Wealth and poverty, progress and regress are the type of realities usually related on moral grounds. Scientifically serious causal economic relations are not so easy to find. Moral criteria does not require scientific proof of causality. But this search for causal links is also important to reduce the impact of structural factors on human behavior. Probably most of the times in a specific social structure creation of wealth implies a reduction in poverty. It is one or the other. However, both can also be seen as independent, and should be analyzed as parts of different processes. In that sense, it would be a question of one and de other. Finally, it is also found that, under some circumstances, progress, accompanied with increasing wealth for some collectivities and individuals can be analytically related to regress, and many times increasing poverty for other groups and individuals. It is progress with regress; that is regress actively created by progress, not just by default. The models presented below add new members to the group of theories that have attempted an analysis of these twin features of the competitive process. In other words, how many are regressing and become poor because they are losers, and not because they have not played, are not or have not been in the game? All this is important to answer seriously to questions that are not being asked in spite of their obvious importance: How easy is to "make markets work for the poor"?, how convenient is to "improve markets"?, or to "extend markets"? Under what conditions it is better a market deepening? In what kinds of markets? Markets embedded in a complex set of components of the human dimension can accept a question different from: how to regulate the competition?