Dima Assessment Game Theory
The Cournot model of oligopoly assumes that rival firms produce a homogenous product, and each attempts to maximize profits by choosing how much to produce. All firms choose output (quantity) simultaneously. The basic Cournot assumption is that each firm chooses its quantity, taking as given the quantity of its rivals. The resulting equilibrium is a Nash equilibrium in quantities, called a Cournot (Nash) equilibrium (OECD, Glossary of Statistical Terms, https://stats.oecd.org/glossary/detail.asp?ID=3183).
The price is uniform across the market, and the total quantity produces equals the sum of the quantities produces by the first and by the second firm (q = q1 + q2).
The inverse demand function is given: P (q) …show more content…
Therefore, this game suggests the simultaneous moves. The graph below represents a part of the game (as we mentioned, there is an infinite number of possible moves and combinations, therefore, it is impossible to present all of them on the graph), where the firms choose between the level of productions, denoted as n and m. Their pay-offs are the levels of profit, which are the functions of the quantities …show more content…
We can draw the reaction functions of the firms 1 and 2 and depict the equilibrium point q2 = A – 2q1 – c1 – reaction function of the first firm q2 = A/2 - q1/2 – c2/2 – reaction function of the second firm
We know that the equilibrium price P* equals A- q*, which in turn, is the sum of the equilibrium outputs of the firm 1 and 2.
P* (q*) = A – A/3 + 2c2/3 – c1/3 – A/3 + 2c1/3 – c2/2 = A/3 - c2/3 - c1/3.
Q*(P*) = A – A/3 - c2/3 - c1/3 = 2A/3 – c2/3 - c1/3. q1* + q2*= A/3 – 2c1/3 +c2/3 + A/3 – 2c2/3 +c1/3 = 2A/3 – c2/3 - c1/3.
Q* = q1* + q2*
Therefore, the sum of the equilibrium outputs equals the equilibrium market quantity supplied.
The Cournot-Nash equilibrium is not a Pareto-efficient outcome, as both of the players can improve their situation without worsening situation of the second player. For example, the firms could undertake the collusion behavior; the level of the output in a situation both the firms perfectly cooperate, is depicted below.
The levels of output are lower than in the case of the absence of cooperation, thus providing both the firms with greater
The Cournot model of oligopoly assumes that rival firms produce a homogenous product, and each attempts to maximize profits by choosing how much to produce. All firms choose output (quantity) simultaneously. The basic Cournot assumption is that each firm chooses its quantity, taking as given the quantity of its rivals. The resulting equilibrium is a Nash equilibrium in quantities, called a Cournot (Nash) equilibrium (OECD, Glossary of Statistical Terms, https://stats.oecd.org/glossary/detail.asp?ID=3183).
The price is uniform across the market, and the total quantity produces equals the sum of the quantities produces by the first and by the second firm (q = q1 + q2).
The inverse demand function is given: P (q) …show more content…
Therefore, this game suggests the simultaneous moves. The graph below represents a part of the game (as we mentioned, there is an infinite number of possible moves and combinations, therefore, it is impossible to present all of them on the graph), where the firms choose between the level of productions, denoted as n and m. Their pay-offs are the levels of profit, which are the functions of the quantities …show more content…
We can draw the reaction functions of the firms 1 and 2 and depict the equilibrium point q2 = A – 2q1 – c1 – reaction function of the first firm q2 = A/2 - q1/2 – c2/2 – reaction function of the second firm
We know that the equilibrium price P* equals A- q*, which in turn, is the sum of the equilibrium outputs of the firm 1 and 2.
P* (q*) = A – A/3 + 2c2/3 – c1/3 – A/3 + 2c1/3 – c2/2 = A/3 - c2/3 - c1/3.
Q*(P*) = A – A/3 - c2/3 - c1/3 = 2A/3 – c2/3 - c1/3. q1* + q2*= A/3 – 2c1/3 +c2/3 + A/3 – 2c2/3 +c1/3 = 2A/3 – c2/3 - c1/3.
Q* = q1* + q2*
Therefore, the sum of the equilibrium outputs equals the equilibrium market quantity supplied.
The Cournot-Nash equilibrium is not a Pareto-efficient outcome, as both of the players can improve their situation without worsening situation of the second player. For example, the firms could undertake the collusion behavior; the level of the output in a situation both the firms perfectly cooperate, is depicted below.
The levels of output are lower than in the case of the absence of cooperation, thus providing both the firms with greater