A Logical Account of Social Rationality in Strategic Games

We propose a modal logic that enables to reason about different kinds of rationality in strategic games. This logic integrates the concepts of joint action, belief, individual preference and group preference. The first part of the article is focused on the notion of individualistic rationality assumed in classical game theory: an agent decides to perform a certain action only if the agent believes that this action is a best response to what he expects the others will do. The second part of the article explores different kinds of social rationality such as fairness and reciprocity. Differently from individualistically rational agents (alias self-interested agents), social rational agents also consider the benefits of their choice for the group. Moreover, their decisions can be affected by their beliefs about other agents’ willingness to act for the well-being of the group. In the article we also provide a complete axiomatization of our logic of joint action, belief, individual preference and group preference.

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