We consider dynamic group formation in repeated n-person prisoner’s dilemma. Agreements in coalitional bargaining are self-binding in that they are supported as subgame perfect equilibria of repeated games. Individuals are allowed to renegotiate the cooperating group agreement through a process of voluntary participation. We prove that a cooperating group forms as an absorbing state of a Markov...

The focus of this paper is the class of perfect GMV-algebras, which includes all non-commutative analogues of perfect MV-algebras. As in the commutative case, we show that each perfect GMV-algebra possesses a single negation, it is generated by its infinitesimal elements, and can be realized as an interval in a lexicographical product of the lattice-ordered group of integers and an arbitrary la...

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...

Let x = (x0, . . . , xn−1) be an n-chain, i.e., an n-tuple of non-negative integers < n. Consider the operator s : x 7→ x′ = (x0, . . . , x ′ n−1), where x ′ j represents the number of j’s appearing among the components of x. An n-chain x is said to be perfect if s(x) = x. For example, (2,1,2,0,0) is a perfect 5-chain. Analogously to the theory of perfect, amicable, and sociable numbers, one ca...

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...