Decision Sciences: Game Theory

Question 1

What are the 2 differences between perfect and complete information game?

Answer 1

Perfect Information
- all moves are known to all players
- players may not know the payoffs of other players or may not know completely the structure of the game

Complete Information
- players may not see all the other moves of the players
- players know the payoffs and structure of the game
- players may plan in advance

Question 2

What are the 2 differences between simultaneous and sequential games?

Answer 2

Simultaneous Games
- each player has one move
- all players do their moves simultaneously
- ex. rock paper scissors
Sequential Games
- players may have to move several times
- no two players move at the same time
- ex. chess, negotiations

Question 3

What is the difference between perfect and imperfect information?

Answer 3

Perfect Information
- Every player knows all the random and deliberate moves done so far by the time their turn comes
- ex. chess, open bidding, monopoly
Imperfect Information
- there is at least one move/event hidden from some players
- ex. game of the generals

Question 4

What are the differences between complete and incomplete information?

Answer 4

Complete Information
- Players know the structure, order, possible moves, and payoffs for all possible outcomes
- ex. chess, monopoly
Incomplete Information
- players do not have complete information
- some players may have private information (eg. decision of the other player)
- ex. Prisoner’s Dilemma

Question 5

What is Game Theory?

Answer 5

study of strategic decision making where situations are called games and participants are called players
- which strategy yields the best outcome

Question 6

4 composition of game theory

Answer 6

players, rules, consequences, payoffs

Question 7

Define strategy

Answer 7

a sequence of moves of each player (moves: a set of action)

Question 8

Payoff depends on

Answer 8

The choices of all players involved

Question 9

Goal of Game Theory

Answer 9

Identify the optimal strategy

Question 10

Class 1: Simultaneous vs Sequential Games are grouped based on?

Answer 10

number of players (usually should have more than one player)

Question 11

Class 2: Perfect vs Imperfect Information are grouped based on?

Answer 11

Randomness (where random events can influence the outcome of the game)

Question 12

What is the Normal Form of a Game?

Answer 12

table of numbers with a) strategies listed along the margins and b) the payoffs for the participant in the cells (inner cells) as ordered pairs (P1, P2)

Question 13

What does the numbers (0, -1, 1) mean in the payoff ordered pair?

Answer 13

0 - tie (or same number x and y)
(+) - gain/winner
(-) - lose/loser

Question 14

Two companies share a market where they make PhP 50 million each. They both need to decide if they will advertise or not. Advertising costs Php 20 million but gets Php 30 million in revenues from the competitor as long as the competitor does not advertise. What is the Normal Form of the problem?

Answer 14

refer to ppt

Question 15

What is the Maximin Solution?

Answer 15

choosing a strategy that will give the maximum possible payoff in, even when the opponent is able to guess your choice

proposed by Jon Von Neumann
a simultaneous game analysis in normal form

Question 16

Maximin Solution Example 1
Consider the working-on-a-project game in which you and a classmate work together on a course
requirement. Each of you can either work very hard or take it easy. You both want to pass but both of you do not like working very hard. What is the maximin solution and the payoff value?

Answer 16

refer to ppt; Maximin solution (T, T) Payoff Value (1, 1)

Question 17

Maximin Solution Example 2
Another game is the so-called battle of the sexes. Suppose, on a given night, you can watch either House of Dragons (HoD) or The Sandman (TS). You prefer HoD but your partner prefers TS. The worst possible thing to happen is to have an argument and not watch together or at all. What should you do? The problem has no maximin solution why?

Answer 17

refer to ppt; Maximum in the minimum payoff value is zero no matter what

Question 18

Maximin Solution Example 3

Answer 18

refer to ppt; Maximin Solution (Confess, Confess), Payoff value (-10, -10)

Question 19

What is the Nash Equilibrium

Answer 19

• A strategy for each players such that every players’
  action is the best response to the other players’
  actions
• Each player uses his/her best response in the
  game. Switching to another strategy results to a
  lower payoff

conceptualized by John Nash
a simultaneous game analysis in normal form

Question 20

Nash Equilibrium Example 1

Answer 20

refer to ppt; Has Nash Equilibrium (T, T) with payoff (1,1)

Question 21

Nash Equilibrium Example 2

Answer 21

refer to ppt; Nash Equilibrium (HoD, HoD) and (TS, TS) with payoff pairs (2,1) and (1,2)

Question 22

Nash Equilibrium Example 3

Answer 22

refer to ppt; Nash Equilibrium (C, C) with payoff values (-10, -10)