Related papers: Settling the Complexity of Arrow-Debreu Equilibria…
Over the last decade, combinatorial algorithms have been obtained for exactly solving several nonlinear convex programs. We first provide a formal context to this activity by introducing the notion of {\em rational convex programs} -- this…
In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop…
We show that the existence of a computationally efficient calibration algorithm, with a low weak calibration rate, would imply the existence of an efficient algorithm for computing approximate Nash equilibria - thus implying the unlikely…
We consider an economy where agents' consumption sets are given by the cone $\mathbf{L}^0_+$ of non-negative measurable functions and whose preferences are defined by additive utilities satisfying the Inada conditions. We extend to this…
Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…
We study Fisher markets that admit equilibria wherein each good is integrally assigned to some agent. While strong existence and computational guarantees are known for equilibria of Fisher markets with additive valuations, such equilibria,…
We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.
We study the computational complexity of computing Bayes-Nash equilibria in first-price auctions with discrete value distributions and discrete bidding space, under general subjective beliefs. It is known that such auctions do not always…
This paper revisits the Arrow-Debreu general equilibrium framework through the lens of effective trade, emphasizing the distinction between theoretical and realizable market interactions. We develop the Effective Trade Model (ETM), where…
Public goods games in undirected networks are generally known to have pure Nash equilibria, which are easy to find. In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems:…
We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…
We study an Arrow-Debreu economy with externalities generated by multiplex networks. Market equilibrium prices reflect both the preferences and scarcity of goods, consumers' network centralities arising from goods' externalities, as well as…
In 1979, Hylland and Zeckhauser \cite{hylland} gave a simple and general scheme for implementing a one-sided matching market using the power of a pricing mechanism. Their method has nice properties -- it is incentive compatible in the large…
Proportional response is a well-established distributed algorithm which has been shown to converge to competitive equilibria in both Fisher and Arrow-Debreu markets, for various sub-families of homogeneous utilities, including linear and…
We show that computing an equilibrium in atomic splittable congestion games with player-specific affine cost functions $l_{e,i}(x) = a_{e,i} x + b_{e,i}$ is $\mathsf{PPAD}$-complete. To prove that the problem is contained in…
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…
Unlike ordinal-utility matching markets, which are well-developed from the viewpoint of both theory and practice, recent insights from a computer science perspective have left cardinal-utility matching markets in a state of flux. The…
We study a robust utility maximization problem in the case of an incomplete market and logarithmic utility with general stochastic constraints, not necessarily convex. Our problem is equivalent to maximizing of nonlinear expected…
We study linear Fisher markets with satiation. In these markets, sellers have earning limits and buyers have utility limits. Beyond natural applications in economics, these markets arise in the context of maximizing Nash social welfare when…
This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller…