# The Impact of Tribalism on Social Welfare

## TL;DR

This paper investigates how tribalism, modeled as mutual altruism within groups, affects the efficiency of equilibria in strategic games, revealing that tribalism can worsen social welfare compared to purely selfish or altruistic behaviors.

## Contribution

It introduces the concept of a { au}-tribal extension and the Price of Tribalism, analyzing its impact across various game types and equilibrium concepts.

## Key findings

- Price of Tribalism exceeds Price of Anarchy in studied games.
- Upper bounds on Price of Tribalism match lower bounds from examples.
- Tribalism can negatively influence social welfare in strategic settings.

## Abstract

We explore the impact of mutual altruism among the players belonging to the same set -- their tribe -- in a partition of all players in arbitrary strategic games upon the quality of equilibria attained. To this end, we introduce the notion of a {\tau}-tribal extension of an arbitrary strategic game, in which players' subjective cost functions are updated to reflect this, and the associated Price of Tribalism, which is the ratio of the social welfare of the worst Nash equilibrium of the tribal extension to that of the optimum of social welfare. We show that in a well-known game of friendship cliques, network contribution games as well as atomic linear congestion games, the Price of Tribalism is higher than the Price of Anarchy of either the purely selfish players or fully altruistic players (i.e. ones who seek to maximise the social welfare). This phenomenon is observed under a variety of equilibrium concepts. In each instance, we present upper bounds on the Price of Tribalism that match the lower bounds established by our example.