Altruistic and Aggressive Types of Behavior in a Non-Antagonistic Positional Differential Two-Person Game

Abstract

A non-antagonistic positional differential two-person game is considered in which each of the two players, in addition to the usual normal (nor) type of behavior oriented toward maximizing own functional, can use other types of behavior. In particular, it is altruistic (alt), aggressive (agg) and paradoxical (par) types. It is assumed that in the course of the game players can switch their behavior from one type to another. In this game, each player along with the choice of positional strategy also chooses the indicator function defined over the whole time interval of the game and taking values in the set {nor, alt, agg, par}. Player's indicator function shows the dynamics for changing the type of behavior that this player adheres to. The concept of BT-solution for such game is introduced. Using players types of behavior other than normal, can lead to outcomes more preferable to them than in a game with only a normal type of behavior. An example of a game with the dynamics of simple motion in the plane and phase constraints illustrates the procedure for constructing BT-solutions. © 2018