Bounded Rationality in a Cournot Duopoly Game
| Autor | Mariano Runco |
| Cargo | Department of Economics, College of Public Policy and Justice, Auburn University at Montgomery |
| Páginas | 79-94 |
Ensayos Revista de Economía–Volumen XXXIV, núm.2, noviembre 2015, pp. 79-94
Bounded Rationality in a Cournot Duopoly G ame
Mariano Runco
Fecha de recepción: 22 XII 2014 Fecha de aceptación: 02 VII 2015
Abstract
This paper analyzes choices and welfare in a Cournot duopoly setting with
linear demand using four models of bounded rationality. The models studied in
this paper are Level-k, Cognitive Hierarchy, Asymmetric Quantal Response
and Noisy Introspection. It is found that in the Level-k model choices, profits
and welfare alternate around the Nash Equilibrium levels depending on
whether the level is odd or even. In the Cognitive Hierarchy model the choices
of the first two types (L-0 and L-1) coincide with the choices in the Level-k
model, a L-2 produces a smaller quantity while the q uantity of a L-3 is higher
or lower depending on the value of a particular parameter in the model. Both in
the Asymmetric Quantal Resp onse and Noisy Introspection models we find
that choices are spread around the Nash Equilibrium level for all parameter
values and thus welfare is below the Nash Equilibrium benchmark. We also
use parameter estimates from other well-known experiments to obtain an
approximation to empirically plausible welfare levels.
JEL Classification: C72; D21.
Keywords: Cournot Game; Bounded Rationality; Level-k Model; Asymmetric
Quantal Response Equilibrium, Noisy Introspection; Cognitive Hierarchy.
Resumen
Este artículo analiza las elecciones de cantidad y los efectos sobre el bienestar
en un modelo de duopolio de Cournot con demanda lineal. Los modelos que se
estudian en este trabajo son los de racionalidad acotada Nivel-k, Jerarquía
Cognitiva, Re spuesta Quantal Asimétrica e Introspección Imprecisa. Se
encuentra que en el modelo de Nivel-k las elecciones de cantidad y los niveles
de bienestar alternan alrededor del nivel de equilibrio de Nash, dependiendo de
si los niveles son pares o impares. En el modelo de Jerarquía Cogniti va, las
Department of Economics, College of Public Policy and Justice, Auburn University at
Montgomery. Address: Senators Dr, Montgomery, AL 36117, USA. Tel.: +1 334-578-0473.
Fax: 334-244-3792. Email: mrunco@aum.edu.
Ensayos Revista de Economía
80
elecciones de los primeros dos niveles (Nivel 0 y 1) coinciden con las
elecciones del modelo Nivel-k, mientras que los niveles 2 y 3 difieren. Los
restantes dos modelos generan elecciones de ca ntidad alrededor del equilibrio
de Nash y, por lo tanto, niveles de bienestar inferiores. Finalmente, se usan
estimaciones experimentales de parámetros para obtener aproximaciones a los
niveles de bienestar empíricamente validas.
Clasificacion JEL: C72; D21.
Palabras Clave: juego de Cournot; rac ionalidad acotada; modelo de nivel-k,
equilibrio de respuesta cuantil asimétrico; jerarquía cognitiva, introspección
imprecisa.
Introduction
This paper analyzes a standar d Cournot duopoly game with linear demand
using several well-known non-equilibrium models of bounded rationality
(Level-k, Cognitive Hierarch y, Noisy Introspection and Asymmetric Quantal
Response). The motivation for the analysis comes from the fact that
equilibrium concepts correctly describe behavior when agents participate in a
game repeatedly, thus having time to learn. However, there are many situations
where the possibility of learning is indeed quite limited. For exa mple, if the
environment where managers operate changes due to variations in cost or
demand we should expect convergence to equilibrium to be slow or
impossible. Moreover, Courno t competition can be interpreted as a choice of
capacity (Kreps and Scheinkman, 1983) followed by price co mpetition, and
since the investment in capacity is generally a sunk cost we should expect
constraints in the ability of firms to adjust1. The four models analyzed here
include Nash Equilibrium as a particular case, thus they will always describe
behavior better than it. The question of which one describes choices more
realistically is an empirical one, which will not be attempted here.
Nevertheless, it is interesting to investigate what theoretical results can be
derived from these models of bounded rationality an d what are their
implications.
There are several reasons why subjects may fail to choose the Nash
Equilibrium strategies. This concept requires the mutual consistency of actions
and beliefs, that is, what one player chooses must be optimal given her beliefs
about the choice of the other player. And conversely, what a player thinks t he
1 There exists vast evidence showing that experimental subjects, typically undergraduate
students, deviate from the Nash Equilibrium prediction in simple Cournot games. See
Camerer (2003) and Kagel and Roth (1995) for a comprehensive survey of experimental
results.
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