Power values and framing in game theory

This dissertation consists of five chapters and covers three topics, all in the broader field of game theory. There are three main chapters. In Chapter 3 the focus is on power measures, functions that assign a power to every node in any graph. The connectivity power measure is introduced and characterized on the class of graphs. The connectivity power measure assigns to every node in any graph the number of connected sets the node is a part of. Chapter 4 focuses on graph games, cooperative games with cooperation restricted by communication networks represented by graphs. The average connected contribution value and the larger family of power values are introduced and axiomatized on the class of graph games. The average connected contribution value of a player in a graph game is defined as the average of the player's marginal contributions in connected coalitions the player is a part of. In Chapter 5 a new framing of the well-studied prisoner’s dilemma game is introduced. The new framing is achieved by representing the game in an unconventional way by telling players that they are deciding what their opponents have to do. It is shown in a laboratory experiment that the framing affects the decisions of subjects.