Auction design in the presence of collusion

We study a problem of optimal auction design in the realistic case in which the players can collude both on the way they play in the auction and on their participation decisions. Despite the fact that the principal's opportunities for extracting payments from the agents in such a situation are limited, we show how the asymmetry of information between the colluding agents can be used to reduce the revenue losses from collusion. In a class of environments we show that the principal is even able to achieve the same revenue as when the agents do not collude. For cases in which it is not possible to do so we provide an optimal mechanism in the class of mechanisms with linear and symmetric menus and discuss the potential benefits of using asymmetric and nonlinear mechanisms. To address the problem of multiplicity of equilibria we show how the optimal mechanisms can be implemented as uniquely collusion-proof mechanisms.Collusion, mechanism design, auctions

2013-2 Correlated Equilibria and Communication Equilibria in All-pay Auctions

Correlated equilibria and communication equilibria in all-pay auctions∗ Gregory Pavlov

Arbitration, Mediation and Cheap Talk

Consider an agent (manager,artist, etc.) who has imperfect private information about his productivity. At the beginning of his career (period 1, “short run”), the agent chooses among publicly observable actions that generate imperfect signals of his productivity. The actions can be ranked according to the informativeness of the signals they generate. The market observes the agent’s action and the signal generated by it, and pays a wage equal to his expected productivity. In period 2 (the “long run”), the agent chooses between a constant payoff and a wage proportional to his true productivity, and the game ends. We show that in any equilibrium where not all types of the agent choose the same action, the average productivity of an agent choosing a less informative action is greater. However, the types choosing that action are not uniformly higher. In particular, we derive conditions for the existence of a tripartite equilibrium where low and high types pool on a less informative action while medium (on average, lower) types choose to send a more informative signal.signalling, career concerns

Optimal (and Benchmark-Optimal) Competition Complexity for Additive Buyers over Independent Items

The Competition Complexity of an auction setting refers to the number of additional bidders necessary in order for the (deterministic, prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism to achieve greater revenue than the (randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the additional bidders. We prove that the competition complexity of $n$ bidders with additive valuations over $m$ independent items is at most $n(\ln(1+m/n)+2)$, and also at most $9\sqrt{nm}$. When $n \leq m$, the first bound is optimal up to constant factors, even when the items are i.i.d. and regular. When $n \geq m$, the second bound is optimal for the benchmark introduced in [EFFTW17a] up to constant factors, even when the items are i.i.d. and regular. We further show that, while the Eden et al. benchmark is not necessarily tight in the $n \geq m$ regime, the competition complexity of $n$ bidders with additive valuations over even $2$ i.i.d. regular items is indeed $\omega(1)$. Our main technical contribution is a reduction from analyzing the Eden et al. benchmark to proving stochastic dominance of certain random variables

The Chandra LETGS high resolution X-ray spectrum of the isolated neutron star RX J1856.5-3754

We present the Chandra LETGS X-ray spectrum of the nearby (~60 pc) neutron star RX J1856.5-3754. Detailed spectral analysis of the combined X-ray and optical data rules out the nonmagnetic neutron star atmosphere models with hydrogen, helium, iron and solar compositions. We also conclude that strongly magnetized atmosphere models are unable to represent the data. The data can be explained with a two-component blackbody model. The harder component with temperature of kT_bb~63 eV and a radius R_bb~2.2 km of the emitting region well fits the X-ray data and can be interpreted as radiation from a hot region on the star's surface.Comment: 4 pages, 3 color figures; acceped by A&A Letters; http://www.xray.mpe.mpg.de/~burwitz/burwitz_refereed.htm