Paul Krasucki - Academia.edu (original) (raw)
Papers by Paul Krasucki
C2-We continue the work of Aumann [1], Geanakoplos and Polemarchakis [4], Cave [3] and Bacharach ... more C2-We continue the work of Aumann [1], Geanakoplos and Polemarchakis [4], Cave [3] and Bacharach [2] on common knowledge and consensus, extending the results of [4], [3] and [2] to the case where the number n of communicants is greater than two, but communication is in pairs. When n> 2, then communication in pairs does not lead to common knowledge for the group. We show that, nevertheless, conditional probabilities will converge in any fair protocol for communication, i.e., when none of the participants is blocked from communication. We show that the Cave-Bacharach generalisation of the results of [4] and [1] does not hold for pairwise communication when n> 2, and hence any proof for this case must use methods different from those of [1] and [4]. In particular, our proof uses a convexity condition that is obeyed by conditional probabilities, but is not implied by Cave’s union consistency principle.
"A dissertation submitted to the Graduate Faculty in Computer Science ... " Thesis (Ph.... more "A dissertation submitted to the Graduate Faculty in Computer Science ... " Thesis (Ph. D.) -- City University of New York, 1988. Includes bibliographical references (leaves 115-119).
We will show how reaching consensus among n individuals communicating in pairs depends on the top... more We will show how reaching consensus among n individuals communicating in pairs depends on the topology of the communications graph. In particular we show that the consensus on the value of union consistent function is guaranteed in any non-cyclic fair protocol. We also anylyze protocols where individuals exchange (simultaneously) information in pairs. Finally we prove a surprising result that a certain non-trivial level of common knowledge of some formula which was not initially common knowledge is a necessary condition for a disagreement.
We investigate how like-minded agents can reach consensus on their decisions even if they receive... more We investigate how like-minded agents can reach consensus on their decisions even if they receive different information. The model used here was introduced by Aumann, and subsequently refined by Geanakop- los and Polemarchakis, Bacharach, Cave, Parikh and Krasucki ((Aum76,GP82,Cav83,Bac85,PK)). The main result is that when any number of like-minded agents communicate according to some fair protocol whether they want to trade or not, and their decision is based solely on whether the conditional probability of some fixed event exceeds some threshold value, they must reach consensus in a finite time. We also investigate some necessary conditions which functions communicated have to satisfy in order to guarantee consensus in fair protocols.
Theoretical Aspects of Reasoning About Knowledge, 1994
In asynchronous distributed systems logical time is usually interpreted as "possible causality", ... more In asynchronous distributed systems logical time is usually interpreted as "possible causality", a partial order on event occurrences. We investigate the relationship between passage of time and changes in the knowledge of agents. We show that there is a certain duairy between knowledge transition systems (defined here to model changes in the states of knowledge of agents) and partially ordered sets of event occurrences (the model of n-Asynchronously Communicating Sequential Agents).
Journal of Economic Theory, 1990
B2-Communication, Consensus and Knowledge C2-We continue the work of Aumann [1], Geanakoplos and ... more B2-Communication, Consensus and Knowledge C2-We continue the work of Aumann [1], Geanakoplos and Polemarchakis [4], Cave [3] and Bacharach [2] on common knowledge and consensus, extending the results of [4], [3] and [2] to the case where the number n of communicants is greater than two, but communication is in pairs. When n > 2, then communication in pairs does not lead to common knowledge for the group. We show that, nevertheless, conditional probabilities will converge in any fair protocol for communication, i.e., when none of the participants is blocked from communication. We show that the Cave-Bacharach generalisation of the results of [4] and [1] does not hold for pairwise communication when n > 2, and hence any proof for this case must use methods different from those of [1] and [4]. In particular, our proof uses a convexity condition that is obeyed by conditional probabilities, but is not implied by Cave's union consistency principle. B6-J. Econ. Theory B7 B8 C4 B4-CUNY Graduate Center (Computer Science department),
Journal of Economic Theory, 1996
We analyze n agents communicating in order to reach consensus. We show how some conditions on the... more We analyze n agents communicating in order to reach consensus. We show how some conditions on the topology of the communication graph (the order in which individuals communicate) are sufficient to guarantee consensus on the value of a function satisfying the``sure-thing'' condition. Journal of Economic Literature Classification Numbers: C62, C78.
ISMIS, 1990
In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge i... more In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge in a group of individuals whose knowledge partitions are not wholly independent.
Symposium on Logic in Computer Science: …, 1986
Sadhana, 1992
We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain ... more We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain regular, downward closed, sets of strings. We show that in suitable circumstances, all such sets can occur as levels of knowledge but that the lack of synchrony, or the lack of asynchrony when there are only two processors in the group, can create more or less severe restrictions.
Sadhana, 1992
We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain ... more We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain regular, downward closed, sets of strings. We show that in suitable circumstances, all such sets can occur as levels of knowledge but that the lack of synchrony, or the lack of asynchrony when there are only two processors in the group, can create more or less severe restrictions.
ISMIS, 1990
In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge i... more In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge in a group of individuals whose knowledge partitions are not wholly independent.
Sadhana, 1992
We investigate the properties of the state of knowledge of a system of a processes taking part in... more We investigate the properties of the state of knowledge of a system of a processes taking part in a distributed computation. In particular we show a 1-1 correspondence between levels of knowledge and certain regular sets of strings on the alphabet {K 1 , ..., K n } where 1, ..., n are processes and K i stands for "i knows that" Introduction: You and I approach an intersection. You have the right of way. You should go, I should stop; that is the law and we both know it. However, that is not enough. You should know that I know. You do not want to risk your life merely to assert your right of way. Also, I should know that you know I am going to stop. If not, you will stop (even though you have the right of way) and neither of us will go; we do not want a deadlock. David Lewis in [L] and Clark and Marshall [CM2] argue that the condition of common knowledge is necessary for such coordinated actions. For another example of the relevance of common knowledge, it is proved in [HM] that clock synchronisation is impossible without common knowledge. Yet another example that we have not seen in the literature but is doubtless discussed somewhere is that mutual deterrence between the superpowers also depends on common knowledge.
C2-We continue the work of Aumann [1], Geanakoplos and Polemarchakis [4], Cave [3] and Bacharach ... more C2-We continue the work of Aumann [1], Geanakoplos and Polemarchakis [4], Cave [3] and Bacharach [2] on common knowledge and consensus, extending the results of [4], [3] and [2] to the case where the number n of communicants is greater than two, but communication is in pairs. When n> 2, then communication in pairs does not lead to common knowledge for the group. We show that, nevertheless, conditional probabilities will converge in any fair protocol for communication, i.e., when none of the participants is blocked from communication. We show that the Cave-Bacharach generalisation of the results of [4] and [1] does not hold for pairwise communication when n> 2, and hence any proof for this case must use methods different from those of [1] and [4]. In particular, our proof uses a convexity condition that is obeyed by conditional probabilities, but is not implied by Cave’s union consistency principle.
"A dissertation submitted to the Graduate Faculty in Computer Science ... " Thesis (Ph.... more "A dissertation submitted to the Graduate Faculty in Computer Science ... " Thesis (Ph. D.) -- City University of New York, 1988. Includes bibliographical references (leaves 115-119).
We will show how reaching consensus among n individuals communicating in pairs depends on the top... more We will show how reaching consensus among n individuals communicating in pairs depends on the topology of the communications graph. In particular we show that the consensus on the value of union consistent function is guaranteed in any non-cyclic fair protocol. We also anylyze protocols where individuals exchange (simultaneously) information in pairs. Finally we prove a surprising result that a certain non-trivial level of common knowledge of some formula which was not initially common knowledge is a necessary condition for a disagreement.
We investigate how like-minded agents can reach consensus on their decisions even if they receive... more We investigate how like-minded agents can reach consensus on their decisions even if they receive different information. The model used here was introduced by Aumann, and subsequently refined by Geanakop- los and Polemarchakis, Bacharach, Cave, Parikh and Krasucki ((Aum76,GP82,Cav83,Bac85,PK)). The main result is that when any number of like-minded agents communicate according to some fair protocol whether they want to trade or not, and their decision is based solely on whether the conditional probability of some fixed event exceeds some threshold value, they must reach consensus in a finite time. We also investigate some necessary conditions which functions communicated have to satisfy in order to guarantee consensus in fair protocols.
Theoretical Aspects of Reasoning About Knowledge, 1994
In asynchronous distributed systems logical time is usually interpreted as "possible causality", ... more In asynchronous distributed systems logical time is usually interpreted as "possible causality", a partial order on event occurrences. We investigate the relationship between passage of time and changes in the knowledge of agents. We show that there is a certain duairy between knowledge transition systems (defined here to model changes in the states of knowledge of agents) and partially ordered sets of event occurrences (the model of n-Asynchronously Communicating Sequential Agents).
Journal of Economic Theory, 1990
B2-Communication, Consensus and Knowledge C2-We continue the work of Aumann [1], Geanakoplos and ... more B2-Communication, Consensus and Knowledge C2-We continue the work of Aumann [1], Geanakoplos and Polemarchakis [4], Cave [3] and Bacharach [2] on common knowledge and consensus, extending the results of [4], [3] and [2] to the case where the number n of communicants is greater than two, but communication is in pairs. When n > 2, then communication in pairs does not lead to common knowledge for the group. We show that, nevertheless, conditional probabilities will converge in any fair protocol for communication, i.e., when none of the participants is blocked from communication. We show that the Cave-Bacharach generalisation of the results of [4] and [1] does not hold for pairwise communication when n > 2, and hence any proof for this case must use methods different from those of [1] and [4]. In particular, our proof uses a convexity condition that is obeyed by conditional probabilities, but is not implied by Cave's union consistency principle. B6-J. Econ. Theory B7 B8 C4 B4-CUNY Graduate Center (Computer Science department),
Journal of Economic Theory, 1996
We analyze n agents communicating in order to reach consensus. We show how some conditions on the... more We analyze n agents communicating in order to reach consensus. We show how some conditions on the topology of the communication graph (the order in which individuals communicate) are sufficient to guarantee consensus on the value of a function satisfying the``sure-thing'' condition. Journal of Economic Literature Classification Numbers: C62, C78.
ISMIS, 1990
In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge i... more In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge in a group of individuals whose knowledge partitions are not wholly independent.
Symposium on Logic in Computer Science: …, 1986
Sadhana, 1992
We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain ... more We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain regular, downward closed, sets of strings. We show that in suitable circumstances, all such sets can occur as levels of knowledge but that the lack of synchrony, or the lack of asynchrony when there are only two processors in the group, can create more or less severe restrictions.
Sadhana, 1992
We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain ... more We corrdate the level of knowledge of certain formulas in a , ffroup of individuals with certain regular, downward closed, sets of strings. We show that in suitable circumstances, all such sets can occur as levels of knowledge but that the lack of synchrony, or the lack of asynchrony when there are only two processors in the group, can create more or less severe restrictions.
ISMIS, 1990
In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge i... more In this paper we develop a theory of probabilistic common knowledge and probabilistic knowledge in a group of individuals whose knowledge partitions are not wholly independent.
Sadhana, 1992
We investigate the properties of the state of knowledge of a system of a processes taking part in... more We investigate the properties of the state of knowledge of a system of a processes taking part in a distributed computation. In particular we show a 1-1 correspondence between levels of knowledge and certain regular sets of strings on the alphabet {K 1 , ..., K n } where 1, ..., n are processes and K i stands for "i knows that" Introduction: You and I approach an intersection. You have the right of way. You should go, I should stop; that is the law and we both know it. However, that is not enough. You should know that I know. You do not want to risk your life merely to assert your right of way. Also, I should know that you know I am going to stop. If not, you will stop (even though you have the right of way) and neither of us will go; we do not want a deadlock. David Lewis in [L] and Clark and Marshall [CM2] argue that the condition of common knowledge is necessary for such coordinated actions. For another example of the relevance of common knowledge, it is proved in [HM] that clock synchronisation is impossible without common knowledge. Yet another example that we have not seen in the literature but is doubtless discussed somewhere is that mutual deterrence between the superpowers also depends on common knowledge.