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Long-run dynamic equilibrium in a state space model under symmetrical controlability

Cristina Sánchez‐González, M. V. Fernández, Javier Montes-Ruiz Cabello

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Abstract

In several occasions the dynamic behaviour of a specific economic variable is influenced by the optimal behaviour of agents that participate in the Economy. This economic variable denominated state variable is observed by each agent in a different way and it offers different answers for each one of them in the optimal process relative to decision making. These answers represent the control parameters for state variables and they determine the future behaviour. The answer of each agent depends on the perception they have about the state variables since their expectative about other agents interact in the system behaviour. We offer a model with a only state variable and only control parameter and two agents with symmetrical behaviour and it is enough to analyse one of them and generalise the results for the other. One of the most common examples that it is possible to analyse under this view is the two oligopolistics behaviour case. State variable will be joint volume offered by them and control variable will be the volume produced for each one of them.

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What this paper is about

In several occasions the dynamic behaviour of a specific economic variable is influenced by the optimal behaviour of agents that participate in the Economy. This economic variable denominated state variable is observed by each agent in a different way and it offers different answers for each one of them in the optimal process relative to decision making. These answers represent the control parameters for state variables and they determine the future behaviour. The answer of each agent depends on the perception they have about the state variables since their expectative about other agents interact in the system behaviour. We offer a model with a only state variable and only control parameter and two agents with symmetrical behaviour and it is enough to analyse one of them and generalise the results for the other. One of the most common examples that it is possible to analyse under this view is the two oligopolistics behaviour case. State variable will be joint volume offered by them and control variable will be the volume produced for each one of them.

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Available abstract

In several occasions the dynamic behaviour of a specific economic variable is influenced by the optimal behaviour of agents that participate in the Economy. This economic variable denominated state variable is observed by each agent in a different way and it offers different answers for each one of them in the optimal process relative to decision making. These answers represent the control parameters for state variables and they determine the future behaviour. The answer of each agent depends on the perception they have about the state variables since their expectative about other agents interact in the system behaviour. We offer a model with a only state variable and only control parameter and two agents with symmetrical behaviour and it is enough to analyse one of them and generalise the results for the other. One of the most common examples that it is possible to analyse under this view is the two oligopolistics behaviour case. State variable will be joint volume offered by them and control variable will be the volume produced for each one of them.

Key concepts: Variable (mathematics), State variable, State space, State (computer science), Control variable, Control (management), Mathematics, Process (computing)

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