Hi @pseudoname, your previous post got me thinking about Game...

Hi @pseudoname, your previous post got me thinking about Game Theory and Bayersian Decision Making.

I did 2 subjects in Game Theory in my master degree in Operations Research. In operations research, game theory is a mathematical theory that deals with some kind of decisions in a competitive situation. The theory of games started in the 20th century and it was proposed by John Von Neuman and Morgenstern. It uses the minimax principle to decide the strategy within a competitive situation. Game theory is a branch of applied mathematics that provides tools for analyzing situations in which parties (called players) make decisions that are interdependent. This interdependence causes each player to consider the other player's possible decisions( or strategies) in formulating strategy. Anyway, I think your Hypothetical Case is too complication to apply Game Theory. I think may be Bayesian Decision Theory may be more applicable. I actually did a minor thesis on Bayesian Decision Theory. A Bayesian decision maker proceeds by assigning a numerical utility to each of the possible consequences of an action, and a probability to each of the uncertain events that may affect that utility. The weighted average of the utility with respect to the probability is then used as the criterion of choice. Bayesian Decision Theory is the statistical approach to pattern classification. It leverages probability to make classifications, and measures the risk (i.e. cost) of assigning an input to a given class.
Anyway, I just like to bring these two analysis tools for other maths/statistics experts here to solve your case. I won’t contribute further to this discussion as my brains literally hurts after digging out my past and trying to understand how I did it.

NOT LONG NOW.