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GAME THEORY - Coggle Diagram
GAME THEORY
Cournot:
General knowledge
- Prices fixed, competing on output
- Price fixation gives certain degree of market power
- Profit function is continuous
Common problems and how to solve:
- firm profits: find general profit function then substitute
- best reply: partially differentiate profit with respect to output
- Intersection: solve the equations
Costs
- Lower marginal costs is the biggest advantage
- Fixed costs, SR, therefore negligible in long run since can be seen as lower average total cost
Cournot conjecture
- Firms won't change output regardless of competition deviation
Bertrand competition
General knowledge
- output is fixed
- competition based on price
- price fixed gives no market power
- Nash equilibrium: set price at marginal costs
Aim to just under sell the competition
- if prices are equal then they split the market
- This results in perfectly competitive market
- if one firm has cost advantage then it will be successful
Set level of Q
- if Q=whole market, P1<P2
if Q=1/2 P1=P2
Q=0 P1>P2
this will demonstrate that the firm will never want to increase cost as result is it will lose its demand
Other key games
prisoners dilemma
Socially optimal to coordinate, but unlikely due to higher pay off individually
Stag/hare
Optimal to coordinate
- 2 Nash equilibria
- comittment can solve potential issues
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Stackleberg
General knowledge
- cornout competition with sequential choices
- first mover advantage
- Profit defined purely in terms of own actions
- players never regret actions
- use of backwards induction to make choices
subgame perfection
- players in a game know the structure
- who makes a decision at each node in the tree
- what choices are available
- payoff to each history of the game
- each time they make a decision, given knowledge of the game, they correctly anticipate future decisions
- Choose payoff that is the maximising action
- no one regrets actions
- strategies are chosen before game starts
- A has to have a best reply to all of B's choices
- B is NOT responding to previous actions