Before going further, you'll need to understand the concept of game theory. Game theory is basically a branch of applied mathematics. In-game theories (How Game Theory Strategy Improves Decision Making), there are different available tools with the help of which different situations are analyzed. There are parties in-game theories mostly referred to as players and the decision they have taken are interdependent. This is a kind of playing chess in which the turn of one player is associated with the future strategy of the opponent player.

Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of this form. It includes as special cases axiomatic characterisations for choice functions based on (sets of) total orders, (sets of) weak orders, (sets of) coherent lower previsions and (sets of) probability measures.