We develop a non-stochastic version of Miao and Wang (2018) that preserves its key equilibrium mechanisms while allowing explicit computation of the fundamental value. We show that the stock price equals its fundamental value and that the price-to-dividend ratio remains constant over time. Hence, the stock price does not constitute a rational bubble in the standard theoretical sense. Our results support the critique of Hirano and Toda (2025). At the same time, our analysis suggests that the framework of Miao and Wang (2018) offers a useful alternative perspective on asset price dynamics alongside the standard rational bubble theory. We further clarify the distinction between equilibrium multiplicity and rational bubbles and contribute to a systematic classification of bubble theories.
This paper studies a new axiom of choice functions, equal treatment of individuals in an indifference class (ETI), in the context of matching problems. We show that when a choice function satisfies ETI, substitutability, and size monotonicity, any individual for whom equal treatment applies must be either always accepted whenever available or never accepted. The set of admissible choice functions expands substantially when any one of these three axioms is dropped. ETI is also incompatible with q-acceptance. We characterize the minimum degree of q-acceptance violation under ETI, substitutability, and either size monotonicity or consistency. Under size monotonicity, the minimum is characterized by a partition of indifference classes into two groups. By contrast, under consistency, it is characterized by the size of a particular indifference class.
When exactly does a preference ordering on acts have an additive state-dependent utility representation per indifference curve? Following the analogy of a sliding balance, a perfect reflection of the well-known betweenness models for lotteries, we find three answers for monetary acts on a finite state space. In the first two, we exploit the axiom of weak decomposability, identified by Grant, Kajii, and Polak (2000) as the key axiom to extend betweenness to acts, but leaving the continuity and monotonicity of state utility in setpoints an open issue. Our first theorem confirms the necessity of continuity, while the second shows that monotonicty in setpoints requires the additional axiom of ratiomonotonicity. It formalises the idea that sliding a setpoint towards a gain decreases its momentum compared to losses. This observation, in turn, suggests to extend the primitive of a preference ordering with a benchmark for discerning gains from losses within an act. Thus we arrive at the Additive Sliding Balance Utility model for orderings anchored to such a benchmark. In the third theorem, we characterise this class with an even more straightforward betweenness axiom: the balance point of an act should be in between those of its parts.
