## Abstract

This paper describes a line of research on learning by experience in repeated games and dynamic decision situations. The behavior is modelled as an unconsciously performed decision algorithm involving very little conscious deliberation. We consider three types of theoretical concepts

1) Learning Direction Theory

2) Impulse Equilibrium

3) Generalized Impulse Balance

A player i’s period payoff depends only on the period strategies π0 of a random player and the strategies π_{1},…,π_{n} of n personal players, but not on t. At the beginning of each period t, a personal player i compares his payoff to the obtained one in period t-1 with the payoff y_{i} he could have maximally obtained in t-1 by other strategies ρ_{i} given the strategies actually used by the other players. A positive difference z_{i}=y_{i}-x_{i} indicates an impulse from π_{i} to ρ_{i}

Let h_{i} (π_{i},π_{-i}) be player i’s period payoff if he plays π_{i} and where π_{-i} stands for the combination of the period strategies of all other players. Then

(1) s_{i}=max(_{πi∈Πi}) min(_{π-i∈Π-i}) h_{i} (π_{i},π_{-i} )

is player i’s pure strategy maximum, also referred to as player i’s security level s_{i}

Π_{i} is the set of all possible π_{i} and Π_{-i} is the setoff all possible π_{-i}. Player i’s payoff cannot be reduced to a level below s_{i} by the behavior of the other player j even if they know which strategy π_{i} player i is going to play. Therefore s_{i} is a natural benchmark for the distinction between losses and gains. Any payoff x_{i} with x_{i} < s_{i} involves a loss l_{i} = s_{i} - x_{i} and x_{i} > s_{i} is connected to a given g_{i} = x_{i} – s_{i}. Define:

|μ-η|_{+}=max[μ-η,0]

|μ-η|_{-}=min[μ-η,0]

The success measure connected to the theories covered by the paper is the transformed payoff:

The strength of an impulse from π_{n} to ρ_{i} is measured by the difference of the transformed payoffs from π_{i} to ρ_{i}. In the context of the paper by Chmura and myself (2008) the concept of impulse balance was defined for 2x2 game only. In this case the difference z_{i} = y_{i} - x_{i} in terms of the untransformed payoff is always positive. However in the area of 3 players we cannot avoid a definition based on the transformed payoff.