Arxiv:1802.06888V1 [Cs.AI] 5 Jan 2018 Superrational Types
Superrational types Fernando A. Tohm´e 1,2 and Ignacio D. Viglizzo2,3 1Departmento de Econom´ıa, Universidad Nacional del Sur (UNS), Bah´ıa Blanca, Argentina 2Instituto de Matem´atica de Bah´ıa Blanca (INMABB), Universidad Nacional del Sur-CONICET, Bah´ıa Blanca, Argentina 3Departmento de Matem´atica, Universidad Nacional del Sur (UNS), Bah´ıa Blanca, Argentina July 2, 2018 Abstract We present a formal analysis of Douglas Hofstadter’s concept of superrationality. We start by defining superrationally justifiable ac- tions, and study them in symmetric games. We then model the beliefs of the players, in a way that leads them to different choices than the usual assumption of rationality by restricting the range of conceivable choices. These beliefs are captured in the formal notion of type drawn from epistemic game theory. The theory of coalgebras is used to frame type spaces and to account for the existence of some of them. We find conditions that guarantee superrational outcomes. arXiv:1802.06888v1 [cs.AI] 5 Jan 2018 1 Introduction Game Theory has, traditionally assumed that agents make decisions accord- ing to the criterion of full rationality [7]. In contrast to the case of bounded rationality ([24], [21]), agents choose the best actions to achieve their goals without limitations to their ability to do so. The research on behavioral fac- tors in decision-making, initiated by Kahneman and Tversky ([13]) lead to a dearth of results under weaker rationality assumptions. On the other hand, 1 the interest in overcoming “undesirable” results such as inefficient equilibria in social dilemmas lead to alternative concepts, diverging from the rationality assumption [12], [19].
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