Notion Of Common Knowledge Research Articles

ARROW UPDATE LOGIC

We presentArrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

Endogenizing institutions and institutional changes

Abstract:This paper proposes an analytical-cum-conceptual framework for understanding the nature of institutions as well as their changes. First, it proposes a new definition of institution based on the notion of common knowledge regarding self-sustaining features of social interactions with a hope to integrate various disciplinary approaches to institutions and their changes. Second, it specifies some generic mechanisms of institutional coherence and change – overlapping social embeddedness, Schumpeterian innovation in bundling games, and dynamic institutional complementarities – useful for understanding the dynamic interactions of economic, political, social, organizational, and cognitive factors.

Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted. We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the philosophy of language.

Common Knowledge and Games with Perfect Information

It is by now rather well understood that the notion of common knowledge (first introduced by Lewis (1969) and later formalized by Aumann (1976)) plays a central role in the theory of games. (An event E is common knowledge between two individuals, if each knows E, each knows the other knows E, etc…). Indeed, most justifications of Nash's (1951) equilibrium concept usually include (perhaps only implicitly) the assumption that it is common knowledge among the players that both the Nash equilibrium in question will be played by all and that all players are expected utility maximizers. (We shall henceforth call expected utility maximizers, “rational”.) We hope to illustrate in an informal manner that there is in fact a large class of extensive form games, in which each of which it is not possible for rationality to be common knowledge throughout the game.

Equilibrium Contracts for Syndicates with Differential Information

This paper proposes a concept of the core for games with differential information, using Aumann’s notion of common knowledge. The concept is applied to solve the syndicate problem, for cases in which members have different private information on the uncertain prospects of each syndicate action and the contract (the risk sharing rule and the decision rule) is to be determined before they exchange their information.