Microeconomics 10: Game theory and Oligopoly Flashcards
• This week we start by introducing some concepts in game theory, the analysis of strategic interaction • Game theory can cover interactions between individuals, firms or governments. The games we are going to be most interested in this week are between firms competing in oligopoly. • This will allow us to analyse a number of different models of oligopoly.
Describe the simplest way to illustrate Game Theory
- The simplest way to illustrate a game is with a payoff matrix – this can be used when we have two players
choosing from a finite number of strategies (i.e. they
do not have a continuous choice). - In the simplest case, we have two strategies for each
player. - We normally have the first player choosing a row,
and the second choosing a column.
Using an example, describe ‘dominant strategy equilibrium’ in Game Theory
A simple example:
B chooses Left B chooses right A chooses Top 1, 2 0,1 A chooses 2,1 1, 0 bottom
- The numbers in each cell represent the payoffs to
each player, starting with the row player (A in this
case), then the column player (B). - A higher number is better for the player than a lower number.
- If B chooses Left, A prefers Bottom (2 > 1);
- If B chooses Right, A also prefers Bottom (1 > 0).
- So A will always play Bottom – we call this a
dominant strategy for A - Similarly for B, Left is always better than Right (2 > 1 when A chooses Top; 1 > 0 when A chooses Bottom), so this is B’s dominant strategy.
- The equilibrium is (Bottom, Left) with payoffs of (2,
1). - We call this a dominant strategy equilibrium
Describe Nash Equilibrium
- Nash equilibrium is based on the concept of best
response:
– An action is a best response to another action if it is the
best the player can do, given what the other player is
doing
– This means there is no incentive to change action. - Note that it is not necessarily true that the same
action will be a best response to every action by
another player – that means we may not have a
dominant strategy, but could have different best
responses in different situations.
What’s Game Theory?
Game theory is the analysis of strategic interaction. Within Economics, it
can cover interactions between individuals, firms or governments.
Describe whether Nash equilibrium is necessarily unique
- For a Nash equilibrium to exist, we need both players
simultaneously to be playing a best response to each
other’s actions:
– When neither player can gain from unilaterally changing their
action. it proves that Nash equilbrium is not necessarily unique
Describe & explain, with an example including a payoff matrix, when there’s no pure strategy Nash equilibrium
B chooses Left B chooses right
A chooses Top 1, 0 0,1
A chooses 0,1 1, 0
bottom
- In this game, whichever player has a payoff of zero
would always gain by changing their strategy. -
For example, if we start at (Top, Left), B would switch
to playing Right; from there, A would switch to
playing Bottom; and so on
We say in this case there is no pure strategy Nash
equilibrium – that is, no equilibrium where each
player plays a given strategy with certainty. - However there would still be a mixed strategy
equilibrium where each player randomises over their
two choices, playing each with a certain probability.
Describe & explain ‘The Prisoner’s Dilemma’
- Two prisoners are being interviewed separately
about a crime they have committed.
– There is little other evidence available to the police, but
without a confession they can prove that a minor offence
was committed, for which each prisoner would receive a 1-
month sentence.
– If one prisoner confesses, while placing most of the blame
on the other, the prisoner who confesses will be released
while the other prisoner will receive a 6-month sentence.
– If both prisoners confess, each will receive a 3-month
sentence. Payoffs are minus the length of the sentenceB confess B deny A confess 1, 0 0,1 A deny 0,1 1, 0
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