Lecture 6 - Game Theory Flashcards
Features of the standard oligopoly model?
What are 2 choices of firms and which model do they refer to?
- Consumers are price takers
- Firms produce a homogeneous (i.e., identical) product
- The number of firms is small and fixed (there is no entry)
Firms’ choices are either:
1) Output Quantity (COURNOT)
2) Price (BERTRAND)
A Cournot oligopoly is a model in which…?
- Each firm chooses its quantity
- Simultaneously
- And independently (i.e., without cooperation)
Nash Equilibrium and Best Response?
- A NE is an action profile such that no player can benefit from a unilateral deviation (i.e., from choosing another action keeping constant the others’ actions)
- A best response is an action such that the player cannot benefit from changing action given the action of the other player(s)
- In a NE all players are choosing a best response and there is no incentive to deviate from that choice
What are the NE’s that strategic games can have?
- A unique NE (1 set of action superior to all)
- Multiple NE (as in Stag Hunt) (2 Sets with both best responses)
- No NE (as in Matching Pennies) (no set has both best responses)
What is the use of solving models and deriving equilibria?
Once we understand how a given market works, we can use the model to predict how the market will change as a function of changes in some exogenous condition: exercise known as “comparative statics”
Weakly and Strictly Domination?
One strategy is strictly dominated by another if it yields strictly inferior outcomes for that person regardless of others’ choices.
Because an equilibrium never uses a strictly dominated
strategy, the same equilibria persist when strictly dominated strategies are deleted, but after deletion it can be that some remaining strategies become strictly dominated. A criterion that exploits this feature deletes strictly dominated strategies until none remain, and then selects those equilibria that remain in the reduced game. If a single equilibrium survives then the game is called dominance solvable.
An equilibrium can, however, use a strategy that is
weakly dominated in that it would be strictly dominated were it not for ties—in decision theory such a strategy is said to be inadmissible.
A prominent criterion selects equilibria that use only admissible strategies, and sometimes this is strengthened by iterative deletion of strictly dominated strategies after deleting the inadmissible strategies. A stronger refinement uses iterative deletion of (both strictly and weakly) dominated strategies until none remain; however, this procedure is ambiguous because the end result can depend on the order in which weakly dominated strategies are deleted.
Strategy Dominant, Weakly Dominant and Strictly Dominant when?
A strategy is dominant if, regardless of what any other players do, the strategy earns a player
a larger payoff than any other. Hence, a strategy is dominant if it is always better than any
other strategy, for any profile of other players’ actions.
A strategy is weakly dominant if, regardless of what any other players do, the strategy earns
a player a payoff at least as high as any other strategy, and, the strategy earns a strictly
higher payoff for some profile of other players’ strategies.
A strategy is strictly dominant if, regardless of what any other players do, the strategy earns
a player a strictly higher payoff than any other.
What is a best response?
A best response is a player’s strategy that yields the most favourable outcome for that player, given all other players’ strategies.
What is a Nash Equilibrium?
A stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged.
Cournot Competition Definition?
Firms choose quantity, market determines the price
Bertrand Competition Definition?
Firms choose prices, demand determines the quantity
