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A new proof of the existence of a Walrasian equilibrium with an infinite dimensional commodity space is provided, which allows agents’ preferences to be discontinuous. The new theorems include as corollaries the existence results of Mas-Collel, Yannelis and Zame, Araujo and Monteiro, and Mas-Collel and Richard, among others.

We extend a result on existence of Walrasian equilibria in He and Yannelis (Econ Theory 61:497-513, 2016) by replacing the compactness assumption on consumption sets made there by the standard assumption that these sets are closed and bounded from below. This provides a positive answer to a question explicitly raised in He and Yannelis (Econ Theory 61:497–513, 2016). Our new equilibrium existence theorem generalizes many results in the literature as we do not require any transitivity or completeness or continuity assumption on preferences, initial endowments need not be in the interior of the consumption sets, preferences may be interdependent and price-dependent, and no monotonicity or local non satiation is needed for any of the agents.

The paper examines notions of incentive compatibility in an environment with ambiguity-averse agents. In particular, we propose the notion of maxmin transfer coalitional incentive compatibility, which is immune to coalitional manipulations and thus more stable than the individual incentive compatibility condition. The main result characterizes the set of allocations that satisfy the maxmin transfer coalitional incentive compatibility condition. We show that an allocation satisfies maxmin transfer coalitional incentive compatibility if and only if it is maxmin interim efficient. This result extends that of De Castro and Yannelis (J Econ Theory 177:678–707, 2018) in the sense that ambiguity not only resolves the conflict between efficiency and incentive compatibility, it also accommodates stability. Furthermore, this result is false in a finite economy where agents are subjective expected utility maximizers.

We generalize the classical equilibrium existence theorems by dispensing with the assumption of continuity of preferences. Our new existence results allow us to dispense with the interiority assumption on the initial endowments. Furthermore, we allow for non-ordered, interdependent and price-dependent preferences.

This paper investigates the existence of a nondegenerate pure-strategy Bayesian-Nash equilibrium in a double auction between one seller and several heterogeneous buyers in the independent private value framework. It begins with three examples describing some of the model's particular features. After studying a number of continuity-related properties of the interim payoff functions, we construct a sequence of strategy profiles that converges to a nondegenerate monotone Bayesian-Nash equilibrium of the game under some strict monotonicity conditions. The equilibrium existence result is applied to a double auction with risk-averse bidders.

To justify the use of Wald's maxmin preferences in an asymmetric information economy, we introduce a mechanism designer who can convince/persuade agents to adopt Wald's maxmin preferences. We show that more efficient and individually rational allocations become incentive compatible if the mechanism designer persuades agents to use Wald's maxmin preferences instead of Bayesian preferences. Thus, we justify the Wald's maxmin preferences by showing that agents can be persuaded to use them in order to enlarge the set of efficient, individually rational and incentive compatible allocations.

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value.

We extend the previous work of De Castro et al. ( 2017a , 2017b ) into mixed strategies.

It is known that the core of an economy with externalities may be empty. We consider two concepts of dominance that allow us to prove that the set formed by individually rational, Pareto optimal allocations is stable and coincides with the core that, consequently, is non-empty.

In a partition model, we show that each maximin individually rational and ex ante maximin efficient allocation of a single good economy is implementable as a maximin equilibrium. When there are more than one good, we introduce three conditions. If none of the three conditions is satisfied, then a maximin individually rational and ex ante maximin efficient allocation may not be implementable. However, as long as one of the three conditions is satisfied, each maximin individually rational and ex ante maximin efficient allocation is implementable. Our work generalizes and extends the recent paper of de Castro et al. (Games Econ Behav 2015. doi: 10.1016/j.geb.2015.10.010).