Simplified three player Kuhn poker

We study a very small three player poker game (one-third street Kuhn poker), and a simplified version of the game that is interesting because it has three distinct equilibrium solutions. For one-third street Kuhn poker, we are able to find all of the equilibrium solutions analytically. For large enough pot size, $P$, there is a degree of freedom in the solution that allows one player to transfer profit between the other two players without changing their own profit. This has potentially interesting consequences in repeated play of the game. We also show that in a simplified version of the game with $P>5$, there is one equilibrium solution if $5 < P < P^* \equiv (5+\sqrt{73})/2$, and three distinct equilibrium solutions if $P > P^*$. This may be the simplest non-trivial multiplayer poker game with more than one distinct equilibrium solution and provides us with a test case for theories of dynamic strategy adjustment over multiple realisations of the game. We then study a third order system of ordinary differential equations that models the dynamics of three players who try to maximise their expectation by continuously varying their betting frequencies. We find that the dynamics of this system are oscillatory, with two distinct types of solution. We then study a difference equation model, based on repeated play of the game, in which each player continually updates their estimates of the other players' betting frequencies. We find that the dynamics are noisy, but basically oscillatory for short enough estimation periods and slow enough frequency adjustments, but that the dynamics can be very different for other parameter values.Comment: 41 pages, 2 Tables, 17 Figure

How Should Claims For Religious Exemptions Be Weighed?

Many philosophers and jurists believe that individuals should sometimes be granted religiouslygrounded exemptions from laws or rules. To determine whether an exemption is merited in a particular case, the religious claim must be weighed against the countervailing values that favour the uniform application of the law or rule. This paper develops and applies a framework for assessing the weight of religious claims to exemption, across two dimensions. First, the importance of the burdened religious practice, which is determined by its level of obligatoriness and centrality, according to the beliefs of the individual claimant. Second, the extent of the burden on the practice, which depends on the cost the individual bears if she both undertakes the religious practice and obeys the law or rule, where costs are assessed using an impartial account of individual interests. Exemptions should be granted when claims are weighty on either of these dimensions and the countervailing value is relatively weak. The final section of the paper responds to an important objection to this approach, which concerns administrability

Can Christians Join the Overlapping Consensus? Prospects and Pitfalls for a Christian Justification of Political Liberalism

The success of political liberalism depends on there being an overlapping consensus among reasonable citizens—including religious citizens—upon principles of political morality. This paper explores the resources within one major religion—Christianity—that might lead individuals to endorse (or reject) political liberalism, and thus to join (or not join) the overlapping consensus. I show that there are several strands within Christian political ethics that are consonant with political liberalism and might form the basis for Christian citizens’ membership of the overlapping consensus. Nonetheless, tensions remain, and it is not clear that Christians could wholeheartedly endorse the political conception or give unreserved commitment to political liberal ideals

Enforcing social norms: The morality of public shaming

Public shaming plays an important role in upholding valuable social norms. But, under what conditions, if any, is it morally justifiable? Our aim in this paper is systemically to investigate the morality of public shaming, so as to provide an answer to this neglected question. We develop an overarching framework for assessing the justifiability of this practice, which shows that, while shaming can sometimes be morally justifiable, it very often is not. In turn, our framework highlights several reasons to be concerned about the increasingly widespread phenomenon of online public shaming

Insolubilization process increases enzyme stability

Enzymes complexed with polymeric matrices contain properties suggesting application to enzyme-controlled reactions. Stability of insolubilized enzyme derivatives is markedly greater than that of soluble enzymes and physical form of insolubilized enzymes is useful in column and batch processes

Upstream Transients at Planetary Bow Shocks

Kinetic processes occurring upstream of planetary bow shocks can greatly perturb the magnetosphere-striking solar wind. Collisionless shocks are highly non-linear systems with complicated feedback mechanisms. Transient events form part of the growing evidence that shocks are highly variable and far more complex than a large-scale quasi-static picture would suggest. In this thesis we survey Cluster magnetic field, thermal ion, and energetic particle observations upstream of Earth’s bow shock to investigate events known as foreshock cavities. Foreshock cavities exhibit depressions in magnetic field magnitude and thermal ion density, associated with enhanced fluxes of energetic ions. Two models of foreshock cavity formation exist and we attempt to discriminate between them. Cavities are found in all parts of the Cluster orbit upstream of the bow shock but preferentially in fast, moderate magnetic field strength solar wind streams. Localising foreshock cavity observations in a coordinate system organised by physical processes in the foreshock, reveals a systematic change in foreshock cavity location with the cone angle between the solar wind flow and magnetic field. At low (high) cone angles foreshock cavities are observed outside (inside) the expected boundary of the intermediate ion foreshock. This result favours a model of foreshock cavities as isolated bundles of magnetic flux preferentially filled with energetic particles. We present a case study locating an isolated foreshock cavity precisely with respect to measured bow shock position. We use Cluster’s multispacecraft nature to constrain the cavity extent. Associated particle populations are studied in detail. A second case study is shown to coincide with a transition from the deep ion foreshock to the electron foreshock. This event has some features expected from the new model of cavities as brief encounters with a spatial boundary in the global foreshock. Finally, we present the first observations of explosive events resembling Hot Flow Anomalies near Saturn’s bow shock

The Greater Boston Housing Report Card 2009: Positioning Boston in a Post-Crisis World

Presents an annual survey of Greater Boston's market conditions, including economic and demographic trends; housing production; rents; home prices; housing affordability; foreclosures; and public spending in support of housing. Analyzes implications

Frequency reassignment in cellular phone networks

In cellular communications networks, cells use beacon frequencies to ensure the smooth operation of the network, for example in handling call handovers from one cell to another. These frequencies are assigned according to a frequency plan, which is updated from time to time, in response to evolving network requirements. The migration from one frequency plan to a new one proceeds in stages, governed by the network's base station controllers. Existing methods result in periods of reduced network availability or performance during the reassgnment process. The problem posed to the Study Group was to develop a dynamic reassignment algorithm for implementing a new frequency plan so that there is little or no disruption of the network's performance during the transition. This problem was naturally formulated in terms of graph colouring and an effective algorithm was developed based on a straightforward approach of search and random colouring