Microeconomics 10: Game theory and Oligopoly

Question 1

Describe the simplest way to illustrate Game Theory

Answer 1

• 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.

Question 2

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

Answer 2

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

Question 3

Describe Nash Equilibrium

Answer 3

• 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.