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.

1
Q

Describe the simplest way to illustrate Game Theory

A
  • 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.
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2
Q

Using an example, describe ‘dominant strategy equilibrium’ in Game Theory

A

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
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3
Q

Describe Nash Equilibrium

A
  • 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.
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4
Q

What’s Game Theory?

A

Game theory is the analysis of strategic interaction. Within Economics, it
can cover interactions between individuals, firms or governments.

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5
Q

Describe whether Nash equilibrium is necessarily unique

A
  • 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
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6
Q

Describe & explain, with an example including a payoff matrix, when there’s no pure strategy Nash equilibrium

A

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.
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7
Q

Describe & explain ‘The Prisoner’s Dilemma’

A
  • 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 sentence
                                B confess    B deny A confess                   1, 0                 0,1  A deny                        0,1                 1, 0

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