1,580 research outputs found
Constant Rank Bimatrix Games are PPAD-hard
The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash
equilibrium (NE) of a rank-, i.e., zero-sum game is equivalent to linear
programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an
FPTAS for constant rank games, and asked if there exists a polynomial time
algorithm to compute an exact NE. Adsul et al. (2011) answered this question
affirmatively for rank- games, leaving rank-2 and beyond unresolved.
In this paper we show that NE computation in games with rank , is
PPAD-hard, settling a decade long open problem. Interestingly, this is the
first instance that a problem with an FPTAS turns out to be PPAD-hard. Our
reduction bypasses graphical games and game gadgets, and provides a simpler
proof of PPAD-hardness for NE computation in bimatrix games. In addition, we
get:
* An equivalence between 2D-Linear-FIXP and PPAD, improving a result by
Etessami and Yannakakis (2007) on equivalence between Linear-FIXP and PPAD.
* NE computation in a bimatrix game with convex set of Nash equilibria is as
hard as solving a simple stochastic game.
* Computing a symmetric NE of a symmetric bimatrix game with rank is
PPAD-hard.
* Computing a (1/poly(n))-approximate fixed-point of a (Linear-FIXP)
piecewise-linear function is PPAD-hard.
The status of rank- games remains unresolved
A field deployable method for a rapid screening analysis of inorganic arsenic in seaweed
The authors thank the support for getting the seaweed samples from the projects funded under the Department of Agriculture, Food and the Marine’s Competitive research programmes in Ireland. Reference number 14 SF 860. The authors thank Corny Brombach for the graphical abstract.Peer reviewedPublisher PD
Nitric oxide modulates expression of extracellular matrix genes linked to fibrosis in kidney mesangial cells
Mesangial cells are thought to be important mediators of glomerular inflammation and fibrosis. Studies have established a direct role for nitric oxide (NO) in the regulation of gene expression in mesangial cells. Representational difference analysis was used to investigate changes in gene expression elicited by the treatment of S-nitroso-L-glutathione in rat mesangial cells. Seven upregulated and 11 downregulated genes were identified. Four out of 11 downregulated genes (connective tissue growth factor, thrombospondin-1, collagen type I all and collagen type I alpha 2) are known to be linked to inflammation and fibrosis. Results were verified across species in mesangial cells treated with a series of NO donors using Northern blot analysis, quantitative real-time PCR and protein analysis methods. Induction of endogenous NO production by cytokine stimulation also triggered regulation of the genes. One example gene, connective tissue growth factor, was studied at the promoter level. Promoter-reporter gene studies in mesangial cells demonstrated that NO acts at the transcriptional level to suppress gene expression. Our results reveal a complex role of NO in regulating gene expression in mesangial cells and suggest an antifibrotic potential for NO
Entropy and typical properties of Nash equilibria in two-player games
We use techniques from the statistical mechanics of disordered systems to
analyse the properties of Nash equilibria of bimatrix games with large random
payoff matrices. By means of an annealed bound, we calculate their number and
analyse the properties of typical Nash equilibria, which are exponentially
dominant in number. We find that a randomly chosen equilibrium realizes almost
always equal payoffs to either player. This value and the fraction of
strategies played at an equilibrium point are calculated as a function of the
correlation between the two payoff matrices. The picture is complemented by the
calculation of the properties of Nash equilibria in pure strategies.Comment: 6 pages, was "Self averaging of Nash equilibria in two player games",
main section rewritten, some new results, for additional information see
http://itp.nat.uni-magdeburg.de/~jberg/games.htm
Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
Over the years, researchers have studied the complexity of several decision
versions of Nash equilibrium in (symmetric) two-player games (bimatrix games).
To the best of our knowledge, the last remaining open problem of this sort is
the following; it was stated by Papadimitriou in 2007: find a non-symmetric
Nash equilibrium (NE) in a symmetric game. We show that this problem is
NP-complete and the problem of counting the number of non-symmetric NE in a
symmetric game is #P-complete.
In 2005, Kannan and Theobald defined the "rank of a bimatrix game"
represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be
computed in rank 1 games in polynomial time. Observe that the rank 0 case is
precisely the zero sum case, for which a polynomial time algorithm follows from
von Neumann's reduction of such games to linear programming. In 2011, Adsul et.
al. obtained an algorithm for rank 1 games; however, it does not solve the case
of symmetric rank 1 games. We resolve this problem
Two-population replicator dynamics and number of Nash equilibria in random matrix games
We study the connection between the evolutionary replicator dynamics and the
number of Nash equilibria in large random bi-matrix games. Using techniques of
disordered systems theory we compute the statistical properties of both, the
fixed points of the dynamics and the Nash equilibria. Except for the special
case of zero-sum games one finds a transition as a function of the so-called
co-operation pressure between a phase in which there is a unique stable fixed
point of the dynamics coinciding with a unique Nash equilibrium, and an
unstable phase in which there are exponentially many Nash equilibria with
statistical properties different from the stationary state of the replicator
equations. Our analytical results are confirmed by numerical simulations of the
replicator dynamics, and by explicit enumeration of Nash equilibria.Comment: 9 pages, 2x2 figure
The Path to Eliminating Raccoon Rabies in the Eastern US-Obstacles and Opportunities in Urban-Suburban Landscapes
Rabies in terrestrial wildlife poses a significant public and animal health threat. Oral rabies vaccination (ORV) targeting specific vector species has proven effective in eliminating certain rabies variants in Europe and Canada. The goal of eliminating the raccoon rabies variant (RRV) in the US is achievable through an integrated ORV program at the landscape scale. Current wildlife rabies management in the US includes extensive air and ground ORV programs in 16 eastern states coordinated by Wildlife Services (WS)’ National Rabies Management Program. More than 10 million vaccine-baits are distributed annually targeting raccoons (Procyon lotor) and striped skunks (Mephitis mephitis) with the long-term goal of eliminating RRV. Achieving vaccine-induced herd immunity in target species in developed landscapes has proven challenging due to abundant anthropogenic food sources, higher wildlife densities, decreased home ranges, habitat fragmentation, and non-target bait competition. Effectively managing RRV in the urban-suburban landscape requires greater understanding of meso-carnivore ecology in these landscapes and critical analyses of current baiting strategies. Preliminary results from urban-suburban studies demonstrate fewer potential ORV bait encounters for target species than expected, lower seroconversion rates compared to rural habitats and patchy bait distribution patterns. New technologies including the use of Point of Interest GPS units to document ground bait distribution in combination with research conducted by WS including ORV field trials, urban density studies, and raccoon, skunk, and opossum (Didelphis virginiana) ecology have provided valuable insight to overcome the obstacles of urban rabies management and make eliminating RRV a reality
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