Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Effects of Combined Ketamine/Xylazine Anesthesia on Light Induced Retinal Degeneration in Rats

Objectives: To explore the effect of ketamine-xylazine anesthesia on light-induced retinal degeneration in rats. Methods: Rats were anesthetized with ketamine and xylazine (100 and 5 mg, respectively) for 1 h, followed by a recovery phase of 2 h before exposure to 16,000 lux of environmental illumination for 2 h. Functional assessment by electroretinography (ERG) and morphological assessment by in vivo imaging (optical coherence tomography), histology (hematoxylin/eosin staining, TUNEL assay) and immunohistochemistry (GFAP and rhodopsin staining) were performed at baseline (ERG), 36 h, 7 d and 14 d post-treatment. Non-anesthetized animals treated with light damage served as controls. Results: Ketamine-xylazine pre-treatment preserved retinal function and protected against light-induced retinal degeneration. In vivo retinal imaging demonstrated a significant increase of outer nuclear layer (ONL) thickness in the non-anesthetized group at 36 h (p,0.01) and significant reduction one week (p,0.01) after light damage. In contrast, ketamine-xylazine pre-treated animals showed no significant alteration of total retinal or ONL thickness at either time point (p.0.05), indicating a stabilizing and/or protective effect with regard to phototoxicity. Histology confirmed light-induced photoreceptor cell death and Müller cells gliosis in non-anesthetized rats, especially in the superior hemiretina, while ketamine-xylazine treated rats showed reduced photoreceptor cell death (TUNEL staining: p,0.001 after 7 d), thicker ONL and longer IS/OS. Fourteen days after light damage, a reduction of standard flash induced a-wave amplitudes and a-wav

National identity predicts public health support during a global pandemic

Understanding collective behaviour is an important aspect of managing the pandemic response. Here the authors show in a large global study that participants that reported identifying more strongly with their nation reported greater engagement in public health behaviours and support for public health policies in the context of the pandemic.Changing collective behaviour and supporting non-pharmaceutical interventions is an important component in mitigating virus transmission during a pandemic. In a large international collaboration (Study 1, N = 49,968 across 67 countries), we investigated self-reported factors associated with public health behaviours (e.g., spatial distancing and stricter hygiene) and endorsed public policy interventions (e.g., closing bars and restaurants) during the early stage of the COVID-19 pandemic (April-May 2020). Respondents who reported identifying more strongly with their nation consistently reported greater engagement in public health behaviours and support for public health policies. Results were similar for representative and non-representative national samples. Study 2 (N = 42 countries) conceptually replicated the central finding using aggregate indices of national identity (obtained using the World Values Survey) and a measure of actual behaviour change during the pandemic (obtained from Google mobility reports). Higher levels of national identification prior to the pandemic predicted lower mobility during the early stage of the pandemic (r = -0.40). We discuss the potential implications of links between national identity, leadership, and public health for managing COVID-19 and future pandemics