Lecture 5 - Game Theory

Question 1

What are static games?

Answer 1

Few firms only play games once in one period.

Question 2

What are dynamic games?

Answer 2

Play same games over and over again in different periods.

Question 3

Oligopolies do not really change their…

Answer 3

Prices much. They don’t have price competition.

Question 4

What is game theory?

Answer 4

A set of tools used by economists and many others to analyse players’ strategic decision making.

Question 5

What is a game?

Answer 5

An interaction between players (such as individuals or firms) in which players use strategies. Strategies trying to gain more market shares or maximise their own profits.

Question 6

What are the payoffs of a game?

Answer 6

The payoffs of a game are the players’ valuation of the outcome of the game (e.g. profits for firms, utilities for individuals).

Question 7

The rules of the game determine…

Answer 7

The timing of players’ moves and the actions players can make at each move.

Question 8

What is an action?

Answer 8

An action is a move that a player makes at a specified stage of a game.

Question 9

What is a strategy?

Answer 9

A strategy is a battle plan that specifies the action that a player will make based on the information available at each move and for any possible contingency.

Question 10

Strategic interdependence occurs when a…

Answer 10

Player’s optimal strategy depends on the actions of others.

Question 11

What are the assumptions of game theory?

Answer 11

• All players are interested in maximising their own payoffs. Individuals are interested in maximising their utilities based on their rival’s actions too. Firms are interested in maximising their profits.
• All players have common knowledge about the rules of the game. They all know how to play the game.
• Each player’s payoff depends on actions taken by all players. They don’t act independently.
• Complete information (payoff function is common knowledge among all players). Players in the game all know each others payoffs. At which conditions are their payoffs higher or lower at different strategies.

Question 12

Complete information games are games in which…

Answer 12

Players know how other players evaluate the possible outcomes of the game.

Question 13

Simultaneous move games are games in which…

Answer 13

All players must choose their actions at the same time (and thus without observing any other player’s action).

Question 14

Sequential move games are games in which…

Answer 14

At least some players observe the actions of another player prior to having to choose their own actions.

Question 15

Incomplete information games are games in which…

Answer 15

At least some players do not know at least some other player’s evaluation of possible outcomes.

Question 16

In a static game each player acts…

Answer 16

Simultaneously, only once and has complete information about the payoff functions but imperfect information about rivals’ moves. Examples: employer negotiations with a potential new employee, teenagers playing “chicken” in cars.

Question 17

Rational players will avoid strategies that are…

Answer 17

Dominated by strategies.

Question 18

We can precisely predict the outcome of any game in which every player has a…

Answer 18

Dominant strategy.

Question 19

What is a dominant strategy?

Answer 19

A strategy that produces a higher payoff than any other strategy for every possible combination of its rivals’ strategies.

Question 20

The best response is a strategy that…

Answer 20

Maximises a player’s payoff given its beliefs about its rivals’ strategies.

Question 21

A set of strategies is a Nash equilibrium if, when…

Answer 21

All other players use these strategies, no player can obtain a higher payoff by choosing a different strategy.

Question 22

No player has an incentive to deviate from a…

Answer 22

Nash equilibrium.

Question 23

What is a mixed strategy?

Answer 23

It is when a player chooses among possible actions according to probabilities the player assigns.

Question 24

A pure strategy assigns a probability of…

Answer 24

1 to a single action.

Question 25

A mixed strategy is a probability distribution over…

Answer 25

Actions.

Question 26

When a game has multiple or no pure-strategy Nash equilibria, a mixed-strategy Nash equilibrium can…

Answer 26

Help to predict the outcome of the game.

Question 27

Explain what happens in dynamic games.

Answer 27

• Players move either sequentially or repeatedly.
• Players have complete information about payoff functions.
• At each move, players have perfect information about previous moves of all players.

Question 28

sequential

Answer 28

two stage game played once. hence said to occur in a snignel period.but in the first stage player one moves first and in the second stage player two moves and the game ends with the palyers recievin gpalyofss base don their actions.

Question 29

What are sequential games?

Answer 29

• Two stage game played once.
• Hence said to occur in a single period.
• But in the first stage, player one moves first and in the second stage, player two moves and the game ends with the players receiving payoffs based on their actions.

Question 30

What are repeated games?

Answer 30

• A single period simultaneously move game.
• Repeated at least twice and possibly many times.
• Although players move simultaneously in each period, they know about their rivals moves in previous periods so they have history information.
• So a rivals previous moves may affect the players current actions and as a result it is a dynamic game.

Question 31

What is a major difference between a dynamic game and a static game?

Answer 31

A dynamic game requires us to distinguish between strategies and actions.

Question 32

Dynamic games are analysed in their…

Answer 32

Extensive form.

Question 33

The extensive form specifies…

Answer 33

• the n players.
• the sequence of their moves.
• the actions they can take at each move.
• the information each player has about players’ previous moves.
• the payoff function over all possible strategies.

Question 34

A set of strategies forms a…

Answer 34

Subgame perfect Nash equilibrium if the players’ strategies are a Nash equilibrium in every subgame.

Question 35

A repeated game is a…

Answer 35

Static game that is played repeatedly.

Question 36

In a repeated game, a firm can influence its rival’s behaviour by…

Answer 36

Signalling and threatening to punish.

Question 37

In a single period game, one firm cannot punish the other firm for…

Answer 37

Cheating on a cartel/collusive agreement. They both cooperate with each other on this.

Question 38

In a single period game, one firm cannot punish the other firm for…

Answer 38

Cheating on a cartel/collusive agreement. They both cooperate with each other. However, if the firms play period after period, there is a way for firm to get punished by the other.

Question 39

What is an auction?

Answer 39

A sale in which a good or service is sold to the highest bidder.
Players have to devise bidding strategies without complete information about payoffs.
Examples of things that are exchanged via auction - cars, art etc.

Question 40

What are the rules of the game/key components?

Answer 40

1. Number of units sold.
   - US Treasury holds regular auctions of US government bonds selling to many buyers.
2. Format of the bidding.
   - English auction: ascending-bid auction; last bid wins. Starts at lowest price acceptable to seller and repeatedly encourages potential buyers to bid more than the previously highest bid. The auction ends when no one is willing to bid more than the current highest bid.
   - Dutch auction: descending-bid auction; first bid wins. Seller starts of with highest price and if no one is willing to buy they gradually reduce the price until someone accepts the offered price.
   - Sealed-bid auction: private, simultaneous bids submitted without seeing other bids. Highest bidder wins. Depends if it is first price or second price auction. In a first price auction, the winner pays its own highest bid. Governments often use this type of auction. In second price auction, the winner pays the amount bid by the second highest bidder .
3. Value that potential bidders place on the good.
   - Private value: each potential bidder values item differently. Sets personal bid. May be a unique item. Individual bidders know how much the good is worth to them but don’t know how much other bidders value it.
   - Common value: good has same fundamental value to all. No buyers know exactly what that common value is. Example: trees.

Question 41

Second price sealed bid auction.

Answer 41

Bidding your highest value leaves you better off than any other value.
The amount that you bid affects whether you win but it does not affect how much you pay if you win, because you will pay the second highest bid.
In a second-price sealed-bid auction, the winner pays the amount bid by the second-highest bidder.

Question 42

English auction.

Answer 42

Best strategy is to raise the current highest bid as long as the bid is less than the value you place on the good, the true maximum value.
Strategy is to raise your bid by smallest permitted amount until you reach the value you place on the good being auctioned.
The winner pays slightly more than the value of the second-highest bidder.

Question 43

Dutch auction/First price sealed bid auction.

Answer 43

In a Dutch or first-price sealed bid auction, you should shave your bid below your value.
Strategy is to bid an amount that is equal to or slightly greater than what you expect will be the second-highest bid given that your value is the highest.
Reducing your bid reduces probability of winning but increases consumer surplus if you win.

Question 44

In auctions with private values and other plausible conditions:

Answer 44

The expected revenue is the same across all auction formats in which the winner is the person with the highest value.

Question 45

What is the Winner’s Curse?

Answer 45

That the auction winner’s bid exceeds the common value item’s value.

Question 46

Overbidding occurs when…

Answer 46

There is uncertainty about the true value of the good.

Question 47

In what type of auctions does the Winner’s Curse occur in?

Answer 47

Common value but not private value auctions.