Narrow Results

The Mr. Sum and Mr. Product puzzle has been frequently used as an example in the analysis of the Logic of Knowledge and Public Communications. In this paper we solve a related number theoretic problem and give an interpretation of our result in terms of common knowledge shared by the players.

This paper explores an efficient technique for the extraction of common subtrees in decision trees. The method is based on a Suffix Tree string matching process and the algorithm is applied to the problem of finding common decision rules in path planning.

In the realm of multi-agent systems, establishing social self-awareness in agents stands as a critical challenge within the broader scope of artificial general intelligence research. Addressing this challenge, in this paper, we draw upon Tomasello’s social self-awareness theory as a foundational framework, and employ Non-Axiomatic Reasoning System (NARS), an artificial general intelligence model, to simulate analogical and recursive reasoning methods used by socially embodied agents. In this paper, we assume that an agent can possess sensorimotor capabilities and physical common sense, it explores the process of constructing a “core self” through embodied reasoning. On this basis, we explore deeper into the construction process of social self-awareness. As a result, we clarify how agents generate common knowledge about themselves through recursive reasoning regarding the mental states of others and communication dynamics. Following this initial step, metaphors are generated utilizing analogical reasoning, intertwining public knowledge with these metaphors to facilitate mutual comprehension between humans and machines. This paper delves into the simulation of perspective representation and recursive reasoning within social embodied agents, employing NARS — an overarching artificial intelligence platform. The experimental results substantiate the viability of constructing a social self-agent within a machine framework grounded in embodied reasoning.

This study examines how previous information literacy training before and during law school, law student gender, law student age, where one attends law school, year in law school, and previously obtained education affects law students’ selection of information sources, their understanding of common knowledge, and their decision of whether or not to give attribution to these sources. The problem addressed in this study is that plagiarism is frequently discovered in student’s writings. This study seeks to discover why. Is it due to source selection, lack of knowledge of citation and common knowledge, or something else? The data collected from these research endeavors suggests the outcomes of this study are that law students do exhibit some differences in understanding of citation and citation behavior based on age and their year in law school. They also exhibit some differences regarding their understanding of common knowledge based on their year in law school, where they received their information literacy training, and where they attend law school. Yet, the outcomes suggest no statistically significant differences are discovered regarding where one attends law school and law student citation and source selection.

The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying mechanism design on richer type spaces.

We ask when ex post implementation is equivalent to interim (or Bayesian) implementation for all possible type spaces. The equivalence holds in the case of separable environments; examples of separable environments arise (1) when the planner is implementing a social choice function (not correspondence) and (2) in a quasilinear environment with no restrictions on transfers. The equivalence fails in general, including in some quasilinear environments with budget balance.

In private value environments, ex post implementation is equivalent to dominant strategies implementation. The private value versions of our results offer new insights into the relationship between dominant strategy implementation and Bayesian implementation.

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice for all beliefs at every type profile. In an interdependent value environment with single crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones.

The contraction property requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having an eigenvalue less than one.

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.

Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.

Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe — about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the part of other players, as to what a player will do. Common knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures implies that the conjectures form a Nash equilibrium. When n ≥ 3 and there is a common prior, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures, imply that the conjectures form a Nash equilibrium. Examples show the results to be tight.