Micro- Strategic interaction, Collusion Flashcards
How do you find a SPNE
Draw a decision tree and work backwards (backwards induction) and the SPNE is shown by a route where very decision is in the best interest of the party making it, who knows that the subsequent moves made by opponent will be in their best interest too.
How to find SPNE in stackelberg duopoly
Create the profit function to optimise, and perform backwards induction. find FOC by differentiating wrt the variable that the firm can change and set =0, and check it’s a max by SOC and then r arrange for the quantity for the best response function. Do the same back down the chain.
What is the Cournot output
She firms choose quantity independently and at the same time
What is the difference between a one shot game and repeated games
In the one shot game there is no repercussions, where as in repeated moves the one shot strategy may not be the best move, and cooperation may give better returns in the long run.
What must happen in the final sub game
Players much play a Nash Equilibrium, as players know all previous games are ‘locked in’ and wish to maximise their payoff for the final game, which is done by playing Nash equilibrium (in strategically independent environment)
For a series of games of finite length, what is the result for the prisoners dilemma (the SPE)
Defection at every stage as we know the final stage must be DD as it’s the Nash equilibrium, and then working back, each subsequent game can’t affect the next so again the prisoners will seek to optimise payout (which is at NE).
Equation for payoff of infinite series of a given payoff x with a discount factor δ
x / 1 - δ
General geometric series equation
a(1-r^n)/(1-r)
r is the common ration
n is the number of terms in the geometric series therefore r^n -> 0
Two forms of collusion
Explicit and tacit collusion
Explicit means firms have explicitly built the agreement to reduce quantity, raise prices etc
Tacit - no explicit agreement
