scholarly journals Imitation and Local Interactions: Long Run Equilibrium Selection

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 30
Author(s):  
Eugenio Vicario
Keyword(s):  
Periodic Boundary ◽  
Sufficient Conditions ◽  
Equilibrium Selection ◽  
Periodic Boundary Conditions ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Long Run ◽  
Multi Agent ◽  
Necessary And Sufficient ◽  
Long Run Equilibrium

In this paper, we analyze the long run dynamics of a multi-agent game played on a one-dimensional lattice with periodic boundary conditions, i.e., a ring. Agents repeatedly play a 2 × 2 coordination game with neighbors where the payoff dominant action and the risk dominant action are distinct. Necessary and sufficient conditions for both the actions to be the unique long run equilibrium are provided. The result is obtained through the application of the radius and modified coradius technique.

GENERALIZED DECIMATION INVARIANT SEQUENCES IN DIMENSION N

2002 ◽  
Vol 12 (04) ◽  
pp. 709-737 ◽  
Author(s):  
A. BARBÉ ◽  
F. VON HAESELER
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
One Dimensional ◽  
Necessary And Sufficient

We generalize the concept of one-dimensional decimation invariant sequences, i.e. sequences which are invariant under a specific rescaling, to dimension N. After discussing the elementary properties of decimation-invariant sequences, we focus our interest on their periodicity. Necessary and sufficient conditions for the existence of periodic decimation invariant sequences are presented.

On the threshold strategies in optimal stopping problems for diffusion processes

2017 ◽  
Vol 54 (3) ◽  
pp. 963-969 ◽  
Author(s):  
Vadim Arkin ◽  
Alexander Slastnikov
Keyword(s):  
Diffusion Process ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Payoff Function ◽  
Threshold Strategy ◽  
One Dimensional ◽  
Stopping Set ◽  
Optimal Stopping Problems ◽  
Necessary And Sufficient

Abstract We study a problem when the optimal stopping for a one-dimensional diffusion process is generated by a threshold strategy. Namely, we give necessary and sufficient conditions (on the diffusion process and the payoff function) under which a stopping set has a threshold structure.

System Properties of One-Dimensional Distributed Systems

1977 ◽  
Vol 99 (2) ◽  
pp. 85-90 ◽  
Author(s):  
L. S. Bonderson
Keyword(s):  
Distributed Systems ◽  
Sufficient Conditions ◽  
State Variables ◽  
One Dimensional ◽  
First Order ◽  
Lumped Element ◽  
Order Form ◽  
Power Product ◽  
System Properties ◽  
Necessary And Sufficient

The system properties of passivity, losslessness, and reciprocity are defined and their necessary and sufficient conditions are derived for a class of linear one-dimensional multipower distributed systems. The utilization of power product pairs as state variables and the representation of the dynamics in first-order form allows results completely analogous to those for lumped-element systems.

scholarly journals Evolutionary prisoner's dilemma games with one-dimensional local interaction and imitation

2009 ◽  
Vol 41 (1) ◽  
pp. 154-176 ◽  
Author(s):  
Hsiao-Chi Chen ◽  
Yunshyong Chow
Keyword(s):  
Convergence Rate ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Local Interaction ◽  
One Dimensional ◽  
Long Run ◽  
Action Dynamics ◽  
The Impact ◽  
Full Cooperation ◽  
Long Run Equilibrium

In this paper we explore the impact of imitation rules on players' long-run behaviors in evolutionary prisoner's dilemma games. All players sit sequentially and equally spaced around a circle. Players are assumed to interact only with their neighbors, and to imitate either their successful neighbors and/or themselves or the successful actions taken by their neighbors and/or themselves. In the imitating-successful-player dynamics, full defection is the unique long-run equilibrium as the probability of players' experimentations (or mutations) tend to 0. By contrast, full cooperation could emerge in the long run under the imitating-successful-action dynamics. Moreover, it is discovered that the convergence rate to equilibrium under local interaction could be slower than that under global interaction.

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