A Detail-free Mediator and the 3 Player Case

Two players can make use of a trusted third party who mediates and partially resolves their conflict. Usually, the mediator should be aware of the situation and give suggestions to the players accordingly. However, a corrupt mediator can have a big influence on the outcome of the game. We single out a transparent mediator which can be safely applied in any two player game without loss of efficiency. That is, the mediator is independent of the game and the desired outcome. Technically, we show that any correlated equilibrium of any two player game can be obtained as Nash equilibria of the game, extended with cheap, pre-play communication, where players can communicate through the proposed mediator. The key idea is that after the mediated communication the players can have a plain conversation. In particular, the mediating communication device is transparent, controllable and is the same for all games and for all equilibrium distributions. We extend the result to three player games and show that one of the players can play the role of the mediator. We implement the set of correlated equilibrium in Nash equilibria of an extended game where the players have a plain conversation. The central assumption is that players can be invited to eavesdrop a private conversation. We extend the analysis to games with incomplete information and to the set of communication equilibria.cheap talk, communication device, correlated equilibrium, communi- cation equilibrium, detail-free mechanism, mediator

A Detail-free Mediator and the 3 Player Case

Two players can make use of a trusted third party who mediates and partially resolves their conflict. Usually, the mediator should be aware of the situation and give suggestions to the players accordingly. However, a corrupt mediator can have a big influence on the outcome of the game. We single out a transparent mediator which can be safely applied in any two player game without loss of efficiency. That is, the mediator is independent of the game and the desired outcome. Technically, we show that any correlated equilibrium of any two player game can be obtained as Nash equilibria of the game, extended with cheap, pre-play communication, where players can communicate through the proposed mediator. The key idea is that after the mediated communication the players can have a plain conversation. In particular, the mediating communication device is transparent, controllable and is the same for all games and for all equilibrium distributions. We extend the result to three player games and show that one of the players can play the role of the mediator. We implement the set of correlated equilibrium in Nash equilibria of an extended game where the players have a plain conversation. The central assumption is that players can be invited to eavesdrop a private conversation. We extend the analysis to games with incomplete information and to the set of communication equilibria

A detail-free mediator

We present an extension to any finite complete information game with two players. In the extension, players are allowed to communicate directly and, additionally, send private messages to a simple, detail-free mediator, which, in turn, makes public announcements as a deterministic function of the private messages. The extension captures situations in which people engage in face-to-face communication and can observe the opponent's face during the conversation before choosing actions in some underlying game. We prove that the set of Nash equilibrium payoffs of the extended game approximately coincides with the set of correlated equilibrium payoffs of any underlying game

Collusive communication schemes in a first-price auction

We study optimal bidder collusion at first-price auctions when the collusive mechanism only relies on signals about bidders' valuations. We build on Fang and Morris (2006) when two bidders have low or high private valuation of a single object and additionally each receives a private noisy signal from an incentiveless center about the opponent's valuation. We derive the unique symmetric equilibrium of the first price auction for any symmetric, possibly correlated, distribution of signals, when these can only take two values. Next, we find the distribution of 2-valued signals, which maximizes the joint payoffs of bidders. We prove that allowing signals to take more than two values will not increase bidders' payoffs if the signals are restricted to be public. We also investigate the case when the signals are chosen conditionally independently and identically out of n > 2 possible values. We demonstrate that bidders are strictly better o¤ as signals can take on more and more possible values. Finally, we look at another special case of the correlated signals, namely, when these are independent of the bidders' valuations. We show that in any symmetric 2-valued strategy correlated equilibrium, the bidders bid as if there were no signals at all and, hence, are not able to collude

A Physical Survey of Meteoroid Streams: Comparing Cometary Reservoirs

In this work, we present an optical survey of mm-sized meteoroids using the Canadian Automated Meteor Observatory's (CAMO) mirror tracking system. The system tracks meteors to magnitude +7.5 through an image-intensified telescopic system which has a spatial accuracy of $\sim$1 m and a temporal resolution of 10 ms. We analyze 41 meteors from 13 showers with known parent bodies, recorded between 2016 and 2022. We fit a numerical ablation and fragmentation model to our data which models meteoroid fragmentation as erosion into 10 - 500 $\mu$m constituent grains and uses the observed wake as a hard constraint on the model parameters. We measure average bulk meteoroid densities which are consistent with in situ measurements: 602 $\pm$ 155 kg m$^{-3}$ for Jupiter-family and 345 $\pm$ 48 kg m$^{-3}$ for Halley-type showers. The Geminids had the highest measured bulk density of 1387 $\pm$ 240 kg m$^{-3}$, consistent with carbonaceous material. We fail to reproduce the high bulk density ($>3000$ kg m$^{-3}$) for Jupiter-family meteoroids previously reported in the literature derived using fragmentation models on data sets with fewer observational constraints. We also provide estimates of the meteoroid grain sizes, grain mass distributions, and energy necessary to trigger the erosion for meteoroids in the analyzed showers.Comment: Accepted for publication in Icaru

First holistic modelling of meteoroid ablation and fragmentation: A case study of the Orionids recorded by the Canadian Automated Meteor Observatory

18 mm-sized Orionid meteoroids were captured in 2019 and 2020 by the Canadian Automated Observatory's mirror tracking system. Meteor position measurements were made to an accuracy of $\sim1$ m and the meteors were tracked to a limiting magnitude of about $+7.5$ at the faintest point. The trajectory estimation shows the intrinsic physical dispersion of the Orionid radiant is $0.400^{\circ} \pm 0.062^{\circ}$. An erosion-based entry model was fit to the observations to reproduce ablation and fragmentation for each meteor, simultaneously reproducing the light curve, the dynamics, and the wake. Wake observations were found to directly inform the grain mass distribution released in the modelled erosion. A new luminous efficiency model was derived from simultaneous radar and optical observations and applied in the modelling to improve its accuracy. The results show that the apparent strength of Orionids varies with radiant location and time of appearance during the period of shower activity. The average differential grain mass distribution index was 2.15, higher than found from in-situ estimates, possibly due to the evolution of the physical properties of meteoroids since ejection. All Orionids showed leading fragment morphology which was best explained by stopping the erosion at the peak of the light curve, leaving a non-fragmenting meteoroid with $\sim10\%$ of the original mass. The inverted Orionid meteoroid average bulk density of $\sim300$ kg m$^{-3}$, corresponding to porosities of $\sim90\%$, is consistent with in-situ measurements of larger dust particles by Vega-2 at 1P/Halley and Rosetta at 67P.Comment: Accepted for publication in Icaru