On Game-Theoretic Risk Management (Part Two) -- Algorithms to Compute Nash-Equilibria in Games with Distributions as Payoffs (original) (raw)
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STRATEGIC PAYOFFS OF NORMAL DISTRIBUTIONBUMP INTO NASH EQUILIBRIUMIN 2 × 2 GAME
In this paper we assume that strategic payoffs are Normal distribution, and discuss how the parameters of Normal distributions affect the NE payoff distribution that is also concerned by players. We find that distortions of NE payoff distributions are dominated by the distance between variances of strategic payoffs in small means cases and the variances of the dominantly strategic payoffs in large means case. We also find that the variances of strategic payoffs lead to the higher means of the NE payoff distributions, which contain risk premium and the dominantly strategic payoffs, whatever the means of strategic payoffs. However, compared with the dominant strategy that is NE of static game, our model obtains that the mean magnitudes of strategic payoffs lead to establish the different radeoff relationship between means and variances of the NE payoff distribution in the decision-making process.