Converting game theoretical 2x2 games to their n-person counterparts

Abstract

In this thesis five archetypical 2x2 games and their linearly converted N-person variants are discussed. These games are: the Prisoner’s Dilemma; Chicken; Battle of the Sexes; Hero; and Stag hunt. First, the scenarios of these games and their variations are elaborated upon to serve as an illustration. Second, the underlying social phenomena and the strategic pressures reflecting these have been discussed for 2x2 games. It is here argued the games fall into one of three dilemmas: (1) social dilemma; (2) coordination dilemma; (3) trust dilemma. Furthermore, the choice is made to linearly convert these 2x2 games to their N-person counterparts. In doing so, functions are adapted to allow for a relatively trivial conversion from the 2x2 games to their N-person variants. As such, the strategic pressures for N-person counterparts are discussed and compared to their 2x2 variants in light of their respective underlying social phenomena. Consecutively, the essential properties of both the 2x2 games and their N-person counterparts are identified with respect to the strategic pressures they represent. In turn, this work forms an abstract framework which may serve as a foundation for an implementation within an interactive environment for educational or experimental purposes. As such, the considerations to bear in mind with regard to the games themselves, their conversion, and their properties may be used to allow for meaningful analysis in multi-agent settings.