Weakly acyclic games form a natural generalization of the class of games that have the finite improvement property (FIP). In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler...

A common objective in mechanism design is to choose the outcome (for example, allocation of resources) that maximizes the sum of the agents’ valuations, without introducing incentives for agents to misreport their preferences. The class of Groves mechanisms achieves this; however, these...

We compare here the relative strength of four widely used procedures on finite strategic games: iterated elimination of weakly/strictly dominated strategies by a pure/mixed strategy. A complication is that none of these procedures is based on a monotonic operator. To deal with this problem we...

The rationalizability concept was introduced in Bernheim [Ber84] and Pearce [Pea84] to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number of ways that differ in seemingly unimportant minor...

We provide elementary and uniform proofs of order independence for various strategy elimination procedures for finite strategic games, both for dominance by pure and by mixed strategies. The proofs follow the same pattern and focus on the structural properties of the dominance relations. They...

We propose an abstract approach to coalition formation that focuses on simple merge and split rules transforming partitions of a group of players. We identify conditions under which every iteration of these rules yields a unique partition. The main conceptual tool is a specific notion of a...