Unbeatable Imitation

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent

Lympho-vascular invasion in BRCA related breast cancer compared to sporadic controls

<p>Abstract</p> <p>Background</p> <p>Germline mutations in the BRCA1 gene predispose to the development of breast cancer, exhibiting a specific histological phenotype. Identification of possible hallmarks of these tumors is important for selecting patients for genetic screening and provides inside in carcinogenetic pathways.</p> <p>Since BRCA1-associated breast cancers have pushing borders that prevent them from easily reaching vessels and are often of the medullary (like) type that is known to have a low rate of lympho-vascular invasion (LVI), we hypothesized that absence of LVI could characterize BRCA1 related breast cancer.</p> <p>Methods</p> <p>A population of 68 BRCA1 related invasive breast cancers was evaluated for LVI by an experienced breast pathologist blinded to mutation status, and compared to a control group matched for age, grade and tumor type.</p> <p>Results</p> <p>LVI was present in 25.0% of BRCA1 related cases, compared to 20.6% of controls (P = 0.54, OR = 1.29, CI 0.58-2.78).</p> <p>Conclusion</p> <p>LVI is frequent in BRCA1 germline mutation related breast cancers, but seems to occur as often in sporadic controls matched for age, grade and tumor type. Apparently, these hereditary cancers find their way to the blood and lymph vessels despite their well demarcation and often medullary differentiation.</p

Existence of Mixed Strategy Equilibria in a Class of Discontinuous Games with Unbounded Strategy Sets.

We prove existence of mixed strategy equilibria for a class of discontinuous two-player games with non-compact strategy sets. As a corollary of our main results, we obtain a continuum of mixed strategy equilibria for the first- and second-price two-bidder auctions with toeholds. We also find Klemperer’s (2000) result about the existence of mixed strategy equilibria in the classical Bertrand duopoly