On stability of Bertrand-Nash equilibrium in a simple model of the labour market

We examine a Bertrand-Edgeworth model of competition in a labour market where the workers simultaneously set wages disregarding any influence their current decision may have on opponents' future decisions. The iterated best response process is shown to converge in finite time to a Bertrand-Nash solution, where wages are set at the market-clearing level. This convergence result is also shown to hold when the assumption of static expectations is replaced by milder restrictions on beliefs about opponents'' wages.

Existence of pure strategy equilibria in Bertrand-Edgeworth games with imperfect divisibility of money

This paper incorporates imperfect divisibility of money in a price game where a given number of identical firms produce a homogeneous product at constant unit cost up to capacity. We find necessary and sufficient conditions for the existence of a pure strategy equilibrium. Unlike in the continuous action space case, under discrete pricing there may be a range of symmetric pure strategy equilibria - which we fully characterize - a range which may or may not include the competitive price. Also, we determine the maximum number of such equilibria when competitive pricing is itself an equilibrium.Bertrand-Edgeworth competition; Price game; Oligopoly; Pure strategy equilibrium; Discrete pricing

Pricing and matching under duopoly with imperfect buyer mobility

Recent contributions have explored how lack of buyer mobility affects pricing. For example, Burdett, Shi, and Wright (2001) envisage a two-stage game where, once prices are set by the firms, the buyers play a static game by choosing independently which firm to visit. We incorporate imperfect mobility in a duopolistic pricing game where the buyers are involved into a multi-stage game. The firms are shown to have an incentive to give service priority to loyal customers. Under this rationing rule, equilibrium prices converge to their value under perfect buyer mobility as the number of stages of the buyer game increasesBertrand competition, matching, imperfect mobility, sequential equilibrium, buyerloyalty

Existence of pure strategy equilibrium in Bertrand-Edgeworth games with imperfect divisibility of money

This paper incorporates imperfect divisibility of money in a price game where a given number of identical firms produce a homogeneous product at constant unit cost up to capacity. We find necessary and sufficient conditions for the existence of a pure strategy equilibrium. Unlike in the continuous action space case, with discrete pricing there may be a range of symmetric pure strategy equilibria - which we fully characterize - a range which may or may not include the competitive price. Also, we determine the maximum number of such equilibria when competitive pricing is itself an equilibrium.Bertrand-Edgeworth competition

Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice

We study the quantum (zero-temperature) critical behaviors of confined particle systems described by the one-dimensional (1D) Bose-Hubbard model in the presence of a confining potential, at the Mott insulator to superfluid transitions, and within the gapless superfluid phase. Specifically, we consider the hard-core limit of the model, which allows us to study the effects of the confining potential by exact and very accurate numerical results. We analyze the quantum critical behaviors in the large trap-size limit within the framework of the trap-size scaling (TSS) theory, which introduces a new trap exponent theta to describe the dependence on the trap size. This study is relevant for experiments of confined quasi 1D cold atom systems in optical lattices. At the low-density Mott transition TSS can be shown analytically within the spinless fermion representation of the hard-core limit. The trap-size dependence turns out to be more subtle in the other critical regions, when the corresponding homogeneous system has a nonzero filling f, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the n=1 Mott transition this gives rise to a modulated TSS: the TSS is still controlled by the trap-size exponent theta, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.Comment: 26 pages, 34 figure

Bubbling (or just frothy) house prices?

Housing

The decline in the U.S. personal saving rate: is it real and is it a puzzle?

Since the mid-1990s, the national income and product accounts personal saving rate for the United States has been trending down, dropping into negative territory for three months during the past two years. This paper examines measurement problems surrounding two of the standard definitions of the personal saving rate. The authors conclude that, despite these measurement problems, the recent decline of the U.S. personal saving rate to low levels seems to be a real economic phenomenon and may be a cause for concern for several reasons. After examining several possible explanations for the trend advanced in the recent literature, the authors conclude that none of them provides a compelling explanation for the steep decline and negative levels of the U.S. personal saving rate.Consumer behavior ; Saving and investment

Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly

The paper extends the analysis of price competition among capacity-constrained sellers beyond the cases of duopoly and symmetric oligopoly. We first provide some general results for the oligopoly and then focus on the triopoly, providing a complete characterization of the mixed strategy equilibrium of the price game. The region of the capacity space where the equilibrium is mixed is partitioned according to the features of the mixed strategy equilibrium arising in each subregion. Then computing the mixed strategy equilibrium becomes a quite simple task. The analysis reveals features of the mixed strategy equilibrium which do not arise in the duopoly (some of them have also been discovered by Hirata (2008)).Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium