Related papers: Knight--Walras Equilibria
This paper gives a constructive treatment of McKenzie's theorem on the existence of general equilibria. While the full theorem does not admit a constructive proof, and hence does not admit a computational realisation, we show that if we…
We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We…
Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…
Bringing fairness to energy resource allocation remains a challenge, due to the complexity of system structures and economic interdependencies among users and system operators' decision-making. The rise of distributed energy resources has…
This work studies equilibrium problems under uncertainty where firms maximize their profits in a robust way when selling their output. Robust optimization plays an increasingly important role when best guaranteed objective values are to be…
We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a…
We revisit the foundations of fairness and its interplay with utility and efficiency in settings where the training data contain richer labels, such as individual types, rankings, or risk estimates, rather than just binary outcomes. In this…
We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the…
We revisit the connection between bargaining and equilibrium in exchange economies, and study its algorithmic implications. We consider bargaining outcomes to be allocations that cannot be blocked (i.e., profitably re-traded) by coalitions…
A generalized framework is developed which uses a set description instead of wavefunction to emphasize the role of the observer. Such a framework is found to be very effective in the study of the measurement problem and time's arrow.…
This article presents a detailed technical framework for modeling with Bertrand-Nash equilibrium prices under Mixed Logit demand. Two coercive fixed-point equations provide more stable computational methods than those obtained from the…
Neural networks (NNs) lack measures of "reliability" estimation that would enable reasoning over their predictions. Despite the vital importance, especially in areas of human well-being and health, state-of-the-art uncertainty estimation…
We introduce the notion of fault tolerant mechanism design, which extends the standard game theoretic framework of mechanism design to allow for uncertainty about execution. Specifically, we define the problem of task allocation in which…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
The war of attrition with two-sided asymmetric information is a foundational model in political economy, yet it generically admits a continuum of perfect Bayesian equilibria. This paper characterizes the sources of equilibrium multiplicity.…
We derive tractable necessary and sufficient conditions for the absence of buy-and-hold arbitrage opportunities in a perfectly liquid, one period market. We formulate the positivity of Arrow-Debreu prices as a generalized moment problem to…
We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables $\{w_{ij}\}$ describing the…
We propose a pseudo-market solution to resource allocation problems subject to constraints. Our treatment of constraints is general: including bihierarchical constraints due to considerations of diversity in school choice, or scheduling in…
In a world where more decisions are made using artificial intelligence, it is of utmost importance to ensure these decisions are well-grounded. Neural networks are the modern building blocks for artificial intelligence. Modern neural…
In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the…