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

x = novelty

iy = reward expectancy

Complex Plane

fn 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.

Power Concentrates

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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

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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