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Evaluating gambles using dynamics

Ole Peters’ and Murray Gell-Mann’s manuscript is now available as SFI working paper 14-05-013 and on the arXiv at http://arxiv.org/abs/1405.0585  The paper presents the foundations of a possible new decision theory by re-visiting the defining decision-theory problem of evaluating a gamble. This new decision theory recognizes that optimal behavior depends on the situation, i.e. the dynamic an individual is subjected to. Simple expectation-value optimization does not constitute rationality.

The theory makes full use of far-from equilibrium stochastic processes, instead of starting with an equilibrium assumption.

Noting that a gamble is specified as a random variable, the authors point out that this is insufficient information to evaluate it. In addition, a dynamic must be specified, i.e. a type of repetition for the gamble. This leads to a stochastic process (rather than a random variable) that is non-ergodic. On the non-ergodic stochastic process an ergodic observable can be defined, which is a growth rate. Depending on the type of repetition, different growth rates are ergodic, and different types of behavior are optimal. Rather than specifying human behavior through utility functions and optimizing with respect to those, a stochastic process is specified and behavior is optimized according to its dynamics.

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