3/27/24: Interacting with others
King-Casas et al. (2005): the trust game
"hyper-fMRI" with two players - Signal in one person's brain correlates with signal in other's brain Trials divided into fair (like-for-like), malevolent (trust-betrayal), benevolent (unexpected rewards) Unexpected rewards associated with striatum activity Timing of activity shifts over the course of experiment - Initially responds to actual rewards - Subsequently responds to anticipated rewards
What are the game theory paradigms?
1. The Prisoner's Dilemma 2. The Ultimatum Game 3. The Public Goods Game 4. The Trust Game
Game Theory
A type of mathematical model that captures how an individual's success in making decisions is influenced by the decisions of others
Behavioral Economics
Application of game theory to real-life social decisions.
Neuroeconomics
At micro-economic level, human interactions are based on evolved cognitive mechanisms for exchange, trust, fairness In theory, these mechanisms may also be used at the level of macro-economics, determining the way that institutions and governments relate to each other Leverages economic models to make cognitive processes more quantifiable Powerful "psychometric-neuro metric" comparisons
Singer et al (2004): Prisoner's Dilemma w/ faces
Before imaging: play game with players who cooperate or defect: Some players instructed, others free to choose - The players know that the other player either has free will or is instructed During Imaging: Shown faces of previous players who had cooperated, defected, or had not played (neutral) but no game was played Seeing cooperators activates the striatum Seeing intentional agents activates TPJ/STS (ToM) region - Engagement of theory of mind and mentalizing regions when thinking of people who had free will and cooperated - Reward related regions when you have a history of cooperation with someone (trust)
Cooperation vs. competition
Being cooperative compromises one's own time and resources. If my genes (and my traits) are to survive, then they have to be of benefit to me, not you But short-term interests have to be balanced against the longer term gains to be had through group living
What is the optimal individual solution for both players in the prisoner's dilemma?
Betrayal (defection) is the optimal individual solution for both players because: Defection = 5 or 0 years Silence = 10 years or 6 months
Insula
Brain region activated in response to negative emotions like disgust Insula activated in response to unfair offers in ultimatum game
Anterior cingulate cortex (ACC)
Brain region involved in processing emotions and decision-making Activated in response to unfair offers in the ultimatum game
Dorsolateral prefrontal cortex (DLPFC)
Brain region related to control of responses and social fairness Activated in response to unfair offers in ultimatum game Brain region involved in inhibiting self-interest and promoting fairness
Striatum Activity
Brain region showing response to unexpected rewards in neuroeconomic experiments Talked about in King-Casas et al (2005)
fMRI of Prisoner's Dilemma
Desire to cooperate at the beginning of the experiment People cooperate at the beginning of the experiment, then as the game goes on more self-interested behavior crops up DD (mutual non-cooperation) results in hatred Unreciprocated cooperation results in guilt (if you didn't cooperate and your partner did) and anger (vice versa)
The public goods game
Each chooses how much to contribute and the amounts are redistributed (plus gains) Free-riding: Not contributing to the group effort, tends to decrease with punishment or incentives The tension is between wanting to minimize individual loss (not giving money) and the multiplier (making more money back)
Prisoner's Dilemma
Experimental paradigm of cooperation vs. betrayal Two susptects Each prisoner must choose to betray the other (termed 'defect') or to remain silent (termed 'cooperate') - choice not revealed to the other Amount of time spent in prison depends on your respone and the other suspect
The trust game
Game Paradigm: Investor given a sum of money Investor decides how much money to give trustee Investment is tripled Trustee decides how much money to return to the investor and investor must accept offer
How is game theory used in economics?
Game theory has been used to find the optimal decision for an individual (i.e. the one that has the greatest benefits for the least costs), taking into account the decisions of others
Ultimatum game
Game where a proposer offers a share of money to a responder Responder can reject and then no one gets money
How is game theory used in biology?
In biology, game theory has been used to model evolution based on the concept of fitness rather than decision
How is game theory used in psychology?
In psychology, game theory is applied to 'real life' social decision-making; individual gain may be sacrificed for other principles (fairness); related to neuroeconomics
Evolutionary fitness score
Measure of an individual's success in passing on genes
Iterative prisoner's dilemma
Model explaining cooperation emergence in evolutionary biology
Rilling et al. (2002): Prisoner's Dilemma
Mutual cooperation (CC) had highest activity in reward related regions (Striatum, OFC) , even though not associated with the maximum monetary rewards Mutual cooperation when playing the computer (AI) was not associated with striatal activity Even though monetary rewards the same as when playing human
Iterative Versions of Prisoner's dilemma
Prisoner's Dilemma played over multiple rounds with prison sentences replaced by monetary rewards
Heinrich et al: Culture and the Ultimatum Game
Punishing unfairness is universal but the definition of fairness is not It relates to community size, but not education or wealth Larger communities expect higher (approaching 50/50) offers For instance, if the community is 50 people, if you give someone an unfair offer it has more consequences because you'll likely see them again 20% in ultimatum game is not a universal threshold
Nash equilibrium
Strategy where the lowest offer is made and any offer is accepted Offers lower than 20% are generally rejected
Axelrod and Hamilton (1981): Evolution of Cooperation
Study by Axelrod and Hamilton using computational modeling to analyze cooperation and defection in evolutionary scenarios Uses computational modeling: 1000 agents (can cooperate or defect) - Given evolutionary fitness score In a population of individuals (10K agents) containing pure cooperators and pure defectors, cooperation is always bred out (low fitness score) In a population of selective cooperators (playing tit-for-tat or intelligent cooperation), cooperation comes to dominate - A mechanism by which cooperation can emerge even in a population in which the best individual strategy is to not cooperate
Sanfey et al. (2003): fMRI
Study using fMRI to analyze responses to fair and unfair offers Fair (50/50) and unfair (80/20) offers from a human or computer More likely to accept unfair offers from a computer Humans > computers: Unfair offers activate insula, anterior cingulate cortex (ACC), and dorsolateral prefrontal cortex (DLPFC) Insula activity is interpreted as a negative emotional response (e.g. disgust) Insula activity is greater for unfair offers rejected than unfair offers accepted DLPFC related to control of responses
Knoch et al. (2006): TMS and fairness
TMS over the dorsolateral prefrontal cortex (DLPFC) in the 'responder' brain increases the tendency to accept unfair offers (but not the perception of fairness itself) Normal DLPFC function is to increase fairness/inhibit self- interest
What does cooperation depend on?
TRUST: - Previous history and reputation - Social norms for exchange (and their enforcement)
What are the ways we may deviate from rational decision-making? (taking others into account vs. individual)
Taking others into account (left side of scale): Aversion to risk and losses Fairness Optimal collective decision Cooperation Social Norms Reputation Individual (right side of scale): Maximize individual goals "Objective" rational self-interest Minimize individual losses
What is the dilemma in "the prisoners dilemma"?
The dilemma arises because the best collective decision is for both players to cooperate (i.e. remain silent). This gives the lowest collective prison sentence (6 months each)
Selective cooperators: evolution of cooperation
Tit-for-tat → respond in kind, when other agents cooperate they cooperate, when other agents defect they defect
Rilling et al. (2008): Prisoner's Dilemma
Unreciprocated cooperation (you cooperate, partner defects) associated with amygdala and insula activity and self-reports of anger, irritation, disappointment
AI and Prisoner's Dilemma
When playing with AI vs humans, self-interested behavior crops up sooner