (an agent's choice eliminates the last possibility of a negative condition) into one responsibility modality, and evaluate it on outcomes in a modal logic over extensive form games.
Key results
- Proves C and S are mutually undefinable in extensive form games (C_a p not definable via S; S_a p not definable via C).
- Shows no responsibility gap for non-trivial statements in any two-agent extensive form game.
- Shows higher-order responsibility gaps vanish: the i-th order gap truth set is empty for i >= |Omega(G)|-1.
Surprising findings
- Strategic seeing-to-it with a negative condition can ascribe responsibility to an agent who takes no action at all, motivating the actus reus requirement.
- Formulae S_a S_a phi and S_a phi are not semantically equivalent, while C_a C_a phi is equivalent to C_a phi.
Limitations
- Results are for perfect-information extensive form games; the gap results do not extend to imperfect information.
- Responsibility gap in games with more than two agents is shown by example, and the paper does not give a general characterisation for that case.
Experimental setup
Baselines: strategically seeing-to-it achievement seeing-to-it counterfactual responsibility
Builds on: STIT logic counterfactual responsibility (principle of alternative possibilities) deliberative seeing-to-it
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