Approximate well-supported Nash equilibria in symmetric bimatrix games

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+\delta)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $\delta$

Engaging Hashima: Memory Work, Site-Based Affects, and the Possibilities of Interruption

How is memory embodied, narrated, interrupted, and reworked? Here, we take a postphenomenological approach to memory work that is attentive to how site-based affects prompt and ossify, but also transmogrify, memory of place. With reference to an intensely traumatized, but also domesticated and entropied, environment—the island of Hashima, off the coast from Nagasaki City in Japan—we demonstrate the relevance and explanatory reach of culturally specific accounts of memory, time, and place; how an attentiveness to cultural context in the making of meaning helps mark out the epistemological violences that accrue around sites such as Hashima as objects of analysis in and of themselves; and the affective capacities of the materialities and forces that compose such sites, which can present a welter of surfaces and interiorities that are sensuously “felt” as memory

Approximate Well-supported Nash Equilibria below Two-thirds

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee

Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries

Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point by querying it. The learning objective is to know, for any point in the simplex, a label that occurs within some distance $\epsilon$ from that point. We present two algorithms for this task: Constant-Dimension Generalised Binary Search (CD-GBS), which for constant $m$ uses $poly(n, \log \left( \frac{1}{\epsilon} \right))$ queries, and Constant-Region Generalised Binary Search (CR-GBS), which uses CD-GBS as a subroutine and for constant $n$ uses $poly(m, \log \left( \frac{1}{\epsilon} \right))$ queries. We show via Kakutani's fixed-point theorem that these algorithms provide bounds on the best-response query complexity of computing approximate well-supported equilibria of bimatrix games in which one of the players has a constant number of pure strategies. We also partially extend our results to games with multiple players, establishing further query complexity bounds for computing approximate well-supported equilibria in this setting.Comment: 38 pages, 7 figures, second version strengthens lower bound in Theorem 6, adds footnotes with additional comments and fixes typo

The affinity purification and characterization of ATP synthase complexes from mitochondria.

The mitochondrial F₁-ATPase inhibitor protein, IF₁, inhibits the hydrolytic, but not the synthetic activity of the F-ATP synthase, and requires the hydrolysis of ATP to form the inhibited complex. In this complex, the α-helical inhibitory region of the bound IF₁ occupies a deep cleft in one of the three catalytic interfaces of the enzyme. Its N-terminal region penetrates into the central aqueous cavity of the enzyme and interacts with the γ-subunit in the enzyme's rotor. The intricacy of forming this complex and the binding mode of the inhibitor endow IF₁ with high specificity. This property has been exploited in the development of a highly selective affinity procedure for purifying the intact F-ATP synthase complex from mitochondria in a single chromatographic step by using inhibitor proteins with a C-terminal affinity tag. The inhibited complex was recovered with residues 1-60 of bovine IF₁ with a C-terminal green fluorescent protein followed by a His-tag, and the active enzyme with the same inhibitor with a C-terminal glutathione-S-transferase domain. The wide applicability of the procedure has been demonstrated by purifying the enzyme complex from bovine, ovine, porcine and yeast mitochondria. The subunit compositions of these complexes have been characterized. The catalytic properties of the bovine enzyme have been studied in detail. Its hydrolytic activity is sensitive to inhibition by oligomycin, and the enzyme is capable of synthesizing ATP in vesicles in which the proton-motive force is generated from light by bacteriorhodopsin. The coupled enzyme has been compared by limited trypsinolysis with uncoupled enzyme prepared by affinity chromatography. In the uncoupled enzyme, subunits of the enzyme's stator are degraded more rapidly than in the coupled enzyme, indicating that uncoupling involves significant structural changes in the stator region

Nucleotide-binding sites can enhance N-acylation of nearby protein lysine residues.

Acyl-CoAs are reactive metabolites that can non-enzymatically S-acylate and N-acylate protein cysteine and lysine residues, respectively. N-acylation is irreversible and enhanced if a nearby cysteine residue undergoes an initial reversible S-acylation, as proximity leads to rapid S → N-transfer of the acyl moiety. We reasoned that protein-bound acyl-CoA could also facilitate S → N-transfer of acyl groups to proximal lysine residues. Furthermore, as CoA contains an ADP backbone this may extend beyond CoA-binding sites and include abundant Rossmann-fold motifs that bind the ADP moiety of NADH, NADPH, FADH and ATP. Here, we show that excess nucleotides decrease protein lysine N-acetylation in vitro. Furthermore, by generating modelled structures of proteins N-acetylated in mouse liver, we show that proximity to a nucleotide-binding site increases the risk of N-acetylation and identify where nucleotide binding could enhance N-acylation in vivo. Finally, using glutamate dehydrogenase as a case study, we observe increased in vitro lysine N-malonylation by malonyl-CoA near nucleotide-binding sites which overlaps with in vivo N-acetylation and N-succinylation. Furthermore, excess NADPH, GTP and ADP greatly diminish N-malonylation near their nucleotide-binding sites, but not at distant lysine residues. Thus, lysine N-acylation by acyl-CoAs is enhanced by nucleotide-binding sites and may contribute to higher stoichiometry protein N-acylation in vivo

And then there were four: a study of UK market concentration - causes, consequences and the scope for market adjustment

While concentration measures are a good indicator of market structure, the link with competitiveness is more complex than often assumed. In particular, the modern theory of industrial organisation makes no clear statement regarding the impact of concentration on competition - the focus of this paper is concentration and no inferences are made about competitive aspects of the market. The extent and nature of concentration within the UK listed company audit market as at April, 2002 and, pro forma, after the collapse of Andersen is documented and analysed in detail (by firm, market segment and industry sector). The largest four firms held 90 per cent of the market (based on audit fees) in 2002, rising to 96 per cent with the demise of Andersen. A single firm, Pricewaterhouse-Coopers, held 70 per cent or more of the share of six out of 38 industry sectors, with a share of 50 per cent up to 70 per cent in a further seven sectors. The provision of non-audit services (NAS) by incumbent auditors is also considered. As at April 2002, the average ratio of non-audit fees (paid to auditor) to audit fees was 208 per cent, and exceeded 300 per cent in seven sectors. It is likely, however, that disposals by firms of their management consultancy and outsource firms, combined with the impact of the Smith Report on audit committees will serve to reduce these ratios. Another finding is that audit firms with expertise in a particular sector appeared to earn significantly higher nonaudit fees from their audit clients in that sector. The paper thus provides a solid empirical basis for debate. The subsequent discussion considers the implications for companies and audit firms of the high level of concentration in the current regulatory climate, where no direct regulatory intervention is planned