micro chapter 18

second mover advantage

the strategic advantage that can follow from taking an action that adapts to your rival's choice

types of games

two types: a. one-shot game b. repeated game - finitely repeated games - infinitely repeated game

repeated game

when you face the same strategic interaction with the same rivals and the same payoffs in successive periods

game tree

shows how a game plays out over time, with the first move forming the trunk, each subsequent choice branching out, and the final leaves showing all possible outcomes

What are games considered?

strategic interactions

focal point

- a cue from outside a game that helps you coordinate on a specific equilibrium

coordination games def

- a game in which all players have a common interest in coordinating their choices - coordination is beneficial but difficult

prune the tree method

- a method for solving game trees - start by looking forward to the final period and highlighting out your rivals best responses, then prune the options the rival would never choose off your game tree

payoff table

- a table that lists your choices in each row, lists the other player's choices in each column, and so shows all possible outcomes, listing the payoffs in each cell

what two things are true in a nash equilibrium?

- best responses - correct expectations

the grim trigger strategy

- def: punishes your rival for not cooperating 1. if the other players have cooperated in all previous rounds, then you'll cooperate 2. if any player has defected in any previous round, you'll defect - cooperation can be an equilibrium - cooperation is often not an equilibrium in a one-shot prisoner's dilemma - cooperation is often not an equilibrium in a finitely repeated prisoner's dilemma a. punishment drives cooperation b. threats of punishment work only if they are credible c. (infinitely) repeated play helps solve the prisoner's dilemma

games that play out over time (contd)

- includes the first mover advantage

multiple equilibria

- occurs when there is more than one equilibrium

nash equilibrium

- occurs when you both choose your best response - an equilibrium in which the choice that each player makes is a best response to the choices other players are making b. use the check mark method to find a Nash equilibrium the box with the most check marks is the choice you should make

strategic interactions

- occurs when your best choices may depend on what others choose and when their best choices may depend on what you choose - games are all around us (ie chess) - involves using the interdependence principle

anti-coordination games

- sometimes, the best outcome involves taking a different (but complementary) action - def = games in which your best response is to take a different but complementary action to the other player

reason backward

- start by analyzing the last period of the game. - Use this to figure what will happen in the second-to-last-period, and keep reasoning backward until you can see all the consequences that follow from today's decision

a. step 1 = consider all possible outcomes

- use a payoff table to do this

prisoner's dilemma

- yields a failure to cooperate - the choice that is what gets made is the worst according to the check mark method

anticoordination game -- graphical example x3

- you want to enter new markets that other firms won't enter - in notes

one shot game

a strategic interaction that occurs only once

using tree logic

a. a game tree shows all possible outcomes

the prisoner's dilemma and the failure of cooperation

a. agreements to cooperate are not credible b. the prisoner's dilemma shows how markets can deliver bad outcomes - often, the equilibrium outcome is not the best outcome c. the temptation to take advantage undermines cooperation

understanding the prisoner's dilemma -- an example

a. coke and Pepsi are making advertising decisions. What is your advice? 1. step 1 = consider all possible outcomes and construct the payoff table 2. step 2 = think in terms of "what ifs" 3. step 3 = play your best response 4. step 4 = put yourself in the other players shoes, and figure out their best response graphic -- in notes

games that play out over time

a. in a simultaneous game, you choose without knowing the other player's choice - step 1 = consider all possibilities - step 2 = consider the "what ifs" - step 3 = play your best response - step 4 = put yourself in other player's shoes

using tree logic (contd)

a. look forward and reason backward:

indefinitely repeated game

a. one in which you face the same strategic interaction an unknown number of times b. in this sort of repeated interaction, you'll need a strategic plan that lists how you'll respond to any possible solution

solving coordination problems

a. solution 1 = communication b. solution 2 = focal points, culture, and norms c. solution 3 = laws and regulations

good and bad equilibria

a. sometimes multiple equilibria lead to scenarios in which both good outcomes and bad outcomes are equilibria b. it can be difficult to prevent the bad equilibrium from occurring

the four steps for making good strategic interactions:

a. step 1 = consider all possible outcomes b. step 2 = think about the "what ifs" separately c. step 3 = play your best response d. step 4 = put yourself in someone else's shoes

first mover vs second mover advantage

a. the first-mover advantage is about the benefits of commitment b. the second-mover advantage is about the benefits of flexibility

the first mover advantage

a. the strategic gain from an anticipatory action that can force a rival to respond less aggressively b. a first mover advantage occurs when you commit to being aggressive

coordination games

a. what about situations with multiple equilibria, such as phone tag? - multiple equilibria = occurs when there is more than one equilibrium - this is a coordination games = a game in which all players have a common interest in coordinating their choices b. coordination is beneficial but difficult

collusion and prisoners dilemma

a. when rivals collude to raise prices, they increase their profits

collusion

an agreement by rivals not to compete with each other but instead to charge high prices

c. step 3 = play your best response

best response = the choice that yields the highest payoff given the other player's choices

solve finitely repeated games by...

by looking forward and reasoning backwards

best responses

each player's choice is their best response to what they expect the other to choose

correct expectations

each player's expectation about what the other player will choose is also correct

check mark method

if you put a check market next to each players best response, then an outcome with a check mark from each player is a Nash equilibrium

look forward

in games that play out over time, you should look forward to anticipate the likely consequences of your choices

collusion is.a prisoner's dilemma -- graphical example

in notes

coordination game -- graphical examples x4

in notes

game tree -- graphical example

in notes

good and bad equilibria -- graphical example x3

in notes

multiple equilibria -- graphic example

in notes

payoff table -- graphic

in notes

prune the tree method -- graphical example

in notes

targedy of the commons -- graphic example

in notes

the first mover advantage -- graphical example

in notes

the prisoner's dilemma -- graphic example

in notes

the scheduling game -- graphical example

in notes

finitely repeated games

one in which you face the same strategic interaction a fixed number of times

strategic plan

a list of instructions that describes how to respond to any possible solution