On the Open-Loop Nash Equilibrium in LQ-Games

In this paper we consider open-loop Nash equilibria of the linear-quadratic differential game.As well the finite-planning-horizon, the infinite-planning horizon as convergence properties of the finite-planning-horizon equilibrium if the planning horizon is extended to infinity are studied.Particular attention is paid to computational aspects and the scalar case.

Landscape in the Economy of Conspicuous Consumptions \ud

Psychological states side by side with the bounded rational expectations among social agents contributes to the pattern of consumptions in economic system. One of the psychological states are the envy – a tendency to emulate any gaps with other agents’ properties. The evolutionary game theoretic works on conspicuous consumption are explored by growing the micro-view of economic agency in lattice-based populations, the landscape of consumptions. The emerged macro-view of multiple equilibria is shown in computational simulative demonstrations altogether with the spatial clustered agents based upon the emerged agents’ economic profiles

Preferential Multi-Context Systems

Multi-context systems (MCS) presented by Brewka and Eiter can be considered as a promising way to interlink decentralized and heterogeneous knowledge contexts. In this paper, we propose preferential multi-context systems (PMCS), which provide a framework for incorporating a total preorder relation over contexts in a multi-context system. In a given PMCS, its contexts are divided into several parts according to the total preorder relation over them, moreover, only information flows from a context to ones of the same part or less preferred parts are allowed to occur. As such, the first $l$ preferred parts of an PMCS always fully capture the information exchange between contexts of these parts, and then compose another meaningful PMCS, termed the $l$-section of that PMCS. We generalize the equilibrium semantics for an MCS to the (maximal) $l_{\leq}$-equilibrium which represents belief states at least acceptable for the $l$-section of an PMCS. We also investigate inconsistency analysis in PMCS and related computational complexity issues

Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem

In this brief paper we revise the original motivations of Rolf Mantel to pursue a proof of Sonnenschein´s conjecture. We contend that his work on computational models of general equilibrium lead him to seek an alternative to the usual fixed point theorems used in proofs of existence. Confronted with a paper of Uzawa and his own experience in programming a national planning system he found that the use of theorems like Brouwer´s and Kakutani´s was unavoidable. To check out whether Uzawa was right he sought to find out whether the only properties required of excess demand functions to ensure the existence of equilibria in competitive markets were continuity, homogeneity and Walras´ law. In 1974, he found that this was actually the case. We will see that this result and his interpretation were informed by Mantel´s interest in economic development and planning.Fil: Tohmé, Fernando

Strategic Payments in Financial Networks

In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of ?(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems

Simulation and Estimation of Nonaddative Hedonic Models

Making use of restrictions imposed by equilibrium, theoretical progress has been made on the nonparametric and semiparametric estimation and identification of scalar additive hedonic models (Ekeland, Heckman, and Nesheim, 2002) and scalar nonadditive hedonic models (Heckman, Matzkin, and Nesheim, 2002). However, little is known about the practical aspects of estimating such models or of the characteristics of equilibrium in such models. This paper presents computational and analytical results that fill some of these gaps. We simulate and estimate examples of equilibrium in the additive hedonic models and provide evidence on the performance of several estimation techniques. We also simulate examples of equilibria in nonadditive models and provide evidence on the performance of the nonadditive estimation techniques developed in Heckman, Matzkin, and Nesheim (2002).

A semantical approach to equilibria and rationality

Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and with the environment. Rational behaviors are achieved not only through conscious reasoning, but also through spontaneous stabilization at equilibrium points. Formal theories of rationality are usually guided by informal intuitions, which are acquired by observing some concrete economic, biological, or network processes. Treating such processes as instances of computation, we reconstruct and refine some basic notions of equilibrium and rationality from the some basic structures of computation. It is, of course, well known that equilibria arise as fixed points; the point is that semantics of computation of fixed points seems to be providing novel methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200

Landscape in the Economy of Conspicuous Consumptions

Psychological states side by side with the bounded rational expectations among social agents contributes to the pattern of consumptions in economic system. One of the psychological states are the envy – a tendency to emulate any gaps with other agents’ properties. The evolutionary game theoretic works on conspicuous consumption are explored by growing the micro-view of economic agency in lattice-based populations, the landscape of consumptions. The emerged macro-view of multiple equilibria is shown in computational simulative demonstrations altogether with the spatial clustered agents based upon the emerged agents’ economic profiles.conspicuous consumption; behavioral economics; agent-based simulations