Approximate knowledge of rationality and correlated equilibria

We extend Aumann's [3] theorem deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p su ciently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's [4] theorem on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.

Dipeptidyl-Peptidase IV Activity Is Correlated with Colorectal Cancer Prognosis

Background Dipeptidyl-peptidase IV (EC 3.4.14.5) (DPPIV) is a serine peptidase involved in cell differentiation, adhesion, immune modulation and apoptosis, functions that control neoplastic transformation. Previous studies have demonstrated altered expression and activity of tissue and circulating DPPIV in several cancers and proposed its potential usefulness for early diagnosis in colorectal cancer (CRC). Methods and principal findings The activity and mRNA and protein expression of DPPIV was prospectively analyzed in adenocarcinomas, adenomas, uninvolved colorectal mucosa and plasma from 116 CRC patients by fluorimetric, quantitative RT-PCR and immunohistochemical methods. Results were correlated with the most important classic pathological data related to aggressiveness and with 5-year survival rates. Results showed that: 1) mRNA levels and activity of DPPIV increased in colorectal neoplasms (Kruskal-Wallis test, p<0.01); 2) Both adenomas and CRCs displayed positive cytoplasmic immunostaining with luminal membrane reinforcement; 3) Plasmatic DPPIV activity was lower in CRC patients than in healthy subjects (Mann-U test, p<0.01); 4) Plasmatic DPPIV activity was associated with worse overall and disease-free survivals (log-rank p<0.01, Cox analysis p<0.01). Conclusion/significance 1) Up-regulation of DPPIV in colorectal tumors suggests a role for this enzyme in the neoplastic transformation of colorectal tissues. This finding opens the possibility for new therapeutic targets in these patients. 2) Plasmatic DPPIV is an independent prognostic factor in survival of CRC patients. The determination of DPPIV activity levels in the plasma may be a safe, minimally invasive and inexpensive way to define the aggressiveness of CRC in daily practice.