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 $\delta$

A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Local search: A guide for the information retrieval practitioner

There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR

ICGA Journal 24(2): special issue on Ken Thompson

This special issue of the ICGA_J focuses on Ken Thompson on the occasion of his retirement from Bell Labs in December 2000. The contents touch on Unix and cover ken's contribution to computer games, computer chess and 'ICCA', the International Computer Chess Association

Friedrich Engels travels in a chimney

In their youth, Karl Marx (1818–83) and Friedrich Engels (1820–95) were peripatetic poets, philosophers and revolutionaries. Marx’s satiric verse ‘On Hegel’ (1837) has his subject scouring city streets for truth: ‘Kant and Fichte soar to heavens blue / Seeking for some distant land, / I but seek to grasp profound and true / That which – in the street I find’.¹ But the dash signifies that ‘[w]hat the Hegelian speaker embraces on the streets is not truth but Kot, excrement’.² In his 1873 afterword to Capital, volume 1 (1867), Marx recalled finding the dialectic ‘standing on its head’ in..

BrisBAMN!? Bringing the streets into the museum

Brisbane is the narcotic of Queensland's extreme difference. It is a state of exceptional boredom and brutality. This article discusses an exhibition (Taking it to the streets) that explores a period in Brisbane's history when young people sought to change the world through political activities

Beyond Anything Realism Can Represent? Monstrous Crime in Marx’s Victorian Novel

This article reads Karl Marx’s Capital (volume 1, 1867) as the Bildungsroman of a congenital criminal: its eponymous character, Capital. Following Friedrich Engels’s The Condition of the Working Class in England (1845), Marx detects and dissects capitalism’s crimes. Capital has been called Marx’s ‘Victorian novel’ and compared to English realism’s triple-deckers. Yet his indispensable informants include factory inspectors whose reports, according to Fredric Jameson, provide testimony beyond anything realism can represent. How, then, does Marx’s apparently realist aesthetic convey Capital’s criminal deeds and criminogenic drive? To address this matter, the article examines the Gothicism of Marx’s realism. It highlights his development of Engels’s Gothic realism, demonstrates how Capital begins in media res—its first sentence presenting an immense, monstrous collection of evidence of Capital’s cannibalism—and links this opening crime scene to Marx’s portrayal of the 1863 case of Mary Anne Walkley. Murdered in her workplace, Walkley inhabits an underworld overpopulated by fellow workers killed by wage-labour. The article argues that, because actuality under the rule of Capital is structurally and monstrously criminal, Marx’s Gothic constitutes a realistic medium to represent criminal monsters and structures