This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustr...

This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive player into a game (a player with a singleton set of pure strategies), whose payoff depends on the actions of the active players, and it is justified by the l...

For generations programmed mammal aging was widely thought to be theoretically impossible. However, new evolutionary mechanics concepts have led to renewed interest in programmed aging resulting in a schism between programmed and non-programmed proponents. This article argues that this lack of consensus is damaging medical research and therefore steps should be taken to pro-actively resolve the...

Algorithms for pruning game trees generally rely on a game being zero-sum, in the case of alpha-beta pruning, or constant-sum, in the case of multi-player pruning algorithms such as speculative pruning. While existing algorithms can prune non-zero-sum games, pruning is much less effective than in constant-sum games. We introduce the idea of leaf-value tables, which store an enumeration of the p...

In this lecture we will discuss 2-player zero sum games. Such games are completely competitive , where whatever one player wins, the other must lose. Examples of such games include chess, checkers, backgammon, etc. We will show that in such games: • An equilibrium always exists; • All equilibrium points yield the same payoff for all players; • The set of equilibrium points is actually the carte...