Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Constructive Generalization of Nash Equilibrium   In a society of multiple individuals, if everybody is only interested in
maximizing his own payoff, will there exist any equilibrium for the society?
John Nash proved more than 50 years ago that an equilibrium always exists such
that nobody would benefit from unilaterally changing his strategy. Nash
Equilibrium is a central concept in game theory, which offers the mathematical
foundation for social science and economy. However, the original definition is
declarative without including a solution to find them. It has been found later
that it is computationally difficult to find a Nash equilibrium. Furthermore, a
Nash equilibrium may be unstable, sensitive to the smallest variation of payoff
functions. Making the situation worse, a society with selfish individuals can
have an enormous number of equilibria, making it extremely hard to find out the
global optimal one. This paper offers a constructive generalization of Nash
equilibrium to cover the case when the selfishness of individuals are reduced
to lower levels in a controllable way. It shows that the society has one and
only one equilibrium when the selfishness is reduced to a certain level. When
every individual follows the iterative, soft-decision optimization process
presented in this paper, the society converges to the unique equilibrium with
an exponential rate under any initial conditions. When it is a consensus
equilibrium at the same time, it must be the global optimum. The study of this
paper suggests that, to build a good, stable society (including the financial
market) for the benefit everyone in it, the pursuing of maximal payoff by each
individual should be controlled at some level either by voluntary good
citizenship or some proper regulations.

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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat