Definition and properties to assess multi-agent environments as social intelligence tests

Abstract: Social intelligence in natural and artificial systems is usually measured by the evaluation of associated traits or tasks that are deemed to represent some facets of social behaviour. The amalgamation of these traits is then used to configure the intuitive notion of social intelligence. Instead, in this paper we start from a parametrised definition of social intelligence as the expected performance in a set of environments with several agents, and we assess and derive tests from it. This definition makes several dependencies explicit: (1) the definition depends on the choice (and weight) of environments and agents, (2) the definition may include both competitive and cooperative behaviours depending on how agents and rewards are arranged into teams, (3) the definition mostly depends on the abilities of other agents, and (4) the actual difference between social intelligence and general intelligence (or other abilities) depends on these choices. As a result, we address the problem of converting this definition into a more precise one where some fundamental properties ensuring social behaviour (such as action and reward dependency and anticipation on competitive/cooperative behaviours) are met as well as some other more instrumental properties (such as secernment, boundedness, symmetry, validity, reliability, efficiency), which are convenient to convert the definition into a practical test. From the definition and the formalised properties, we take a look at several representative multi-agent environments, tests and games to see whether they meet these properties.