Two observers, who share a pair of particles in an entangled mixed state, can use it to perform s... more Two observers, who share a pair of particles in an entangled mixed state, can use it to perform some non-bilocal measurement over another bipartite system. In particular, one can construct a specific game played by the observers against a coordinator, in which they can score better than a pair of observers who only share a classical communication channel.
Stochastic Processes and Their Applications, Jan 1, 2004
We show how a stochastic variation of a Ramsey's theorem can be used to prove the existence of th... more We show how a stochastic variation of a Ramsey's theorem can be used to prove the existence of the value, and to construct ε-optimal strategies, in two-player zero-sum dynamic games that have certain properties.
An infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions ar... more An infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, admits a value. The proof relies on a representation of the game as a stochastic game with perfect information, in which Nature operates as a delegate for the players and performs the randomizations for them.
We study the behavioral definition of complementary goods: if the price of one good increases, de... more We study the behavioral definition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. The class of preferences that generate demand complements has Leontief and Cobb–Douglas as its as extreme members.
Two players are engaged in a zero-sum game with lack of information on one side, in which player ... more Two players are engaged in a zero-sum game with lack of information on one side, in which player 1 (the informed player) receives some stochastic signal about the state of nature. I consider the value of the game as a function of player 1’s information structure, and study the properties of this function. It turns out that these properties reflect the fact that in zero sum situation the value of information for each player is positive.
Players who have a common interest are engaged in a game with incomplete information. Before play... more Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a means of correlation.Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.
We prove that every two player non zero-sum stopping game in discrete time admits an -equilibrium... more We prove that every two player non zero-sum stopping game in discrete time admits an -equilibrium in randomized strategies, for every > 0.
A self-proclaimed expert uses past observations of a stochastic process to make probabilistic pre... more A self-proclaimed expert uses past observations of a stochastic process to make probabilistic predictions about the process. An inspector applies a test function to the infinite sequence of predictions provided by the expert and the observed realization of the process in order to check the expert's reliability. If the test function is Borel and the inspection is such that a true expert always passes it, then it is also manipulable by an ignorant expert. The proof uses Martin's theorem about the determinacy of Blackwell games. Under the axiom of choice, there exist non-Borel test functions that are not manipulable.
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is ... more A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure.
Two observers, who share a pair of particles in an entangled mixed state, can use it to perform s... more Two observers, who share a pair of particles in an entangled mixed state, can use it to perform some non-bilocal measurement over another bipartite system. In particular, one can construct a specific game played by the observers against a coordinator, in which they can score better than a pair of observers who only share a classical communication channel.
Stochastic Processes and Their Applications, Jan 1, 2004
We show how a stochastic variation of a Ramsey's theorem can be used to prove the existence of th... more We show how a stochastic variation of a Ramsey's theorem can be used to prove the existence of the value, and to construct ε-optimal strategies, in two-player zero-sum dynamic games that have certain properties.
An infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions ar... more An infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, admits a value. The proof relies on a representation of the game as a stochastic game with perfect information, in which Nature operates as a delegate for the players and performs the randomizations for them.
We study the behavioral definition of complementary goods: if the price of one good increases, de... more We study the behavioral definition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. The class of preferences that generate demand complements has Leontief and Cobb–Douglas as its as extreme members.
Two players are engaged in a zero-sum game with lack of information on one side, in which player ... more Two players are engaged in a zero-sum game with lack of information on one side, in which player 1 (the informed player) receives some stochastic signal about the state of nature. I consider the value of the game as a function of player 1’s information structure, and study the properties of this function. It turns out that these properties reflect the fact that in zero sum situation the value of information for each player is positive.
Players who have a common interest are engaged in a game with incomplete information. Before play... more Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a means of correlation.Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.
We prove that every two player non zero-sum stopping game in discrete time admits an -equilibrium... more We prove that every two player non zero-sum stopping game in discrete time admits an -equilibrium in randomized strategies, for every > 0.
A self-proclaimed expert uses past observations of a stochastic process to make probabilistic pre... more A self-proclaimed expert uses past observations of a stochastic process to make probabilistic predictions about the process. An inspector applies a test function to the infinite sequence of predictions provided by the expert and the observed realization of the process in order to check the expert's reliability. If the test function is Borel and the inspection is such that a true expert always passes it, then it is also manipulable by an ignorant expert. The proof uses Martin's theorem about the determinacy of Blackwell games. Under the axiom of choice, there exist non-Borel test functions that are not manipulable.
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is ... more A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure.
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Papers by Eran Shmaya