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Evolutionary prisoner's dilemma game on a square lattice
A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $(C)$ or to defect $(D)$ unconditionally. The
Phase transitions and volunteering in spatial public goods games.
TLDR
A simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games that leads to "rock-scissors-paper"-type cyclic dominance of the three strategies, cooperate, defect, and loner.
Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions
TLDR
The findings suggest that the consideration of punishment strategies allows one to understand the establishment and spreading of “moral behavior” by means of game-theoretical concepts, demonstrating that quantitative biological modeling approaches are powerful even in domains that have been addressed with non-mathematical concepts so far.
Game theory and physics
TLDR
The prisoner’s dilemma is employed to discuss new insights gained in behavioral ecology using methods from physics to reveal critical phase transitions that fall into the universality class of directed percolation on square lattices and mean-field-type transitions on regular small world networks and random regular graphs.
Sesquilinear-orthogonally quadratic mappings
SummaryThe conditional Jordan-von Neumann functional equation for a mappingG: (X, +, ⊥) → (Y, +), that is,G(x + y) + G(x−y) = 2G(x) + 2G(y) for allx, y ∈ X withx ⊥ y, was first studied by Vajzović in
On orthogonally additive mappings, IV
SummaryThe conditional Cauchy functional equationF: (X, +, ⊥) → (Y, +), F(x + y) = F(x) + F(y) x, y ∈ X, x ⊥ y, has first been studied under regularity (mainly continuity and boundedness) conditions
Phase Diagrams for the Spatial Public Goods Game with Pool-Punishment
The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool
Evolutionary prisoner's dilemma games with voluntary participation.
  • G. Szabó, C. Hauert
  • Economics
    Physical review. E, Statistical, nonlinear, and…
  • 26 August 2002
TLDR
It is demonstrated that cyclic dominance produces self-organizing patterns on square lattices but leads to different types of oscillatory behavior on random regular graphs: the temptation to defect determines whether damped, periodic, or increasing oscillations occur.
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