Optimal Use of Communication Resources

Gossner, Olivier; Hernández, Penélope; Neyman, Abraham

doi:10.1111/j.1468-0262.2006.00720.x

Cited by 45 publications

(86 citation statements)

References 13 publications

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“…It can be applied to analyze the performance of coded power allocation, coded interference alignment, etc, with other information structures and by considering N ≥ 2 individual payoffs instead of a common one (e.g., in a game-theoretic setting [3]). The methodology to assess the performance of good coded policies consists in deriving the right information constraint(s) by building the proof on Shannon theory for the problem of multi-source coding with distortion over multi-user channels wide side information and then to use this constraint to find an information-constrained maximum of the payoff (common payoff case) or the set of Nash equilibrium points which are compatible with the constraint (non-cooperative game case).…”

Section: Discussionmentioning

confidence: 99%

“…Because of its importance and ability to easily illustrate the proposed approach, the problem of PC in interference networks has been selected for the application of the main and general result derived in this paper; note that the latter concerns any decision-making problem which has the same structure (see Sec. II) and generalizes [3] and [4].…”

Section: Introductionmentioning

confidence: 96%

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Coded power control: Performance analysis

Larrousse

Lasaulce

2013

2013 IEEE International Symposium on Information Theory

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Abstract-In this paper, we introduce the general concept of coded power control (CPC) in a particular setting of the interference channel. Roughly, the idea of CPC consists in embedding information (about a random state) into the transmit power levels themselves: in this new framework, provided the power levels of a given transmitter can be observed (through a noisy channels) by other transmitters, a sequence of power levels of the former can therefore be used to coordinate the latter. To assess the limiting performance of CPC (and therefore the potential performance brought by this new approach), we derive, as a first step towards many extensions of the present work, a general result which not only concerns power control (PC) but also any scenario involving two decision-makers (DMs) which communicate through their actions and have the following information and decision structures. We assume that the DMs want to maximize the average of an arbitrarily chosen instantaneous payoff function which depends on the DMs' actions and the state realization. DM 1 is assumed to know non-causally the state (e.g., the channel state) which affects the common payoff while the other, say DM 2, has only a strictly causal knowledge of it. DM 1 can only use its own actions (e.g., power levels) to inform DM 2 about its best action in terms of payoff. Importantly, DM 2 can only monitor the actions of DM 1 imperfectly and DM 1 does not observe DM 2. The latter assumption leads us to exploiting Shannon-theoretic tools in order to generalize an existing theorem which provides the information constraint under which the payoff is maximized. The derived result is then exploited to fully characterize the performance of good CPC policies for a given instance of the interference channel.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Coded power control: Performance analysis

Larrousse

Lasaulce

2013

2013 IEEE International Symposium on Information Theory

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“…Since the conditional entropy H(X|Y ) is concave in the joint distribution of (X, Y ) (see, e.g., Gossner, Hernandez, and Neyman (2004), Lemma 1), we have…”

Section: Growth Of Strategy Sets 21mentioning

confidence: 99%

Growth of strategy sets, entropy, and nonstationary bounded recall

Neyman¹,

Okada²

2009

Games and Economic Behavior

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. One way to express bounded rationality of a player in a game theoretic models is by specifying a set of feasible strategies for that player. In dynamic game models with finite automata and bounded recall strategies, for example, feasibility of strategies is determined via certain complexity measures: Terms of use: Documents inthe number of states of automata and the length of recall. Typically in these models, a fixed finite bound on the complexity is imposed resulting in finite sets of feasible strategies. As a consequence, the number of distinct feasible strategies in any subgame is finite. Also, the number of distinct strategies induced in the first T stages is bounded by a constant that is independent of T .In this paper, we initiate an investigation into a notion of feasibility that reflects varying degree of bounded rationality over time. Such concept must entail properties of a strategy, or a set of strategies, that depend on time.Specifically, we associate to each subset Ψ i of the full (theoretically possible) strategy set a function ψ i from the set of positive integers to itself. The value ψ i (t) represents the number of strategies in Ψ i that are distinguishable in the first t stages. The set Ψ i may contain infinitely many strategies, but it can differ from the fully rational case in the way ψ i grows reflecting a broad implication of bounded rationality that may be alleviated, or intensified, over time.We examine how the growth rate of ψ i affects equilibrium outcomes of repeated games. In particular, we derive an upper bound on the individually rational payoff of repeated games where player 1, with a feasible strategy set Ψ 1 , plays against a fully rational player 2. We will show that the derived bound is tight in that a specific, and simple, set Ψ 1 exists that achieves the upper bound.As a special case, we study repeated games with non-stationary bounded recall strategies where the length of recall is allowed to vary in the course of the game. We will show that a player with bounded recall can guarantee the minimax payoff of the stage game even against a player with full recall so long as he can remember, at stage t, at least K log t stages back for some constant K > 0. Thus, in order to guarantee the minimax payoff, it suffices to remember only a vanishing fraction of the past. A version of the folk theorem is provided for this class of games.(Journal of Economic Literature Classification Number: C72, C73)

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“…After these classic contributions, the concept has arisen separately in several fields of economics, and we provide only a brief partial survey here. Gossner, Hernández, and Neyman (2006) study repeated games in which one of the players, who can forecast the realization of future states of nature, can transmit information to others through his choice of actions. They provide a closed-form characterization, based on entropy, of the set of distributions which the players can achieve.…”

Section: Related Literaturementioning

confidence: 99%

Entropy and the Value of Information for Investors

2010

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Consider any investor who fears ruin when facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure α is more informative than information structure β if, whenever he is willing to buy β at some price, he is also willing to buy α at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists.

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Optimal Use of Communication Resources

Cited by 45 publications

References 13 publications

Coded power control: Performance analysis

Coded power control: Performance analysis

Growth of strategy sets, entropy, and nonstationary bounded recall

Entropy and the Value of Information for Investors

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