Week 7 Lec 14

Question 1

Give examples from multiple domains of strategic interactions from the lens of game theory.

Answer 1

Biology: kin selection and predation
economics: bargaining and auctions
politics

Question 1

Define strategic interaction.

Answer 1

Strategic interactions extend the idea of utility maximization to social scenarios. Environment is strategic when decisions made by one player influences the opportunities and payoff received by the other.

Question 2

What is Game Theory?

Answer 2

Game theory describes and predicts the behaviour of interacting decision makers

Question 3

Name two advantages of game theory.

Answer 3

Creates mathematical taxonomy of multi agent decision problems
Predicts how people behave under different beliefs of what others will do

Question 4

Name two branches of Game Theory

Answer 4

Analytical game theory describes how rational, self interested individuals should behave in strategic situations
Behavioural game theory describes what people actually do and adds emotions, mistakes, limited foresight and doubts about how smart others are

Question 5

What are games and their main purposes?

Answer 5

Games are ways to model real world decision making scenarios
Main purpose: Provide a taxonomy of strategic situations and test predictions of Game Theory

Question 6

What are the two forms of games?

Answer 6

Extensive form games and normal form games

Question 7

What are extensive form games?

Answer 7

Show explicit representation of each move at each decision point
Players do not make moves simultaneously
Used for sequential games
Time stamped decision tree (branches = actions, nodes = payoffs for all players)

Question 8

What are normal-form/ one-shot games?

Answer 8

Used for when players make moves simultaneously or when order of moves is irrelevant
Players make decisions without seeing strategies of other players
Matrix of strategies and outcomes

Question 9

Describe the Prisoner’s Dilemma game.

Answer 9

Game in which players either stay silent (cooperate) or snitch (defect). Dont know what their partner will do. Rational choice would be to cooperate when partner defects and vice versa

Question 10

What does Prisoner’s Dilemma investigate?

Answer 10

Collaboration and altruistic behaviour

Question 11

What is the equilibrium solution for PD?

Answer 11

Both players defect (regardless of outcome, better outcome from defecting)

Question 12

What is the dominant strategy for PD?

Answer 12

Cooperation

Question 13

Which strategy is considered unstable in the PD?

Answer 13

Both players cooperating. This is because each player can improve their outcome if they change their strategy, given the other player doesn’t change theirs

Question 14

What class of social problems can PD help understand?

Answer 14

Used to study social dilemmas that arise when the welfare of one group conflicts with the narrower self interest of the individual

Question 15

What are real world examples of the social dilemmas illustrated by PD?

Answer 15

Cold war, doping in sports, limited resources

Question 16

What is the takeaway for normal form games?

Answer 16

Each player has multiple actions available
Each players goal is to maximize their own utility
Players make choices without observing the other players’ actions

Question 17

What is Nash equilibrium?

Answer 17

Nash equilibria describes outcomes where no player can increase their own payoff by changing their action while keeping the other player’s actions constant

Question 18

What is the Nash equilibrium for Prisoner’s Dilemma?

Answer 18

Single equilibrium: Both players choose to defect

Question 19

What is the Nash equilibrium for Stag Hunt game?

Answer 19

Two equilibria: Both choose to hunt the stag or the hare (both choose to cooperate)

Question 20

What are problems for equilibrium theory?

Answer 20

Sometimes people violate equilibrium theory
Limitations on iterated thinking or notion of selfishness (i.e. motivation to maximize individual payoff)

Question 21

What kind of problems can the stag hunt game help us to understand (applications)?

Answer 21

Allows individual’s attitude towards social risk taking involved in coordinating on mutual trust
Not limited to humans

Question 22

What are the assumptions of Nash equilibrium?

Answer 22

Rationality
Common knowledge
Already in equilibrium

Question 23

Describe the beauty contest game.

Answer 23

Game in which prize is awarded to competitor whose choice corresponds to the average preferences of competitors as a whole.
Requires inferring opinions of general public and invest in what you think other people think is best

Question 24

What is the Nash equilibrium for the beauty contest game and how does actual behaviour compare to it?

Answer 24

Rational choice/equilibrium is 0
People tend to use 0-3 levels of reasoning and few use Nash equilibrium
Lower mean for more educated, more motivated and more time
Learning helps move mean toward 0

Question 25

Can you name 2 explanations why people’s actual behavior might diverge from predictions of equilibrium theory?

Answer 25

With increasing number of steps of thinking
1. More computation required: players might be incapable of using high levels of reasoning because of cognitive limitations
2. Higher level reasoning indicates more strategic behaviour paired w the belief that other players are also more strategic
Players might have different beliefs ab what other players will choose

Question 26

Can you define mentalizing?

Answer 26

Mentalizing describes the capacity to infer and represent another person’s mental states, such as beliefs, intentions, strategies or desires
also called theory of mind, cognitive empathy or perspective taking

Question 27

What are the 5 regions that make up the mentalizing network?

Answer 27

MPFC, Posterior Cingulate Cortex (PCC), Tempoparietal junction (TPJ), Superior temporal sulcus (STS) and temporal pole (TP)

Question 28

Describe Corcicelli & Nagel (2008) study on mentalizing and the beauty contest game.

Answer 28

When subjects made choices facing human opponents, enhanced activity in the MPFC, STS, PCC and bilateral TPJ
High level reasoners had greater activity in MPFC (dorso-medial portion)
Areas involved in mentalizing seem to contribute to higher order thinking in strategic games

Question 29

Describe Thompson (2021) study on mentalizing and the Prisoner’s Dilemma.

Answer 29

Asked how do people achieve stable cooperation
When playing against humans, participants recruited the TPJ and dorso-medial MPFC
Brain regions implicated in social reasoning such as perspective taking and judgement of intentions