(E.) Fantham and (M.) Gagarin <i>Eds</i>. The Oxford Encyclopedia of Ancient Greece and Rome. Oxford: Oxford University Press, 2010. 7 vols, illus. £625. 9780195170726.

Osborne, Robin

doi:10.1017/s0075426911000115

Cited by 22 publications

(40 citation statements)

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“…The set of possible types for each player is thus also part of the definition of a Bayesian game. More formally, the normal form representation of a Bayesian game is given by the following ingredients 23 : (i) the number of players N, (ii) a set of states of nature O, with a prior m(O), (iii) for each player i, a set of actions A i , (iv) for each player i, a set of types w i , (v) for each player i, a mapping t i :O-w i and (vi) for each player i, a payoff function f i :O Â A 1 Â y Â A N -R, determining the score of the player for any possible combination of types and actions.…”

Section: Resultsmentioning

confidence: 99%

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Connection between Bell nonlocality and Bayesian game theory

2013

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In 1964, Bell discovered that quantum mechanics is a nonlocal theory. Three years later, in a seemingly unconnected development, Harsanyi introduced the concept of Bayesian games. Here we show that, in fact, there is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields. This link offers interesting possibilities for Bayesian games, namely of allowing the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general nosignalling boxes. This will lead to novel joint strategies, impossible to achieve classically. We characterize games for which nonlocal resources offer a genuine advantage over classical ones. Moreover, some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium. Finally, we describe new types of question in the study of nonlocality, namely the consideration of nonlocal advantage given a set of Bell expressions.

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Section: Resultsmentioning

confidence: 99%

“…It is convenient to represent geometrically the space of possible payoff functions 23 , i.e., here the set of points in R 2 with coordinates (F 1 ,F 2 ). In case the players share classical advice (and the number of possible strategies is finite), this space is a convex polytope.…”

Section: Resultsmentioning

confidence: 99%

Connection between Bell nonlocality and Bayesian game theory

2013

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“…In a repeated game, the action of a player at a stage game depends not only on the current rewards but also in the sequence of previous rewards see, e.g., [16]. Repeated games, such as prisoner's dilemma have been well-studied and admit a rich set of equilibrium profiles [16] including various punishment strategies.…”

Section: B Repeated Gamementioning

confidence: 99%

Co-primary inter-operator spectrum sharing over a limited spectrum pool using repeated games

Singh¹,

Koufos²,

Tirkkonen³

et al. 2015

2015 IEEE International Conference on Communications (ICC)

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Abstract-We consider two small cell operators deployed in the same geographical area, sharing spectrum resources from a common pool. A method is investigated to coordinate the utilization of the spectrum pool without monetary transactions and without revealing operator-specific information to other parties. For this, we construct a protocol based on asking and receiving spectrum usage favors by the operators, and keeping a book of the favors. A spectrum usage favor is exchanged between the operators if one is asking for a permission to use some of the resources from the pool on an exclusive basis, and the other is willing to accept that. As a result, the proposed method does not force an operator to take action. An operator with a high load may take spectrum usage favors from an operator that has few users to serve, and it is likely to return these favors in the future to show a cooperative spirit and maintain reciprocity. We formulate the interactions between the operators as a repeated game and determine rules to decide whether to ask or grant a favor at each stage game. We illustrate that under frequent network load variations, which are expected to be prominent in small cell deployments, both operators can attain higher user rates as compared to the case of no coordination of the resource utilization.Keywords-Co-primary spectrum sharing, repeated games, spectrum pooling. I. INTRODUCTIONIn the state-of-art mobile communication systems, a network operator possesses a spectrum license that provides exclusive transmission rights for a particular range of radio frequencies. Spectrum assignment based on dedicated licenses resolves the issues related to inter-operator interference but it also results in low spectrum utilization efficiency. Inter-operator spectrum sharing is envisioned as one of the viable approaches to achieve higher operational bandwidth efficiency and meet the increasing mobile data traffic demand in a timely manner [1].In the limited spectrum pool (LSP) scenario, a limited number of operators share a common resource pool by relying on more flexible and adaptive prioritization policies than is currently possible with dedicated licenses [2]. Cognitive radio technologies are effective measures to resolve the sharing conflicts over the LSP under vertical spectrum sharing [3], where the lessor (owner) operator has higher legacy rights over the spectrum than the lessee operator. On the other hand, the co-primary or horizontal spectrum sharing scheme conceptualizes the case where authorized operators possess equal ownership on the spectrum being adopted [4]. However, a priori agreements should be made on the spectrum usage with regard to the long term share of an individual operator.The multilateral use of shared resources in the LSP can, for instance, be achieved with channel allocation schemes originally developed for single-operator systems. These schemes

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“…Games usually model the situation of some conflict between a given number of parties [12]. An interesting connection between Bell nonlocality [5] (which can be realized in quantum mechanics through entangled states) and Bayesian games introduced by Harsanyi [14] was established in [13].…”

Section: Introductionmentioning

confidence: 99%

Strong quantum solutions in conflicting-interest Bayesian games

Rai

Paul

2017

Phys. Rev. A

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Quantum entanglement has been recently demonstrated as a useful resource in conflicting interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. General setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically-correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where average payoff of both the players exceed respective individual maximum for each player over all classically-correlated equilibriums.

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(E.) Fantham and (M.) Gagarin Eds. The Oxford Encyclopedia of Ancient Greece and Rome. Oxford: Oxford University Press, 2010. 7 vols, illus. £625. 9780195170726.

Cited by 22 publications

References 0 publications

Connection between Bell nonlocality and Bayesian game theory

Connection between Bell nonlocality and Bayesian game theory

Co-primary inter-operator spectrum sharing over a limited spectrum pool using repeated games

Strong quantum solutions in conflicting-interest Bayesian games

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