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Geometric Pricing of Games

Yukio Hirashita


Geometric pricing is not risk-neutral. It is deduced from a mixture of the Kelly criterion and the Black-Scholes formula, these are independent of the user preferences. In the traditional scheme of expectation (risk-neutral) pricing advocated by Samuelson and others, the prices of the three payoff-probability vectors ((10, 10), (0.5, 0.5)), ((20, 0), (0.5, 0.5)), and ((30, −70), (0.8, 0.2)) are equivalent. However, they are different in geometric pricing.
In this paper, we define the geometric prices of two-person matrix and bimatrix games. We also calculate some equilibria, including the approximate joint correlated equilibrium in particular.


Geometric price, approximate equilibrium, Optimal proportion of investment

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