The context of social dilemma is of great interest in evolutionary game theory because of its importance in explaining the evolution of cooperation in biological systems. The dilemma strength parameters have been used to numerically characterize the social dilemma to understand how much dilemma existing in a game. However, these parameters cannot be explicitly determined in general. To understand the presence of social dilemma associated with more general game systems, in this chapter, we introduce a new index, “social efficiency deficit” quantifying the payoff difference between social optimum and Nash equilibrium. Whereas the dilemma strength provides a numerical measure of how much dilemma prevailing in a game, the social efficiency deficit depicts the payoff shortfall at Nash equilibrium compared with social optimum. We deliberately delineate the relationship between these two parameters for several game classes such as pairwise Prisoner’s dilemma, Chicken game, etc. Notably, Prisoner’s dilemma possesses an inverse relationship between them. Nevertheless, we also explore the consistency of the new parameter presuming the situation if a certain social viscosity (e.g., network reciprocity) is included into a dilemma game. Additionally, the pertinence of social efficiency deficit for revealing the presence of social dilemma in vaccination game and traffic flow analysis is illustrated at the end.
- Evolutionary game
- Symmetric two-player & two-strategy game
- Social dilemma
- Dilemma strength
- Social efficiency deficit