"Why We're So Nice: We're Wired to Cooperate" Natalie Angier New York Times, 23 July 2002 What feels as good as chocolate on.

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Transcript "Why We're So Nice: We're Wired to Cooperate" Natalie Angier New York Times, 23 July 2002 What feels as good as chocolate on.

"Why We're So Nice: We're Wired to Cooperate" Natalie Angier

New York Times, 23 July 2002

What feels as good as chocolate on the tongue or money in the bank but won't make you fat or risk a subpoena from the Securities and Exchange Commission?

Hard as it may be to believe in these days of infectious greed and sabers unsheathed, scientists have discovered that the small, brave act of cooperating with another person , of choosing trust over cynicism, generosity over selfishness, makes the brain light up with quiet joy .

Studying neural activity in young women who were playing a classic laboratory game called the Prisoner's Dilemma , in which participants can select from a number of greedy or cooperative strategies as they pursue financial gain,researchers found that when the women chose mutualism over "me-ism," the mental circuitry normally associated with reward-seeking behavior swelled to life.

And the longer the women engaged in a cooperative strategy, the more strongly flowed the blood to the pathways of pleasure.

The researchers, performing their work at Emory University in Atlanta, used magnetic resonance imaging to take what might be called portraits of the brain on hugs.

"The results were really surprising to us," said Dr. Gregory S. Berns, a psychiatrist and an author on the new report, which appears in the current issue of the journal Neuron. "We went in expecting the opposite." The researchers had thought that the biggest response would occur in cases where one person cooperated and the other defected, when the cooperator might feel that she was being treated unjustly.

Also: Paul Glimcher invited talk on “Neuroeconomics” [email protected]

[Courtesy CAIDA]

Internet Connectivity

International Trade

[Krempel&Pleumper] A mixture of scales; detailed structure

Corporate Partnerships

Political and Governmental Control

[Krempel]

Online Social Relationships

[Isbell et al.]

Multi-Player Game Theory: Powerpoint Notation Translation

• Players 1,…,n • Actions (0 and 1 w.l.o.g.); joint action x in {0,1}^n • Mixed strategy for i: probability p_i of playing 0 • Payoff matrices M_i[x] for each i (size 2^n) • (Approximate) Nash equilibrium: – Joint mixed strategy p (product distribution) – p_i is (approximate) best response to p for every player i • Nash equilibria always exist; may be exponentially many Given the M_i, how can we compute/learn General problem is HARD.

Nash equilibria?

Graphical Models for Game Theory

• Undirected graph G capturing • Assume:

local interactions

• Each player represented by a vertex • N_i(G) = neighbors of i in G (includes i) M_i(x) expressible as M’_i(x’) over

only

N_i(G) • Graphical game: (G,{M’_i}) • Compact representation of game • Exponential in max

degree

• Analogy to Bayes nets: (<< # of players) • Ex’s: geography, organizational structure, networks

special structure

8 3 7 2 1 4 5 6

An Abstract Tree Algorithm

U1 U2 U3 V T(w,v) = 1 <--> $ an “upstream” Nash where V = v

given

W = w <--> $ u: T(v,ui) = 1 for all i, and v is a best response to u,w W • Downstream Pass: – Each node V receives T(v,ui) from each Ui – V computes T(w,v) and witness lists for each T(w,v) = 1 • Upstream Pass: – V receives values (w,v) from W s.t. T(w,v) = 1 – V picks witness u for T(w,v), passes (v,ui) to Ui How to represent?

How to compute?

An Approximation Algorithm

Discretize u and v in T(v,u), 1 represents approximate Nash • Main technical lemma: If k is max degree, grid resolution t ~ e /(2^k) preserves

global

e -Nash equilibria • An

efficient

algorithm: – Polynomial in n and 2^k ~ size of rep.

– Represent an approx. to

every

Nash U1 – Can generate random Nash, or specific Nash U2 U3 V W

• Table dimensions are probability of playing 0 • Black shows T(v,u) = 1 • Ms want to match, Os to unmatch • Relative value modulated by parent values • t = 0.01, e = 0.05

Extension to exact algorithm: each table is a finite union of rectangles,

exponential

in depth Can also compute a

single exactly

in

polynomial

time equilibrium

NashProp for Arbitrary Graphs

• Two-phase algorithm: – Table-passing phase – Assignment-passing phase • Table-passing phase: – Initialization: T[0](w,v) = 1 for all (w,v) – Induction: T[r+1](w,v) = 1 iff $ u: U1 • T[r](v,ui) = 1 for all i • V=v a best response to W=w, U=u • Table consistency

stronger

U2 U3 V W than best response

Convergence of Table-Passing

• Table-passing obeys • Tables

converge contraction:

– {(w,v):T[r+1](w,v) = 1} contained in {(w,v):T[r](w,v) = 1} and are

balanced

• Discretization scheme: tables converge

quickly

• Never eliminate an equilibrium • Tables give a • Allow e and t

reduced

search space • Assignment-passing phase: – Use graph to propagate a solution consistent with tables – Backtracking local search to be parameters • Alternative approach [Vickrey&Koller]: – Constraint propagation on

junction tree

Graphical Games: Related Work

• Koller and Milch: graphical influence diagrams • La Mura: game networks • Vickrey & Koller: other methods on graphical games

Summarization Games with Bounded Influence

• Have global • Assume

summarization function

• Payoff to player i depends only on x_i, S(x): – Arbitrary payoff function F_i(x_i,S(x)) • Common examples: – Voting (linear S) – Financial markets

bounded influence

of S S(x) • Often expect influence • Assume bounded derivatives of the F_i • Every player

weakly

t to

decay

with n!

influences every other

A Potential Function Argument

summarization value for any mixed strategy

Learning Equilibria, Linear Summarization

summarization value for any mixed strategy

Results

• Algorithm for computing O( e + t )-Nash in time polynomial in 1/e • Algorithm for learning O( e + t )-Nash in time polynomial in 1/e , linear S case • Benefits of a large population