Oligopoly & Game Theory

Market structure of oligopoly

FEW FIRMS, products could be identical or differentiated, some barriers to entry

Duopoly

2 dominant firms

Key features of oligopoly

strategic interaction, compete based on P, Q, ads, etc. (not just imitation), firms take expected strategy of competitors into account

Game theory

study of strategic behavior between competing players

strategic behavior

acting to achieve a goal by anticipating interplay between your own and others’ decisions

What makes a game a game?

Players, rules, strategies, interdependent payoffs

Normal form

both players reveal their strats at the same time, assumes full information (both players know each others’ potential strategies and payouts)

Dominant strategies

your own payouts are the highest, ignores moves of opponents (player 1 - higher row payouts, player 2 - column payouts are higher)

Nash Equilibrium definition & rules

given the strategy of the opponent, no player wants to change their move (pair of mutual best responses); 2 overlapping dominant strategies will always lead to N.E., you can eliminate dominant strategies and make the game smaller to solve for N.E.

Prisoner’s dilemma

game where Nash Equilibrium is suboptimal, competing brings them closer to monopolistic competition and colluding brings them closer to monopoly 

Ways firms compete

price, quantity produced, advertising strat, climate change policy, etc.

How do ologopolists encourage collusion?

repeated interaction, make game sequential, change payouts, social pressure, form groups with trusted competitors

repeated games

players play same game more than once, can’t use normal form, reciprocity and spite come into play

Repeated game strategy

based on your opponent’s strategy in the last round

Tit for tat/copycat

imitating what your opponent did

grim trigger

if your opponent cheats once, you cheat forever (issue of trembling hand perfection, where your hand slips & you accidentally cheat and then you’re punished forever)

Mother Theresa

always cooperating even if your opponent cheats

How does patience help firms in repeated games?

gains to cooperation mainly occur in the future, whereas gains to cheating happen right away

Sequential games

one player moves first and the other person moves with full knowledge of their action

decision tree

shows how decisions of each player lead to payouts with first mover shown first

first-mover advantage

moving first changes the Nash Equilibrium of game in a way that helps the first player

How to solve sequential games?

backwards induction or eliminate strategies that are not the best responses

Commitment in sequential games

second player in the game eliminates some choices and forces the first player down a bath that benefits the second 

credible threats

acting upon these threats actually benefits P2 and doesn’t just harm P1