Strategic Reasoning in Interdependence: Logical and Game-Theoretical Investigations

Abstract

Game theory is the branch of economics that studies interactive decision making, i.e. how entities that can reasonably be described as players of a game should behave, given their preferences and their information. Game theory is usually divided into two main branches: non-cooperative game theory, that studies the strategies that individuals should employ to reach their own goals, and cooperative game theory, that studies instead the effects of individuals joining their forces and getting the most out of their collective strategies. The present work lies somewhat in between the two sides of game theory and studies the relation between the behaviour of individuals and the behaviour of coalitions to which they belong. The first part of the thesis, called "Strategic Reasoning and Coalitional Games", studies what it means for a coalition of players to choose the best among the available alternatives, in particular what it means for a coalition to prefer a strategy above another and in what circumstances are those strategies at a coalition's disposal. Think for instance of a chess player who is setting up an attack against the opposite king. He knows that each of its pieces has invidual strengths (e.g., the knight can go to a central square, the bishop can control an important diagonal), but he is also aware that their real power lies in their combined forces (e.g., the knight and the bishop can together control a central square on an important diagonal). His reasoning starts from an individual perspective but it suddenly shifts to a coalitional one, where notions such as preferences and strategies acquire a more elaborated meaning and display specific formal properties. The thesis investigates them adopting the standard tools of logic and game-theory. The second part of the thesis, called "Strategic Reasoning and Dependence Games", elaborates further upon the study of coalitional reasoning, focusing on the network of interdependence underlying each collective decision. Consider once again the chess player who is deciding what to move. He is perfectly aware that pieces do not always perfectly and harmoniously coordinate. At times they actually obstruct each other while at other times they may even need to sacrifice themselves for their king to survive a mating attack. Their interaction displays a thick network of dependence relations (i.e. what each piece can do for the others) which strongly influences the strategies that can be played. In the classical account of cooperative game theory however this important condition is simply not taken into account. The present work bridges this gap, constructing a theory of coalitional rationality based on the resolution of its underlying dependence relations. Concretely it studies the mathematical properties characterizing those coalitions that arise from their members taking mutual advantage of each other. Finally, it relates those properties to the classical study of collective decision making