Negative Moments of Positive Random Variables

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the Prisoner's Dilemma. Specif cally, for a group of players that collect payoffs by playing a pairwise Prisoner's Dilemma game with their partners, we consider an external entity that distributes a f xed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classif cation of the equilibria of the n-player game as well as of its evolutionary dynamics.

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“…Bernoulli's random variables with mean q. As has been observed by Chao and Strawderman (1972), µ m (q) has the expression…”

Section: The Shared Reward Dilemmamentioning

confidence: 81%

The shared reward dilemma

Cuesta

Jiménez

Lugo

et al. 2008

Journal of Theoretical Biology

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“…where j is binomially distributed with probability p and trials k − 1 (Chao and Strawderman 1972), we have…”

Section: Appendix a Normal-normal Information Structurementioning

confidence: 99%

The Wisdom of Competitive Crowds

Lichtendahl

Grushka‐Cockayne

Pfeifer

2013

Operations Research

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When several individuals are asked to forecast an uncertain quantity, they often face implicit or explicit incentives to be the most accurate. Despite the desire to elicit honest forecasts, such competition induces forecasters to report strategically and nontruthfully. The question we address is whether the competitive crowd's forecast (the average of strategic forecasts) is more accurate than the truthful crowd's forecast (the average of truthful forecasts from the same forecasters). We analyze a forecasting competition in which a prize is awarded to the forecaster whose point forecast is closest to the actual outcome. Before reporting a forecast, we assume each forecaster receives two signals: one common and one private. These signals represent the forecasters' past shared and personal experiences relevant for forecasting the uncertain quantity of interest. In a set of equilibrium results, we characterize the nature of the strategic forecasts in this game. As the correlation among the forecasters' private signals increases, the forecasters switch from using a pure to a mixed strategy. In both cases, forecasters exaggerate their private information and thereby make the competitive crowd's forecast more accurate than the truthful crowd's forecast.

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“…This implies that the problem of computing the mean throughput for our scheme is equivalent to that of computing negative moments of the completion time. The problem of computing negative integer moments has been studied previously in [9] and [10]. In particular, we focus in the result of [10] which states that…”

Section: Throughputmentioning

confidence: 99%

On coding for delay - New approaches based on network coding in networks with large latency

Lucani

Médard

Stojanovic

2009

2009 Information Theory and Applications Workshop

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Abstract-In networks with large latency, feedback about received packets may lag considerably the transmission of the original packets, limiting the feedback's usefulness. Moreover, time duplex constraints may entail that receiving feedback may be costly. In this work, we consider tailoring feedback and coding jointly in such settings to reduce the expected delay for successful in order reception of packets. We find that, in certain applications, judicious choices provide results that are close to those that would be obtained with a full-duplex system.

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Negative Moments of Positive Random Variables

Cited by 96 publications

References 8 publications

The shared reward dilemma

The shared reward dilemma

The Wisdom of Competitive Crowds

On coding for delay - New approaches based on network coding in networks with large latency

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