lectures 12-20 Flashcards
Monopolist and competitor Game
- be able to explain the strategies, SPNE, and NE
* *will someone join the market or no?
evolutionary games
departing from rationality by modeling a specific type of irrationality
*accompanying nash equil. with some form of behavioral anaylsis
strategies being biologically encoded, heritable so players do not know..
- do not need to know the game
- have no control over their game
- gene determines strategy
- evolution=payoffs of the game represent reproductive success- some behaviors are more successful, less successful are not evolutionarily successful
evolutionary games assumptions
- look at symmetric 2 player games
- assume very large population pf players who are hard-wired to play specific strategy, so population could involve a mix of strategies
- players encoded with strategies
- look at average payoffs by strategies across their pairings, strategies whose payoffs are higher than others grow relative to those in other population mixes
- departure from rationality and dynamics to reach equil.
How to find equilibrium in evolutionary game
Hawks and Doves
hawks= some aggressive and prefer to fight
doves= more peaceful dont want to fight
* payofs are shares of resources
*higher share of resources, higher changes of survival and reproduction rates
* if one type is higher than other, reproductive rate is higher and other will die off
evolutionary stable strategy
if all members of a pop. adopt it, no mutant strategy can invade, once all members of pop use this strategy there is no rational alternative
**represents no incentive to deviate in NE
evolutionarily stable state
populations genetic mix is restored after a distubrance, dynamic property of population, the strategy or mix of strategy will keep the same
the selfish gene
evolution is through survival of competing genes
strategic moves mono competitor game
monopolist and competitor game, if one fights or concedes (monopolist has higher payoff if competitor plays out so tries to convince player to play out even though competitor has higher payoff w playing in)
examples of strategic moves
- competitor and monopolist game
- golden balls game
strategic moves
actions taken at a pregame stage that change strategies of the payoffs of the subsequent game
*original one stage game becomes two stage game
two stage game
- first stage: pre game actions (strategic moves)
- second stage: now modifies original game is played
3 types of pregame actions
- commitments
- threats
- promises
Aim of game
alter the outcome of the second-stage game to your own advantage, works only if credible
to do something in first game that makes move credible=
ancillary move
what is a first move?
- action must be observable/seen by other player
- action must be irreversible
unconditional strategic moves
- commitment: player choose a strategy
- depends on sequential or simultaneous
- player A seeks first mover advantage
conditional strategic moves
player A picks stretegy based on which strategy other player takes
- response rule or reaction function
- A moves in second stage of the game
threats
unless action conforms to stated wish, they will respond in a hurtful way
- for every threat there is an implied promise
promise
if action conforms to stated wish, will respond in a way that rewards
- for every promise there is an implied threat
Commitment game: chicken game
- simultaneous game: 2 pure strategy NE
- player needs to convince other player what move they are making w ancillary move
threats and promises games
response rules: future action is conditional on what other players do
threats games: US and Japan
threat: we will close markets if you close yours
- in equil. japan does not plau dominant strategy of closed
threat is effective…
if both threat and implied promise are credible
- threat has to be costly, make implicit promise credible
- big but not too big
promise game example: restaurant pricing game
typical prisoners dilemma game– dominant strategy but inefficient outcome
how to avoid credibility issue?
ancillary move
promise is effective if
if both the promise and implied threat are credible
- has to be costly, this makes implicit threat credible
- small promise, but not too small
a commitment is successful…
only if opponent believes you will care out what you committed to, typically action you commit is not best response
entry deterrence game EX/ commitment games
making the fight credible
credibility: reducing freedom of action
- automatic fulfilment
- delegation
automatic fulfilment
you can leave choice at stage 2 and hand over to a mechanical device or similar procedure that is programmed to carry out commitment, must demonstrate this to other player
delegation
you can delegate power to act to another person or organization that is required to follow rules or procedures
Burning bridges
removing the option to retreat (kamikaze pilots)
cutting off communication
send message to the other player demonstrating your commitment and then cut off communication
credibility: changing your payoffs
- reputation: only good if known, payoffs altered by prospects of repercussion in other games
- dividing the game into small steps: gradualism, reputation built
- teamwork
- irrationality
- contracts
- brinkmanship
Static Games (Bayesian games)
strategic uncertainty
uncertainty about opponents moves in the past of made at same time as you (EX/ battle of sexes)– game tree representation
external uncertainty
uncertainty about external circumstances
EX/ farmer planting a crop– makes a decision on whether or not to plant crops based on weather probability
perfect information
there is neither external no strategic uncertainty
- no info set encloses two or more nodes (game of 3)
- all strategic games are imperfect info.
incomplete information
incomplete info is asymetic
- complete info:
all rules and strategies are common info
bayesian games
games of incomplete info -incentives to reveal or conceal info: signalling
or elicit info: Screening
Joe and Una game
Una is not informed about joes payoffs, so she does not know how to make her decision
- joe can be a party lover or non-party lover, two different payoffs (50-50)
Bayesian nash equil.
- strategy for fully informed player conditional on his type and optimal given expectations about other player
- stratefy for incompletely informed player optimal given her beliefs about other players
BNE simple explanation
combo of players strategies so each players strategy is best response to equil. strategies of all players, whatever type of player
how to solve for BNE
- propose strategy combo: fully informed + incomplete informed
- calculate beliefs generated by proposed strategies (a. fully informed joe and b. Una)
- check each strategy is optimal (consistency check)
strategy can be separating or pooling
for fully informed player
- so equilibria can be separating or pooling
separating strategy
when fully informed player chooses a different action depending on type
pooling strategy
when fully informed player chooses same action no matter the type
