As a selling mechanism, auctions have acquired a central position in the free market economy all over the globe. This development has deepened, broadened, and expanded the theory of auctions in new directions. This chapter is intended as a selective update of some of the developments and...

The purpose of this work is to offer for any zero-sum game with a unique strictly mixed Nash equilibrium, a measure for the risk when deviating from the Nash equilibrium. We present two approaches regarding the nature of deviations; strategic and erroneous. Accordingly, we define two models. In...

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizen are private information. We investigate whether there exist decision schemes (i. e., functions that map profiles of...

Game theory is usually applied to biology through evolutionary games. However, many competitive processes in biology may be better understood by analyzing them on a shorter time-scale than the time-course considered in evolutionary dynamics. Instead of the change in the "fitness" of a player,...

An encyclopedia article on games with incomplete information. Table of contents: 1. Definition of the subject and its importance. 2. Introduction: Modeling incomplete information. 3. Harsanyi’s model: The notion of type. 4. Aumann’s model. 5. Harsanyi’s model and the hierarchies of...

In this note we propose to use the mathematical formalism of Quantum Mechanics to capture the idea that agents’ preferences, in addition to being typically uncertain, can also be indeterminate. They are determined (realized, and not merely revealed) only when the action takes place. An agent...

We address the issue of the representation as well as the evolution of (possibly) mistaken beliefs. We develop a formal setup (a mutual belief space) in which agents might have a mistaken view of what the model is. We then model a communication process, by which agents communicate their beliefs...

Consider a parliamentary committee with an equal number of coalition and opposition members. The opposition needs a strict majority to pass a motion, whereas for the coalition a tie is sufficient to block the motion and maintain the status quo. Passing or blocking the motion is a public good...