Anonymity and equal treatment of equals (ETE) are foundational notions of fairness in mechanism design. However, they are often too strong: they either exclude intuitively fair rules, or choose rules characterized by weaker requirements. We introduce several weak notions of equity to a general environment. These notions of equity define rich classes of rules that often violate ETE, and we identify restrictions under which they imply ETE. We characterize several rules for two division problems: the uniform rule (Sprumont, 1991), sequential allotment rules with equal guarantees (Barbera et al., 1997), and a generalization of random priority rules (Bogomolnaia and Moulin, 2001). For sequential allotment rules, the weakest forms of equity can give one agent nearly the entire surplus over identical agents.

We establish the existence of the universal type structure in presence of conditioning events without any topological assumption, namely, a type structure that is terminal, belief-complete, and non-redundant, by performing a construction à la Heifetz & Samet (1998). In doing so, we answer affirmatively to a longstanding conjecture made by Battigalli & Siniscalchi (1999) concerning the possibility of performing such a construction with conditioning events. In particular, we obtain the result by exploiting arguments from category theory and the theory of coalgebras, thus, making explicit the mathematical structure underlining all the constructions of large interactive structures and obtaining the belief-completeness of the structure as an immediate corollary of known results from these fields.

We propose a new rationalizability concept for dynamic games that combines elements from forward and backward induction reasoning. For that reason, we call it forward and backward rationalizability. It is shown that in terms of outcomes, the concept is equivalent to the pure forward induction concept of extensive-form rationalizability, but both concepts may differ in terms of strategies. We argue that the new concept provides a more compelling theory for how players react to surprises as, in contrast to extensive form-rationalizability, a player always believes that the opponent will choose rationally in the future, and never attributes unreasonable beliefs to an opponent. In terms of strategies, the new concept provides a refinement of pure backward induction reasoning as embodied by backward dominance and backwards rationalizability. These two results together imply that in every dynamic game, all extensive-form rationalizable outcomes are also possible under backwards rationalizability. This may be viewed as a generalization of Battigalli's theorem, which states that in perfect information games without relevant ties, the unique extensive-form rationalizable outcome is the backward induction outcome. Finally, it is shown that the concept of forward and backward rationalizability satisfies the principle of supergame monotonicity: If a player learns that the game was actually preceded by some moves he was initially unaware of, then this new information will only refine, but

A range of empirical puzzles in finance has been explained as a consequence of traders being averse to ambiguity. Ambiguity averse traders can behave in financial portfolio problems in ways that cannot
be rationalized as maximizing subjective expected utility. However, this paper shows that when traders have access to limit orders, investment behavior of an ambiguity-averse decision-maker is observationally equivalent to the behavior of a subjective expected utility maximizer with the same risk preferences; ambiguity aversion
has no additional explanatory power.