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

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

“…Tanimoto geometry (Tanimoto 2007a,b;Tanimoto and Sagara 2007) is used to describe the characteristics of games.…”

Spatial reciprocity for discrete, continuous and mixed strategy setups

“…If both cooperate (defect) they receive the reward R (the punishment P). If, however, one chooses cooperation while the other defects, the later gets the temptation T and the cooperator is left the sucker's payoff S. For simplicity, yet without loss of generality, the payoffs can be rescaled as R = 1, D r = P À S, D g = T À R and P = 0, and then payoff matrix becomes the following expression [66],…”

The impact of initial cooperation fraction on the evolutionary fate in a spatial prisoner's dilemma game

“…where D g = T − R and D r = P − S imply a chicken-type dilemma and a stag-hunt-type dilemma, respectively [2]. We limit the PD game class by assuming 0 ≤ D g ≤ 1 and 0 ≤ D r ≤ 1.…”

“…Assuming an infinite and well-mixed population and relying on so-called replicator dynamics, we know that the equilibrium of a game's dynamics can be classified into four classes: PD, chicken, stag hunt (SH) and trivial depending on its payoff matrix: R S T P . Only an SH game (with features D g ≡ T − R < 0 and D r ≡ P − S > 0 [2]) has a bi-stable equilibrium state, implying that the dynamics bifurcate into either an all-cooperators state or all-defectors state depending on the initial cooperation fraction. In a nutshell, none of the dynamics belonging to the other three classes: PD, chicken and trivial, show dependence on the initial strategy distribution (say the initial cooperation fraction).…”