Neuroscience as the
Foundation of Game Theory
Kaushik Majumdar
Systems Science and Informatics Unit, Indian
Statistical Institute, Bangalore Center
https://sites.google.com/site/isicng/
(Computational Neuroscience Group Home)
Games and Neuroscience
• Games played by players.
• Strategies of the players are modulated by
their behaviors.
• Behaviors are modulated by
neurobiological build up of the players.
• So Neuroscience modulates playing
strategies in the Games.
Subjective Desirability
U1(x) is the first player’s utility function in the
two player inequality aversion game.
U1(x) = x1 – αID – βIA, where
X = [x1 x2], ID = max{x1 – x2, 0}, IA = max{x2 –
x1, 0}, 0 ≤ β ≤ α < 1. α and β are
sensitivities to disadvantageous and
advantageous inequalities respectively.
Game theory and neural basis of social decision making, Lee, Nature Neuroscience,
11(4): 404 - 409, 2006.
Prisoners’ Dilemma with
Inequality Aversion
Brain Areas Involved in Moral
Sensitivity
Neural correlate of moral sensitivity, Moll et al., J. Neurosci., 22(7): 2730 – 2736, 2002.
Moral Emotion
•
Moral emotions differ from basic
emotions in that they are intrinsically
linked to the interests or welfare either of
society as a whole or of persons other
than the self. Moral emotions are readily
evoked by the perception of moral
violations. It has been suggested that, in
contrast to laborious deductive
Moral Emotion (cont)
reasoning, they enable rapid, automatic,
and unconscious cognitive appraisals of
interpersonal events.
More can be seen in:
• A. R. Damasio, Descartes' error: emotion,
reason, and the human brain. Avon, New
York, 1994.
Morality from a Different Angle
• Trading in nonhuman animals is
‘permitted’ under wide ranging conditions
with the ambit of laws made by humans.
Confining, slaughtering and subjecting
them to various experiments are ‘legal’ in
the human society under wide ranging
conditions. But the scope of the same acts
on the humans is much more restricted
under the human legal systems.
Morality (cont)
• From an objective point of view, devoid of
human selfishness, all these acts on
human and nonhuman animals are equally
justifiable or equally unjustifiable. Still the
human laws prevail because humans have
become hugely more powerful than all
other species. That is why eating beef is
moral but eating human meat is a criminal
offence even for a tiger.
Power
• So legality or morality is decided by power.
In a capitalistic society, where capital is
the most powerful entity, gender or racial
inequality may be immoral or unethical,
but inequality between workers and
capitalists is quite natural and acceptable.
Class vs. Power
• Power is a more objective entity than
class. One class dominates the other
simply because the dominating class is
more powerful than the dominated.
• Analysis by power gives a finer resolution
than analysis by class.
Power in Game Theory
• A player plays a game because he/she
has the power to participate in the game
with own strategies.
• A player who is substantially more
powerful than the others, will destroy the
independence of the players by
dominating the other players.
Quantitative Definition of Power
• Here our aim is to define power for any
general system.
• We will first define system momentum.
• Then we will measure the rate of change
in the system momentum.
System Momentum
• Let a system be defined by a totally
differentiable vector field f : Rn+1 → Rm.
Then the system momentum is (∂Mf/∂t),
where M  Rm is a fixed weight vector.
• System power is defined by
(∂2(Mf)/∂t2)(∂f/∂t), which is a straight
forward extension of the notion of power in
classical mechanics, where f is
displacement and M is mass.
Revolution and Evolution
• When ∂f/∂t is large, i.e., a big change in a
small time – called a revolution and when
∂f/∂t is small, i.e., a small change in a big
time – called an evolution. Clearly a lot
more power is needed to make a
revolution happen compared to an
evolution.
Power of Trend in Society
• In a social system f = (f1,……..,fm)T, where
each component fi : Rn+1 → R signifies a
trend, called the ith trend. M =
(m1,……,mm), where each mi is the
number of individuals associated with the
trend. If all but the ith trend in f are fixed
then (∂2(Mf)/∂t2)(∂f/∂t) = mi(∂2fi/∂t2)(∂fi/∂t),
mi is the number of individuals following
the trend.
Power of Trend (cont)
• If mi is large the power associated with the
trend will be high.
• How to have a large mi then?
Simple, create a trend and gather people
in favor of it!
Brain Activation During
Lipreading
Buccino et al., J. Cognitive Neurosci., 16: 1 – 14, 2004.
Human Mirror Neuron System
Human MNS (cont)
• It has been hypothesized that the
fundamental mechanism at the basis of
the experiential understanding of others’
actions is the activation of the mirror
neuron system (Gallese et al., 2004).
• Recently mirror neurons have been
located in different parts of the human
brain (Mukamel et al., 2010).
Dopamine Neurons
• Encodes goal-directed behavior
(pathological case Parkinson’s disease).
• Activate reward expectation.
• Seek novelty.
Novelty & Reward Expectancy
Hypothesis
iy = reward expectancy
x = novelty
Complex
Plane
n
f
as a Discrete Dynamical
System
fn : С → С, where n is the time.
P = M|{(fn + 1 – fn) – (fn – fn – 1)}(fn – fn – 1)| is
the expression for the power. | | denotes
modulus.
When P is high enough M is also increased.
Social Trend
Sequence {fn}n constitutes a Riemann
Surface of individual trend.
At a particular time n the envelope of fn
across all the individuals in the society will
give the social trend.
2.5
2.5
2
2
1.5
1.5
Power
Power
Power Concentrates
1
1
0.5
0.5
0
60
0
60
50
40
40
30
20
Social expectation
10
0
Social novelty
40
30
20
20
0
50
40
Social expectation
20
0
10
0
Social novelty
Consequence
• In a society where power is more or less
uniformly distributed among individuals
and institutions, because of biological
diversity among individuals, some are
more likely to have stronger dopamine
drive for novelty and reward expectation
than most others. Eventually power will
concentrate around them and the
distribution will become unequal.
Multiple Centers of Power
Concentration
2.5
2
1.5
1
0.5
0
60
50
40
40
30
20
20
0
10
0
Consequence
• Multiple powers will try to exert their
influence on the same resources and a
power politics or power game will ensue,
where each one will try to dominate the
other and over iterations of the game the
independence of the players is likely to be
compromised. Many realistic games must
model this phenomenon.
Additional References
• C. Camerer, G. Loewenstein and D.
Prelec, Neuroeconomics: how
neuroscience can inform economics, J.
Economic Literature, 43(1): 9 – 64, 2005.
• E. Fehr and C. F. Camerer, Social
neuroeconomics: the neural circuitry of
social preferences, Trends Cog. Sci.,
11(10): 419 – 427, 2007.
References (cont)
• http://en.wikipedia.org/wiki/Power_(philoso
phy)
• Galles et al., A unifying view of the basis of
social cognition, TINS, 8(9): 396 – 203,
2004.
• M. Iacoboni and M. Dapretto, The mirror
neuron system and consequences of its
dysfunction, Nature Reviews
Neuroscience, 7: 941 – 951, 2006.
References (cont)
• Mukamel et al., Single neuron responses
in humans during execution and
observation of actions, Curr. Biol., 20(8):
750 – 756, 2010.
Thank You