In this paper we distinguish two competing conceptions of dignity, one recognizably Hobbesian and one recognizably Kantian. We provide a formal model of how decision-makers committed to these conceptions of dignity might reason when engaged in an economic transaction that is not inherently insulting, but in which it is possible for the dignity of the agent to be called into question. This is a modified version of the ultimatum game. We then use this model to illustrate ways in which the (...) Kantian evaluative standpoint enjoys a kind of internal stability that the Hobbesian framework lacks. Our interpersonal argument shows that, under certain conditions, Hobbesians prefer to cultivate Kantian commitments in others and promote the presence of Kantians in the population. Our intrapersonal argument shows that agents who are conflicted between Kantian and Hobbesian commitments have powerful reasons not to resolve this commitment in favour of Hobbesian values. Our emulation argument illustrates that in repeated versions of the ultimatum game, the Hobbesian chooses to behave like a Kantian, including publicly repudiating her Hobbesian commitments. Here again, however, the Hobbesian is able to achieve a desired benefit only on the condition that there are genuine Kantians in the population. Finally, our social planning argument explores the reasons why a community of Hobbesians would opt to enshrine a Kantian conception of dignity into law. The paper concludes with some remarks about the policy implications of this work. The value or worth of a man is, as for all other things, his price, that is to say, so much as would be given for the use of his power; and therefore is not absolute, but a thing dependent on the need and judgement of another... The public worth of a man, which is the value set on him by the Common-wealth, is that which men commonly call DIGNITY. Hobbes, _Leviathan X_, 16. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

Normative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, until they can (...) apply limited backward induction. The result is that the game has a solution in the form of a subjective Nash equilibrium, which boundedly rational players can possibly realize. (shrink)