Game Theory

game theory

analytical framework used to formally analyze strategic interaction

cooperative game theory

concerned with general group interest

non cooperative game theory

individual decision maker is only concerned about doing well for themselves

assumptions of game theory

players are rational

apply their rationality to the process of reasoning strategically

players

who faces an interesting choice

timing

are the moves simultaneous or sequential?

choices

what can a player choose?

information

what does each player know when she moves

payoffs

what motivates each player

strictly dominant strategy

payoff is strictly greater greater than any other strategy, regardless of rival’s choice

stricly dominated strategy

payoff is strictly lower than some other strategy regardless of what other player does

pareto inefficiency

no inidividual can be better off without making at least one individual worse off

si

particular strategy for player i

Si

set of possible strategies for player i

iterated elimination of strictly dominated strategies

rational players do not play strictly dominated strategies, and rationality and payoffs are common knowledge

weakly dominated strategies

strategies where another strategy always has higher or equal payoff

hotelling model

place business on space on a spectrum, all consumers will pick the business closest to themselves, best location ends up being the centerbe

best response

choosing the strategy with the highest payoff based on what the other player chooses

expected utility of a strategy

depends on predicted probability of what response the other player chooses

Nash Equilibrium

set of strategies where neither player can choose a strategy with a higher payoff, given the other player’s strategy; si* is the best choice given s-i*

nash’s theorem

for any finite game, there exists at least one nash equilibrium

motivation for nash equilibrium

no regrets (couldn’t have picked a better strategy)

self fulfilling beliefs

nash equilibrium as a rest point

in each stage, player 1 or 2 picks their best response based on the other player’s last move. the nash equilibrium is where it will stop

why is NE stronger than IESDS

NE strategies always survive IESDS, but the converse is not true

cournot model

two firms sell homogenous products; choose quantities but not prices

why can’t collusion be sustained

cheating, graph heads back to nash equilibrium

may indue other effects if you sustain profits

cournot quantity compared to perfect competition and monopoly

less than PC, more than monopoly

cournot price compared to perfect competition and monopoly

more than PC, less than monopoly

what happens to cournot model when number of firms increases?

price and output closer to PC

bertrand model

two firms sell homogenous goods, choose prices

bertrand model with differential goods

two firms selling different goods; firms set p1 and p2 simultanously

merger reasons

cost saving

improve information flow

more efficient pricing

improve services to consumers

merged firms create complimentary products

create legal cartel

horizontal merger

two firms were formerly competitors in the same product market

vertical merger

join firms at different stages in vertical production chain

conglomerate merger

firms merge without clear relationship

coordinated effects (collusion)

coordination of prices will be easier after merger

unilateral effects

less competitors, so less business stealing effects and thus increased prices

williamson trade off

trade off between efficiencies and market power

when is merger welfare improving

when merger induced cost saving is greaer than deadweight loss

efficiency defense

mergers are justified if efficiencies are enough to ensure than price does not increase

business stealing effect

firm i imposes externality on firm j for every unit of increased or decreased prices

diversion rate

the proportion of customers who would switch to a competitor's product if the merged company were to raise the price of one of its products

monopoly profit

profit of previous firms added together, but with efficiency added to cost

efficiency

added to marginal cost in merger evaluation to ensure prices don’t increase

mixed strategies

Pi, randomization over i’s pure strategies

Pi(si)

probability that Pi assigns to the pure strategy si

mixed strategy profile

(P1*, P2*,…) is a mixed strategy nash equilibrium if for each player i, Pi* is a best response to P-1*