Theories of decision making, social choices, behavioural economics, political game theory, coalition formation.

Coalition Formation Rules

Updated: 12 May 2011

Abstract: In this note we examine a scenario where a set of agents has to be sub-divided into coalitions. We assume that agents have preferences over coalitions that contain them. A coalition formation rule (CFR) takes a profile of such preferences and assigns agents to coalitions. We explore the properties of such rules. We find sufficient conditions for a CFR to satisfy the top-coalition property, which is a form of a unanimity condition of top preferences. We also show some impossibility results.

Constrained Choice

Updated: 28 January 2011

Abstract: In this note we consider situations where agents choose a best element from an available set. But the available set may itself depend on the choices of other agents. We call such a scenario constrained choice and design a model to explore its consequences.

Successive Choice

Updated: 25 January 2011

Abstract: In this note we explore the case where an agent encounters alternatives in the form of a list. We characterise a successive choice function over lists in the discrete case. We explore extensions of this characterisation to the probabilistic case.

Order-Dependent Choice and Non-Binary Preferences

Updated: 5 January 2011

Abstract: In this note we consider a model of successive choice based on complete and transitive preferences. When we weaken the conditions of completeness, we find that choice becomes order-dependent. We introduce a tie-breaker rule to solve the problem of incompleteness, but retain order-dependence. The combined effect of order-dependence and this tie-breaker rule will lead us to a generalisation of non-binary preferences (i.e., composite preferences over sets of more than two elements). This generalisation is probabilistic in nature, and in many cases matches common intuition.