Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game

Defining the dilemma game by the proposition, A game cannot sustain an increase of cooperation strategy in its strategy distribution, we deduced that the substance of a dilemma can be expressed by a productive summation of the static factor and the dynamic factor independently. A static factor is an element of the gameʹs structure that influences a possible dilemma, which relates to a gameʹs structural deviation from a situation where the cooperation strategy can be weakly dominant over other strategies. In contrast, a dynamic factor refers to a strategy distributionʹs influence on the dilemma by affecting the game dynamics. In a 2 × 2 game, the existence of a dilemma can be determined only by a static factor. That is, whether or not a dilemma occurs is related only to the structural effect of the game. On the other hand, in a more-than-two-strategies game, both static and dynamic factors determine the occurrence of a dilemma, and the static factor cannot solely explain the occurrence of a dilemma.