Related papers: Computing Economic Equilibria by a Homotopy Method
In our previous paper we proved that every affine economy has a competitive equilibrium. We define a simplex economy as an affine economy consisting of a stochastic allocation (defining the initial endowments) and a variation with…
Processing sets or other unordered, potentially variable-sized inputs in neural networks is usually handled by aggregating a number of input tensors into a single representation. While a number of aggregation methods already exist from…
We present a methodology to robustly estimate the competitive equilibria (CE) of combinatorial markets under the assumption that buyers do not know their precise valuations for bundles of goods, but instead can only provide noisy estimates.…
This chapter explores the role of substitutability in economic models, particularly in the context of optimal transport and matching models. In equilibrium models with substitutability, market-clearing prices can often be recovered using…
The paper aims to find the solution of oligopoly market equilibrium problem through system of nonlinear equations. We propose modified newton method to obtain the solution of system of nonlinear equations. We show that our proposed method…
We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes.…
General equilibrium, the cornerstone of modern economics and finance, rests on assumptions many markets do not meet. Spectrum auctions, electricity markets, and cap-and-trade programs for resource rights often feature non-convexities in…
We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization…
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…
In this paper, we investigate the computation of second-price pacing equilibria (SPPEs), a foundational model in online advertising auctions. We present a polynomial-time algorithm for computing exact SPPEs in instances with a constant…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
Although production is an integral part of the Arrow-Debreu market model, most of the work in theoretical computer science has so far concentrated on markets without production, i.e., the exchange economy. This paper takes a significant…
We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to…
We relate the information exchange between two stochastic systems to the nonequilibrium entropy production in the whole system. By deriving a general formula that decomposes the total entropy production into the thermodynamic and…
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…
Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not…
We present an algorithm for computing pure-strategy epsilon-perfect Bayesian equilibria in sequential auctions with continuous action and value spaces. Importantly, our algorithm includes a verification phase that computes an upper bound on…
We consider demand-side economy. Using Caratheodory's approach, we define empirical existence of equation of state (EoS) and coordinates. We found new insights of thermodynamics EoS, the {\it effect structure}. Rules are proposed as…
We prove the existence of a competitive equilibrium in a production economy with infinitely many commodities and a measure space of agents whose preferences are price dependent. We employ a saturated measure space for the set of agents and…
Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in transformations that are not isochoric (i.e.…