Micro- Game Theory And Oligopoly Flashcards
What’s an oligopoly
interaction among a small number of firms
What’s game theory
mathematical tool to analyze strategic interaction
What are the two game theory models of oligopoly with homogenous goods
quantity-setting: Cournot model
price-setting: Bertrand model
What makes a game static
Players choose their strategies simultaneously (without knowledge of the
others’ choices)
What’s a strictly dominant strategy
A strategy s is strictly dominant for player i if following s gives strictly higher payoffs than any other available strategies, regardless of what the other players do.
What’s a strictly dominated strategy
A player has a (strictly) dominated strategy if, for each possible action that his opponents can take, he has another strategy that leads to a payoff that is strictly greater than the payoff associated with the original strategy.
No matter what other people do, this strategy is always beaten by a particular other one
A rational player will never play a dominated strategy
A solution can be find by sequentially removing dominated strategies with each players knowledge that the other player is rational and will not choose a dominated strategy
What’s Nash equilibrium
A Nash Equilibrium is a profile of strategies such that each player’s strategy is a best response (payoff maximising move taken in response to a set of strategies played by the other players) to the other players’ strategies.
What’s the prisoners dilemma
The prisoner’s dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so.
What’s the battle of the sexes
BoS the players agree that it is better to cooperate than not to cooperate, but disagree about the best outcome.
What is a pure strategy
A pure strategy determines all your moves during the game (and should therefore specify your moves for all possible other players’ moves).
What is a mixed strategy
A mixed strategy is a probability distribution over all possible pure strategies (some of which may get zero weight). After a player has determined a mixed strategy at the beginning of the game, using a randomising device, that player may pick one of those pure strategies and then stick to it.
A mixed strategy of (0,1) is simply a pure strategy of the second option. The numbers in the brackets are between 1 and 0 and represent the probability distribution of choosing the different options.
How to find Nash equilibrium with mixed strategy
For each player, use the probabilities of the other player choosing each move, and the payoff for the player with each outcome to find an expected utility/payoff for each of the options, and then equate them to get the indifference condition.
Where is Nash equilibrium on graph
At intersection of two firms’ BR (best response) functions, which are found by differentiating the profit by the quantity each firm controls.
What kind of products are needed for Bertrand price setting model and what does this mean the price coincides with?
Products are homogeneous (consumers will go to the firm with the lower price) which leads to Bertrand outcome coinciding with competitive outcome.
Main difference between Cournot and Bertrand games.
Cournot is a non-cooperative quantity-choice game.
Bertrand is a non-cooperative price-setting game.
