

Market Structure: Duopoly Game 
The Cournot model predicts that in a market with a small
number of producers, the price will fall between the price in a
competitive market and the monopoly price. To illustrate this
model, we evaluate a market with two producers. 
Cournot duopoly game 
One of the two Cournot duopoly games that we have included as an
experiment use the market demand, seller costs, and strategy sets
that were used for the duopoly experiment reported in Huck, Müller,
and Normann [2001]. The other duopoly experiment that we have
included is a simplified version of the design used by Huck, Müller,
and Normann. We start with the simplified version, because its
payoff matrix has fewer strategies. 
There are two things that you will want to note about the payoff table in figure 1. First, if both firms produce 4 units (q_{1} = 4 and q_{2} = 4), then neither firm can increase its payoff by changing its output, assuming that the other firm doesn't change its output. This is called a Nash equilibrium. Another important point is that this is not the best payoff that can be attained by the two firms. If both firms reduce their output to 3 (so q_{1} = 3 and q_{2} = 3) then the profit of each firm would increase from 16 to 18. The total profit that the two firms obtain in the Nash equilibrium, p_{1} + p_{2} = 32, is lower than the maximum joint profit that they could earn, which is p_{1} + p_{2} = 36, because of the competition between them. The simple duopoly game above has only five output levels for each choice, so the payoff table is fairly easy to understand. However, there are two aspect of the payoff table that are undesirable. First, not all strategies have a unique best response. Specifically, if Firm 1 chooses 3 (or more accurately, if Firm 2 expects Firm 1 to choose 3) then the best response by Firm 2 is to choose either 4 or 5. Similarly, if Firm 2 expects Firm 1 to choose 5, then the best response by Firm 2 is to choose either 3 or 4. Although this game has a unique pure strategy Nash equilibrium, the formulation of the duopoly game by Huck, Müller, and Normann has a unique best response for each firm to each output choice by the other firm. This proves very useful in the description of a simple dynamic of strategy choices, so we also describe their version of the game, and include a configuration for playing the game. 
Original Huck, Müller, and Normann experiment 
As in the case of the simple duopoly game above, the Nash equilibrium outputs (q_{1} = 8 and q_{2} = 8) lead to lower profits for each firm that what they could obtain by colluding and reducing outputs to q_{1} = 6 and q_{2} = 6. For these lower output levels, the profit of each firm would increase from 64 to 72. The total profit that the two firms obtain in the Nash equilibrium, p_{1} + p_{2} = 128, is lower than the maximum joint profit that they could earn, which is p_{1} + p_{2} = 144. 
Duopoly Game Experiment Configurations 
If you are familiar with how to run experiments on EconPort, you can
click on one of the buttons below to add the experiment to your
EconPort profile. If you haven't previously run an EconPort experiment,
read about
EconPort Configuration and Experiment Setup before you install a
configuration.
To include the simple duopoly game in your EconPort experiment
configuration profile, click on the button below. 
To include the Huck, Müller, and Normann duopoly game in your EconPort
experiment configuration profile, click on the button below. 
References 
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