Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

Realignment in the National Football League: Did they do it right?

The National Football League (NFL) in the United States expanded to 32 teams in 2002 with the addition of a team in Houston. At that point, the league was realigned into eight divisions, each containing four teams. We describe a branch‐and‐cut algorithm for minimizing the sum of intradivisional travel distances. We consider first the case where any team can be assigned to any division. We also consider imposing restrictions, such as aligning the AFC (American Football Conference) and the NFC (National Football Conference) separately or maintaining traditional rivalries. We show that the alignment chosen by the NFL does not minimize the sum of intradivisional travel distances, but that it is close to optimal for an alignment that aligns the NFC and AFC separately and imposes some additional restrictions. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 683–701, 2003.     

A reply to Larry cable

Recent counterinsurgency experiences in Iraq and Afghanistan have demonstrated that the local operating environment often is dominated by indigenous power-holders. As counterinsurgents seek to establish control over the local population, collaboration with these agents has become an essential aspect of contemporary counterinsurgency. Although the practice of constructing collaborative relationships with indigenous power-holders might be perceived as unconventional by today's counterinsurgents, the approach itself goes back to the colonial era in which modern counterinsurgency has its roots. This article explores the dynamics, benefits, and dangers of collaborative relationships with indigenous power-holders by analysing an infamous episode in Dutch colonial history, the case of the collaboration between Dutch colonial authorities and warlord Teuku Uma during the Aceh War (1873–1913). This relationship ended in disaster for the Dutch as Uma departed their side at the moment he had become their pivotal asset in the local political landscape. The article explains that the Dutch succeeded to co-opt Uma, but failed to control him as they lacked the will and means to do so. Furthermore this case study provides an insight in the way the Dutch colonial authorities dealt with the complex process of intelligence-gathering in a fragmented indigenous society.     

TRENDS AND MARKERS

The twin concepts of secrecy and transparency are central to any discourse on the freeness and fairness of elections, because they are universally accep ted yardsticks of the degree to which elections can be said to be legitimate. Without challenging this truism, this paper explores these concepts as both theoretical constructs and as manifes ted in empirical situations. It will highlight their ideological function and argue that they have an alienating effect in practice. The article will also attempt to show how secrecy and transparency have helped to shape Lesotho's electoral process and the mode of its management, and will also discuss the issues and questions that it raises. Next, the most critical issues in any debate concerning Lesotho's elections and their management are raised, followed by the recommendation of an ideal way of managing elections to serve the interest of voters better. Lastly, the paper demonstrates the danger of depoliticising elections and relegating them to the legal sphere, which only the courts of law are competent to interpret.     

NEW TERRORISM

New or contemporary international terrorism associated with Islamic fundamentalism and the struggle against Zionism and American interests is a recent phenomenon in Kenya, different to that experienced during the struggle against colonialism. Many explanations have been offered as to why Kenya is being targeted, but have not sufficiently explored its close relationship with the West—especially Britain and the United States, the perceived connection between Israel and the former Presidency of Daniel Arap Moi, domestic forces and government policy. Externally the most important explanations for the increase in regional terrorism are the three waves of global terrorism since 1967, the most recent and significant of which is associated with Osama bin Laden and the Palestinian Intifada. These events reverberated in the region, Sudan and Somalia in particular, but also internally. Both internal and external attribution factors explain the resurgence of new terrorism in Africa. In the case of Kenya, terrorist attacks are associated with the country's internal domestic processes and a naïve approach to broader international issues.     

IED casualties mask the real problem: it's us

Casualty figures suggest that the US/Allied Counter Improvised Explosive Device (C-IED) policy and the present allocation of national assets, resources, and intellectual capital have not been very successful. A number of explanations for why this has been the case are discussed and critiqued here.     

Analyzing Taliban taranas (chants): an effective Afghan propaganda artifact

This article describes and analyzes a little understood Afghan Taliban propaganda tool: chants or taranas . These melodic refrains effectively use historical narratives, symbology, and iconic portraits. The chants are engendered in emotions of sorrow, pride, desperation, hope, and complaints to mobilize and convince the Afghan population of the Taliban's worldview. The chants represent culturally relevant and simple messages that are communicated in a narrative and poetic form that is familiar to and resonates with the local people. They are virtually impossible for the United States and NATO to counter because of Western sensitivities concerning religious themes that dominate the Taliban narrative space, not to mention the lack of Western linguistic capabilities, including the understanding and mastering the poetic nature of local dialects.