The good reasoned choice...
How to make the good decision? A mathematical method of simple formulation and easy application allows us to optimize our choices, in the everyday life as at the time of serious conflicts.
The problem is defined as a dynamic process that includes two decision makers (DMs) in the selection of the same offer. A sequence of a prefixed number of (n) offers is observed, one at a time, randomly. The arrival of offers does not follow any probability distribution. Hence, each DM should rank the currently observed offers among those already observed. Two kinds of ranks follow: relative and absolute ranks.
At each stage of the dynamic process, an offer can be accepted or discarded. Each discarded offer cannot be re-examined in later stages. We assume that each DM has his individual utility and ranking for the selected offer. Since the rankings of the DMs are different, a conflict can arise when an offer is accepted by either DM and refused by his opponent. In this case, a stopping rule should be defined in order to avoid such situations.
Example Game Rules
Numbers are generated by sequences of random produced by independent draws from a given range (between 1 and 6 in this example). The law of drawing different numbers or expressions may be time-invariant (stationary) or else depend on time. For a fixed n (in this case n=12 available events) and a given pattern (here we are looking for appearance of number 6) our goal is to maximize the probability of stopping on the k(th) last appearance of number 6 (if any) in such events of total n, given that we must not return on a previous appearance of 6.
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event($good);
list($accept, $w) = $x->doYouAccept();
if($accept == true && !$select){
$select = true;
$chance = round($w*100, 0);
echo "
- Accept in turn k=$i where chance to be the last appearance of number 6 is %$chance "; }else{ if($good && !$select) echo "
- Number 6 has been appeared at turn k=$i, but we may get better!! "; if($good && $select) echo "
- Number 6 has been appeared again at turn k=$i ... we miss it :( "; } } if(!$select) echo "I am sorry, we loss all our chances!!
"; ?>