COORDINATION ON SADDLE-PATH SOLUTIONS: THE EDUCTIVE VIEWPOINT—LINEAR UNIVARIATE MODELS

2003 ◽  
Vol 7 (1) ◽  
pp. 42-62 ◽  
Author(s):  
George W. Evans ◽  
Roger Guesnerie
Keyword(s):  
Information Structure ◽  
Common Knowledge ◽  
Sufficient Conditions ◽  
Structural Heterogeneity ◽  
Perfect Foresight ◽  
One Step ◽  
Univariate Model ◽  
With Memory ◽  
Forward Looking

We investigate local strong rationality (LSR) in a one-step-forward-looking univariate model with memory one. Eductive arguments are used to determine when common knowledge (CK) that the solution is near some perfect-foresight path is sufficient to trigger complete coordination on that path (i.e., the path is LSR). Coordination of expectations is shown to depend on three factors: the nature of the CK initial beliefs, the degree of structural heterogeneity, and the information structure. Our sufficient conditions for LSR precisely reflect these features and provide basic consistent justifications for the choice of the saddle-path solution.

scholarly journals THE E-MAIL GAME REVISITED — MODELING ROUGH INDUCTIVE REASONING

2007 ◽  
Vol 09 (02) ◽  
pp. 323-339 ◽  
Author(s):  
UWE DULLECK
Keyword(s):  
Information Structure ◽  
Common Knowledge ◽  
Inductive Reasoning ◽  
Rational Behavior ◽  
To Come ◽  
Boundedly Rational Behavior ◽  
Expected Payoffs ◽  
E Mail

I study the robustness of Rubinstein's (1989) E-Mail Game results by varying the information that players can utilize. The article follows one of Morris' (2002) reactions to the E-Mail game "that one should try to come up with a model of boundedly rational behavior that delivers predictions that are insensitive to whether there is common knowledge or a large number of levels of knowledge". Players in my model are presumed to use 'rough inductive reasoning' because they cannot utilize exact information. The information structure in the E-Mail game is generalized and the conditions are characterized under which Rubinstein's results hold. I find that rough inductive reasoning generates a payoff dominant equilibrium where the expected payoffs change continuously (instead of discretely) in the probability of "faulty" communication.

scholarly journals Economic dynamics under heterogeneous adaptive learning: aggregate economy sufficient conditions for stability

2020 ◽  
Vol 20 (1) ◽  
pp. 128-153
Author(s):  
Anna S. Bogomolova ◽  
Dmitriy V. Kolyuzhnov
Keyword(s):  
Adaptive Learning ◽  
Sufficient Conditions ◽  
Structural Heterogeneity ◽  
Dsge Models ◽  
Diagonal Dominance ◽  
Fundamental Nature ◽  
Shock Process ◽  
Heterogeneous Learning ◽  
Endogenous Variables ◽  
Aggregate Economy

We provide sufficient conditions for stability of a linear structurally heterogeneous economy under heterogeneous learning of agents, extending the results of Honkapohja and Mitra (2006), Kolyuzhnov (2011), and Bogomolova and Kolyuzhnov (2019). Sufficient conditions for stability under heterogeneous mixed RLS/SG learning for four classes of models: models without lags and with lags of the endogenous variable and with t or t-1- dating of expectations, are provided for the cases of the diagonal structure of the shock process behaviour or the heterogeneous RLS learning and are presented in terms of structural heterogeneity and are independent of heterogeneity in learning. The results are based on the negative diagonal dominance approach and are provided, first, in terms of the existence of the weights for aggregation of endogenous variables and of expectations across agents, interrelated in a special way, and then in terms of the E-stability of a suitably defined aggregate economy. The fundamental nature of the approach adopted in the paper allows one to apply its results to a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents.

scholarly journals Nonfragile Quantized Dissipative Filter for Nonlinear Networked Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Kewang Huang ◽  
Jianfeng Wang ◽  
Feng Pan
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Networked Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Parameter Perturbation ◽  
Filter Parameter ◽  
Performance Requirements ◽  
One Step ◽  
Error System

To address the problem of filter parameter perturbation in nonlinear networked systems, a nonfragile quantized dissipative filter is designed by considering the coexistence of random one-step time delay, multipacket losses, and quantization error. We acquired the sufficient conditions for the existence of filter by choosing appropriate Lyapunov function as well as utilizing linear matrix inequality. Furthermore, we obtained the parameter expressions of the designed filter. The designed filter could meet the performance requirements of stability and dissipativity for the filter error system under the condition of allowed time delays, packet loss probability, and quantization density. The effectiveness of the designed filter is verified by numerical simulation.

scholarly journals Forward Guidance without Common Knowledge

2018 ◽  
Vol 108 (9) ◽  
pp. 2477-2512 ◽  
Author(s):  
George-Marios Angeletos ◽  
Chen Lian
Keyword(s):  
General Equilibrium ◽  
Common Knowledge ◽  
Feedback Loops ◽  
New Keynesian ◽  
New Keynesian Model ◽  
Aggregate Level ◽  
Standard Practice ◽  
Forward Guidance ◽  
Keynesian Model ◽  
Forward Looking

How does the economy respond to news about future policies or future fundamentals? Standard practice assumes that agents have common knowledge of such news and face no uncertainty about how others will respond. Relaxing this assumption attenuates the general equilibrium effects of news and rationalizes a form of myopia at the aggregate level. We establish these insights within a class of games which nests, but is not limited to, the New Keynesian model. Our results help resolve the forward-guidance puzzle, offer a rationale for the front-loading of fiscal stimuli, and illustrate more broadly the fragility of predictions that rest on long series of forward-looking feedback loops. (JEL D82, D83, D84, E12, E23, E52, E62)

EXPECTATIONS, FORECASTING, AND PERFECT FORESIGHT

1999 ◽  
Vol 3 (2) ◽  
pp. 167-186 ◽  
Author(s):  
Volker Böhm ◽  
Jan Wenzelburger
Keyword(s):  
Economic Growth ◽  
Overlapping Generations ◽  
Sufficient Conditions ◽  
General Linear Model ◽  
Overlapping Generations Model ◽  
Savings Behavior ◽  
Perfect Foresight ◽  
Expectations Formation ◽  
Necessary And Sufficient ◽  
Dominant Influence

The paper studies the nature of expectations formation rules for deterministic economic laws with an expectations feedback within the framework of dynamical systems theory. In such systems, the expectations formation rules, called predictors, have a dominant influence. The concept of a perfect predictor, which generates perfect-foresight orbits, is proposed and analyzed. Necessary and sufficient conditions are given for which local as well as global perfect foresight is possible. The concept is illustrated for the general linear model as well as for models of the cobweb type. For the standard overlapping generations model of economic growth, the existence of perfect predictions depends strongly on the savings behavior of the agents and on the technology.

scholarly journals Minimum Energy Control of 2D Positive Continuous-Discrete Linear Systems

2014 ◽  
Vol 8 (3) ◽  
pp. 165-168
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Final State ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
One Step ◽  
Necessary And Sufficient

Abstract The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.

Algebraic characterization of infinite Markov chains where movement to the right is limited to one step

1977 ◽  
Vol 14 (04) ◽  
pp. 740-747 ◽  
Author(s):  
Ester Samuel-Cahn ◽  
Shmuel Zamir
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Algebraic Characterization ◽  
Transient States ◽  
One Step ◽  
The Right

We consider an infinite Markov chain with states E 0, E 1, …, such that E 1, E 2, … is not closed, and for i ≧ 1 movement to the right is limited by one step. Simple algebraic characterizations are given for persistency of all states, and, if E 0 is absorbing, simple expressions are given for the probabilities of staying forever among the transient states. Examples are furnished, and simple necessary conditions and sufficient conditions for the above characterizations are given.

Sufficient Conditions for Minimum-Phase Second-Order Linear Systems

1995 ◽  
Vol 1 (2) ◽  
pp. 183-199 ◽  
Author(s):  
Jong-Lick Lin ◽  
Jer-Nan Juang
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Common Knowledge ◽  
Sufficient Conditions ◽  
Second Order ◽  
Geometrical Approach ◽  
Minimum Phase ◽  
Sensors And Actuators ◽  
Influence Matrix ◽  
Order Linear

Several sufficient conditions are derived for a second-order linear system to be minimum phase. It is commonly known that a second-order linear system with collocated sensors and actuators is minimum phase. In general, this common knowledge is correct mathematically when the input influence matrix is the transpose of the output influence matrix. In this paper, we extend this knowledge to the case with noncollocated actuators and sensors. First, a conventional approach is used to prove some sufficient conditions of sensor and actuator locations for a system to be minimum phase. Second, a geometrical approach is introduced to discuss the sufficient conditions, and then used to derive other more useful sufficient conditions for a minimum-phase second-order linear system. Many illustrative examples are provided for the readers to better understand the theories developed in this paper.

scholarly journals Identification of games of incomplete information with multiple equilibria and unobserved heterogeneity

10.3982/qe666 ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1659-1701 ◽  
Author(s):  
Victor Aguirregabiria ◽  
Pedro Mira
Keyword(s):  
Private Information ◽  
Multiple Equilibria ◽  
Unobserved Heterogeneity ◽  
Common Knowledge ◽  
Sufficient Conditions ◽  
Finite Mixture Model ◽  
Payoff Function ◽  
Finite Mixture ◽  
Relevant Variables ◽  
Necessary And Sufficient

This paper deals with identification of discrete games of incomplete information when we allow for three types of unobservables: payoff‐relevant variables, both players' private information and common knowledge, and nonpayoff‐relevant variables that determine the selection between multiple equilibria. The specification of the payoff function and the distributions of the common knowledge unobservables is nonparametric with finite support (i.e., finite mixture model). We provide necessary and sufficient conditions for the identification of all the primitives of the model. Two types of conditions play a key role in our identification results: independence between players' private information, and an exclusion restriction in the payoff function. When using a sequential identification approach, we find that the up‐to‐label‐swapping identification of the finite mixture model in the first step creates a problem in the identification of the payoff function in the second step: unobserved types have to be correctly matched across different values of observable explanatory variables. We show that this matching‐type problem appears in the sequential estimation of other structural models with nonparametric finite mixtures. We derive necessary and sufficient conditions for identification, and show that additive separability of unobserved heterogeneity in the payoff function is a sufficient condition to deal with this problem. We also compare sequential and joint identification approaches.

Non-uniqueness for flame propagation when the Lewis number is less than 1

1995 ◽  
Vol 6 (4) ◽  
pp. 287-306 ◽  
Author(s):  
Alexis Bonnet
Keyword(s):  
Activation Energy ◽  
Flame Propagation ◽  
Chemical Reaction ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Heat Diffusion ◽  
High Activation ◽  
High Activation Energy ◽  
One Step ◽  
Species Diffusion

We discuss the question of uniqueness of planar flames for a simple one-step chemical reaction. We show that when the Lewis number is less than unity (i.e. species diffusion is larger than heat diffusion) uniqueness cannot be generally assumed. An example with three flames, two of them being stable, is exhibited. Other related questions, such as sufficient conditions for uniqueness to hold and high activation energy limits, are discussed.

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