On the convergence of evolution processes with time-varying mutations and local interaction

2001 ◽  
Vol 38 (2) ◽  
pp. 301-323 ◽  
Author(s):  
Hsiao-Chi Chen ◽  
Yunshyoung Chow
Keyword(s):  
Nash Equilibrium ◽  
Dynamic System ◽  
Convergence Rates ◽  
Evolutionary Model ◽  
Coordination Game ◽  
Local Interaction ◽  
Mutation Rates ◽  
Time Varying ◽  
Long Run ◽  
Long Run Equilibrium

This paper analyzes players’ long-run behavior in an evolutionary model with time-varying mutations under both uniform and local interaction rules. It is shown that a risk-dominant Nash equilibrium in a 2 × 2 coordination game would emerge as the long-run equilibrium if and only if mutation rates do not decrease to zero too fast under both interaction methods. The convergence rates of the dynamic system under both interaction rules are also derived. We find that the dynamic system with local matching may not converge faster than that with uniform matching.

On the convergence of evolution processes with time-varying mutations and local interaction

2001 ◽  
Vol 38 (02) ◽  
pp. 301-323 ◽  
Author(s):  
Hsiao-Chi Chen ◽  
Yunshyoung Chow
Keyword(s):  
Nash Equilibrium ◽  
Dynamic System ◽  
Convergence Rates ◽  
Evolutionary Model ◽  
Coordination Game ◽  
Local Interaction ◽  
Mutation Rates ◽  
Time Varying ◽  
Long Run ◽  
Long Run Equilibrium

This paper analyzes players’ long-run behavior in an evolutionary model with time-varying mutations under both uniform and local interaction rules. It is shown that a risk-dominant Nash equilibrium in a 2 × 2 coordination game would emerge as the long-run equilibrium if and only if mutation rates do not decrease to zero too fast under both interaction methods. The convergence rates of the dynamic system under both interaction rules are also derived. We find that the dynamic system with local matching may not converge faster than that with uniform matching.

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.

HETEROGENEITY IN INFLATION EXPECTATIONS AND MACROECONOMIC DYNAMICS UNDER EVOLUTIONARILY SATISFICING LEARNING

2020 ◽  
pp. 1-33
Author(s):  
Jaylson Jair da Silveira ◽  
Gilberto Tadeu Lima
Keyword(s):  
Empirical Evidence ◽  
Output Growth ◽  
Inflation Expectations ◽  
Forecast Errors ◽  
Time Varying ◽  
Macroeconomic Dynamics ◽  
Inflation Forecasting ◽  
Long Run ◽  
Ex Ante ◽  
Long Run Equilibrium

Drawing on the empirical evidence that heterogeneity in inflation expectations is persistent and endogenously time-varying, we embed two inflation forecasting strategies—one based on costly ex ante perfect foresight, and the second based on costless ex ante extrapolative trend-following—in a macrodynamic model. Drawing also on the empirical evidence that inflation forecast errors may have to exceed some threshold before agents abandon their previously selected forecasting strategy, we describe agents as switching between forecasting strategies according to evolutionarily satisficing learning. Convergence to a long-run equilibrium consistent with output growth, unemployment and inflation at their natural levels may be achieved even if heterogeneity in inflation forecasting strategies (with predominance of the extrapolative foresight strategy) is an attractor of an evolutionarily satisficing dynamic perturbed by mutant agents. Thus, in keeping with the empirical evidence, heterogeneity in strategies to form inflation expectations (with prevalence of bounded rationality) can be a stable long-run equilibrium.

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

2009 ◽  
Vol 41 (01) ◽  
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.

Exchange rates in India: current account monetarism in a nonlinear context

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Aditi Chaubal
Keyword(s):  
Exchange Rate ◽  
Current Account ◽  
Polynomial Function ◽  
Mean Reversion ◽  
Smooth Transition ◽  
Monetary Model ◽  
Forecast Performance ◽  
Long Run ◽  
Nonlinear Mean Reversion ◽  
Long Run Equilibrium

AbstractThe Indian exchange rate system has evolved from a pegged system to the current managed float. The study examines the presence of a long-run equilibrium in the monthly Indian exchange rate (Rs/USD) using a current account monetary model (or flexible price monetary model) while accounting for different nonlinearities over the period January 1993 to January 2014 (pre-inflation targeting period). The nonlinear adjustment to disequilibria is modelled using a nonlinear error correction model (NLECM). The nonlinear current account monetarism (CAM) model includes nonlinear transformations of long-run dynamics in the ECM to account for different nonlinearities: multiple equilibria (cubic polynomial function), nonlinear mean reversion (rational polynomial function), and smooth and gradual regime switches (exponential smooth transition autoregressive (ESTAR) function). The NLECM-ESTAR model outperforms other alternatives based on model and forecast performance measures, implying the existence of nonlinear mean reversion and smooth transition across different periods of overvaluation and undervaluation of the exchange rate. This implies the presence of asymmetric adjustment to the movements from the long-run equilibrium, but the nature of such transitions is smooth and not abrupt. The paper also establishes the uniqueness of the long-run equilibrium. A comparison to the sticky price monetary model could not be made due to stationary exchange rate disequilibrium.

scholarly journals The role of diversity and tolerance in economic development

2021 ◽  
Author(s):  
Witold Kwasnicki
Keyword(s):  
Economic Growth ◽  
Economic Development ◽  
Industrial Development ◽  
Evolutionary Process ◽  
Evolutionary Model ◽  
Industry Development ◽  
Radical Innovations ◽  
Long Run

AbstractThis paper presents an evolutionary model of industry development, and uses simulations to investigation the role of diversity and heterogeneity in firms’ behaviour, and hence industrial development. The simulations suggest that economic growth is increased with greater variety, in the sense of the evolutionary process approaching the equilibrium faster and also, in the long run, moving faster from one equilibrium to a new, more advanced, equilibrium. This occurs due to higher variety caused by a more tolerant environment, and due to the higher probability of emergence of radical innovations.

scholarly journals Competing Conventions with Costly Information Acquisition

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 53
Author(s):  
Roberto Rozzi
Keyword(s):  
Information Acquisition ◽  
Evolutionary Model ◽  
Equilibrium Selection ◽  
The Other ◽  
Group Interactions ◽  
Social Coordination ◽  
Long Run ◽  
Stochastic Stability Analysis ◽  
The Stability ◽  
The Cost

We consider an evolutionary model of social coordination in a 2 × 2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent’s group: if they pay it, they can condition their actions concerning the groups. We assess the stability of outcomes in the long run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information’s cost. If the cost is too high, players never learn the group of their opponents in the long run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every player plays that group’s favorite action. If both groups are strong enough in preferences, or if none of the groups’ sizes is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.

Sign in / Sign up

Export Citation Format

Share Document