Games and structures

Frequently applications of game theory assume, but do not show, that games are contained in social structures. The new analysis offered here uncovers games embedded in structures by attributing strategies to some positions and deriving the pay-off matrices for others. As structures vary so do the games embedded in them. All strong power structures contain prisoners' dilemma games for at least some range of pay-offs while some contain a chain of prisoners' dilemma games linked by defections. As a result, the development of interpersonal power in strong power structures is produced by free-riding of those low in power. Examples of other types of structures are given and other games are found that do not contain defection chains. Issues of dynamics including rates of change of power and coalition formation as a condition of countervailing power are addressed. New experiments offer support for central formulations.