Your Wish is My Command Sanction-based Obligations in a Qualitative Game Theory

Goffman argues that agents should depict in their mind the decision making of other agents and gives a game-theoretic interpretation of obligations, but decision and game theory are criticized for their ideality assumptions. For example, Simon argues for limited or bounded rationality, and more recently Gmytrasiewitcz and Durfee argue for recursive modelling. In this paper we use recursive modelling to formalize sanctionbased obligations in a qualitative game theory. In particular, we formalize an agent who attributes mental attitudes such as beliefs, goals and desires to the normative – e.g. legal, moral – system which creates and controls its obligations. The wishes (goals, desires) of the normative system are the commands (obligations) of the agent. We propose a framework with three dimensions: the agents, the mental attitudes, and the distinction between violations and sanctions. We introduce obligations in this framework, and we discuss various examples in which the agent reasons about what counts as a violation and when and which sanctions are applied. We introduce a formalization of the framework and the definition of obligation, and we show how the examples can be formalized. Since the agent is able to reason about the normative system’s behavior, our model accounts for many ways in which an agent can violate a norm without believing to