On a duel with time lag and arbitrary accuracy functions

This paper deals with a two-person zero-sum game called duel with the following structure: Each of two players I and II has a gun with one bullet and he can fire his bullet at any time in [0, 1], aiming at his opponent. If I or II fires at timex, he hits his opponent with probabilityp (x) orq(x), respectively. The gun of I is silent, and hence, II does not know whether his opponent has fired or not, and the gun of II is noisy with time lagt, wheret is a positive constant,i.e., if II fires at timex then I knows it at timex +t. Further, if I hits II without being hit himself before, the payoff is 1; if I is hit by II without hitting II before, the payoff is ?1; if they hit each other at the same time or both survive, the payoff is 0. This paper gives optimal strategy for each player and the value of the game.     

Restricted domains,arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives

An n-person social choice problem is considered in which the alternatives are n dimensional vectors, with the ith component of such a vector being the part of the alternatives affecting individual i alone. Assuming that individuals are selfish (individual i must be indifferent between any two alternatives with the same components), that they may be indifferent among alternatives and that each individual may choose his preferences out of a different set of permissible preferences, we prove that any set of restricted domains of preferences admits an n person non-dictatorial Arrow-type social welfare function if and only if it admits a two-person Arrow-type social welfare function: we characterize all the sets of restricted domains of preferences which admit two-person Arrow-type social welfare functions (and therefore also admit n-person Arrow-type social welfare functions) and then we prove that we also characterized all the sets of restricted domains of preferences which admit nondictatorial, nonmanipulable, noncorruptible and rational social choice correspondences.     

“What Counts as an Insult?”

In virtue of what does a linguistic act count as an insult? I discuss five main approaches to this question, according to which an insult is determined by (i) the semantic properties of the expression used; (ii) the insulter, her intention, or attitudes; (iii) the addressee and her personal standard; (iv) the features of the speech act performed; and (v) the standard of the relevant social group. I endorse the last, objectivist account, according to which an act x counts as an insult if and only if x is assessed as demeaning when addressed at A by the standard of the relevant social group at t.     

Federations and transitive group choice

The following is a brief English summary of the paper Mirkin (1979), in which he discusses social welfare functions where the relations involved are solely assumed to be reflexive. Under axioms of independence and neutrality, monotonicity, and two domain assumptions the author shows that such a social welfare function is determined by a ‘federation’,i.e., the set of coalitions such that if that each member considers a not worse than b so does the group. The author then characterizes transitive, completeness, definiteness, (a sort of non-indifference assumption), and majority rule in this framework. He also characterizes those domains on which social welfare functions determined by federations F satisfying I ∈ F if and only if ī ? F, are transitive. We omit proofs, which are given in the Russian version, as well as the author's discussion of these results.     

The Cultural Evolution of Indiscriminate Altruism in a Large Randomly Matching Population

Altruism is hard to explain because altruistic acts are costly to the individuals who perform them. Although past work has identified conditions under which altruism can evolve, there is wide agreement among evolutionary theorists in the social sciences and biology that indiscriminate altruism cannot evolve in a large randomly matching population. Building on earlier work (Mark, 2002 Mark , N. P. ( 2002 ). Cultural transmission, disproportionate acquisition, and the evolution of cooperation . American Sociological Review , 67 , 323 – 344 .[Crossref], [Web of Science ®] , [Google Scholar]), I show that cultural transmission can create a cultural evolutionary force toward indiscriminate altruism in a large randomly matching population. The cultural transmission of a behavior (altruistic or selfish) disproportionately exposes those who acquire that behavior to that behavior prior to its acquisition. That is, individuals who have acquired an altruistic behavior through cultural transmission (i.e., who learned to behave altruistically from other people) were disproportionately exposed to the altruistic acts of others. Likewise, individuals who have acquired a selfish behavior through cultural transmission were disproportionately exposed to the selfish acts of others. Because of this disproportionate prior exposure, altruists have disproportionately benefitted from the altruistic acts of others, and selfish individuals have disproportionately been hurt by the selfish acts of others. If the benefits of being the target of altruistic acts increase one's attractiveness as a behavioral model, then a cultural evolutionary force toward altruism results.

[An appendix to the article is featured as an online supplement at the publisher's website.]     

Change in the Form of Evolution: Transition from Primate to Hominid Forms of Social Organization

In this paper I sketch a model for the transition from biologically to culturally based forms of social organization. The impetus for the transition arises from increased individualization among the non-human primates that can be observed as one moves phylogenetically from the Cercopithecoids and Ceboids (Old and New World monkeys) to the hominoids, especially the African apes. Increased individualization introduced a conflict with coherent and stable social integration that was only resolved among the hominid ancestors to modern Homo sapiens by shifting to a cultural/conceptual, rather than a behavioral/biological, basis for social organization. The shift entailed a change from evolution driven by individual fitness to evolution driven by the structural coherency of a conceptual system for social organization; that is, to selection based on group, rather than individual, level traits. Conceptually the transition depended upon the evolution of mental capacities such as a theory of mind and recursion, both of which are absent or occur only in minimal form among the non-human primates.     

Dynamics of a single species evolutionary model with Allee effects

We investigate the evolutionary outcomes of a single species population subject to Allee effects within the framework of a continuous strategy evolutionary game theory (EGT) model. Our model assumes a single trait creates a phenotypic trade-off between carrying capacity (i.e., competition) and predator evasion ability following a Gaussian distribution. This assumption contributes to one of our interesting findings that evolution prevents extinction even when population exhibits strong Allee effects. However, the extinction equilibrium can be an ESS under some special distributions of anti-predation phenotypes. The ratio of variation in competition and anti-predation phenotypes plays an important role in determining global dynamics of our EGT model: (a) evolution may suppress strong Allee effects for large values of this ratio; (b) evolution may preserve strong Allee effects for small values of this ratio by generating a low density evolutionary stable strategy (ESS) equilibrium which can serve as a potential Allee threshold; and (c) intermediate values of this ratio can result in multiple ESS equilibria.     

On the binary codes with parameters of triply-shortened 1-perfect codes

We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary (n?=?2 ^m ? 3, 2 ^n-m-1, 4) code C, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable partition of the n-cube into six cells. An arbitrary binary (n?=?2 ^m ? 4, 2 ^n-m , 3) code D, i.e., a code with parameters of a triply-shortened Hamming code, is a cell of an equitable family (but not a partition) with six cells. As a corollary, the codes C and D are completely semiregular; i.e., the weight distribution of such codes depends only on the minimal and maximal codeword weights and the code parameters. Moreover, if D is self-complementary, then it is completely regular. As an intermediate result, we prove, in terms of distance distributions, a general criterion for a partition of the vertices of a graph (from rather general class of graphs, including the distance-regular graphs) to be equitable.     

Comparing influence theories in voting games under locally generated measures of dissatisfaction

The Isbell desirability relation (I), the Shapley?CShubik index (SS) and the Banzhaf?CColeman index (BC) are power theories that grasp the notion of individual influence in a yes?Cno voting rule. Also, a yes?Cno voting rule is often used as a tool for aggregating individual preferences over any given finite set of alternatives into a collective preference. In this second context, Diffo Lambo and Moulen (DM) have introduced a power relation which ranks the voters with respect to how ably they influence the collective preference. However, DM relies on the metric d that measures closeness between preference relations. Our concern in this work is: do I, SS, BC and DM agree when the same yes?Cno voting rule is the basis for collective decision making? We provide a concrete and intuitive class of metrics called locally generated (LG). We give a characterization of the LG metrics d for which I, SS, BC and DM agree on ranking the voters.     

Hilbert algebras as implicative partial semilattices

The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.     

Evolution of a semilinear parabolic system for migration and selection without dominance

The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus without dominance is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape (i.e., a bounded, open domain in Rd). The selection coefficients depend on position; the drift and diffusion coefficients may depend on position. The primary focus of this paper is the dependence of the evolution of the gene frequencies on λ, the strength of selection relative to that of migration. It is proved that if migration is sufficiently strong (i.e., λ is sufficiently small) and the migration operator is in divergence form, then the allele with the greatest spatially averaged selection coefficient is ultimately fixed. The stability of each vertex (i.e., an equilibrium with exactly one allele present) is completely specified. The stability of each edge equilibrium (i.e., one with exactly two alleles present) is fully described when either (i) migration is sufficiently weak (i.e., λ is sufficiently large) or (ii) the equilibrium has just appeared as λ increases. The existence of unexpected, complex phenomena is established: even if there are only three alleles and migration is homogeneous and isotropic (corresponding to the Laplacian), (i) as λ increases, arbitrarily many changes of stability of the edge equilibria and corresponding appearance of an internal equilibrium can occur and (ii) the conditions for protection or loss of an allele can both depend nonmonotonically on λ. Neither of these phenomena can occur in the diallelic case.     

Loops, Reflection Structures and Graphs with Parallelism

The correspondence between right loops (P, +) with the property “(*) ?a, b ∈ P : a ? (a ? b) ? b” and reflection structures described in [4] is extended to the class of graphs with parallelism (P, ε, ∥). In this connection K-loops correspond with trapezium graphs, i.e. complete graphs with parallelism satisfying two axioms (T1), (T2) (cf. §3 ). Moreover (P, ε, ∥ +) is a structure loop (i.e. for each a ∈ P the map a ⁺ : P → P; x → a + x is an automorphism of the graph with parallelism (P, ε, ∥)) if and only if (P, +) is a K-loop or equivalently if (P, ε, ∥) is a trapezium graph.     

The square of every two-connected graph is Hamiltonian

A graph G is a line-critical block if κ(G) = 2 and if for any line e of G the graph G ? e has κ(G ? e) = 1.If G is a line-critical block, then G is either a DT-block (i.e., G is a two-connected graph in which every line is incident to a point of degree two), or G contains a specific two-connected subgraph which is a DT-block (Theorem 1). Using this result and results of the preceding paper on DT-graphs, a simple proof of the conjecture that the square of every two-connected graph is Hamiltonian is given.     

Agent-based and multi-agent simulations: coming of age or in search of an identity?

The promise of agent-based for explicating properties of social systems has not yet been fully realized. Agent models sometimes provide only a veneer of, rather than substantive engagement with, social behavior. The problem will be illustrated with Axelrod’s model for evolution of ethnocentrism (a biological model) versus Schelling’s model for spatial segregation based on preferences (a cultural model). The examples show the need to incorporate both the biological and cultural basis for behavior through a schema that includes behavior based on cultural/cognitive processing of information and behavior based on biological/cognitive processing of information. An example of an agent-based model that implements decision making in this manner is discussed. The model accounts for heterogeneity in behavior outcomes and leads to two main predictions: (1) small scale, hunter-gatherer societies in resource scarce environments will have stable adaptations less affected by variation in resource abundance in comparison to groups in resource rich regions where inter-group conflict is more likely and (2) the relationship between community size, population size and administrative complexity will have two distinct patterns, one for patrilineally organized societies and the other for matrilineally organized societies. Both predictions have been verified empirically.     

Ethnic Preferences,Social Distance Dynamics,and Residential Segregation: Theoretical Explorations Using Simulation Analysis∗

In this paper I consider theories of residential segregation that emphasize social distance and ethnic preference dynamics. I argue that these theories are more compelling than many critics have supposed, and I conclude that they deserve to be considered more carefully. I then use simulation methodology to assess the potential impact of social distance and ethnic preference dynamics on ethnic segregation under certain theoretically interesting conditions. Based on the results from the simulation analyses, I offer three conclusions: (1) status preferences and status dynamics have the capacity to produce high levels of status segregation but do not produce high levels of ethnic segregation under the specified simulation conditions; (2) ethnic preferences can, under certain theoretically interesting conditions specified in these simulations, produce high levels of ethnic segregation in the absence of housing discrimination; and (3) ethnic preferences and social distance dynamics can, when combined with status preferences, status dynamics, and demographic and urban-structural settings common in American cities, produce highly stable patterns of multi-group segregation and hyper-segregation (i.e., high levels of ethnic segregation on multiple dimensions) of minority populations. Based on these model-based theoretical explorations I speculate that the persistence of segregation in recent decades may have been overdetermined, that is, it may have been sustained by multiple sufficient causes including not only discrimination, but also social distance and preference dynamics. This raises the possibility that reductions in housing discrimination may not necessarily lead to large declines in ethnic segregation in the short run because social distance and preference dynamics may be able to sustain ethnic segregation at surprisingly high levels in the absence of housing discrimination.     

Late marriage and transition from arranged marriages to love matches: A search-theoretic approach

ABSTRACT

The aim of this study is to explore the mechanism behind how the spread of individualism, the prevalence of love matches, and the increase in search costs affect late marriages in Japan. To this end, I construct a search-theoretic model, which is a combination of the Markov decision process and the evolution of preferences. I present three results. 1) The spread of individualism is driven by those who moderately consider the social status of their family. 2) The spread of individualism and the prevalence of love matches delay the average marriage timing, but its effect is limited. 3) The diversity of individualism prevents people from switching from love matches to arranged marriages, while the search costs are rising.     

Adjoining an Identity to a Reduced Archimedean f-ring, II: Algebras

In “Part I” (presented at Ord05 (Oxford, MS)), we have discussed, for reduced archimedean f-rings, the canonical extension of such a ring, A, to one with identity, uA, and the class U of u-extendable maps (i.e., homomorphisms which lift over the u’s to identity preserving homomorphisms). We showed that U is a category and u becomes a functor from U which is a monoreflection; the maps in U were characterized. This paper addresses the interaction between our functor u, and v , the vector lattice monoreflection in archimedean ?-groups (due to Conrad and Bleier). In short, v restricts to a monoreflection of reduced archimedean f-rings into reduced archimedean f-algebras, ψ ∈ U if and only if v ψ ∈ U, and vu is a monoreflection into reduced archimedean f-algebras with identity. This work was motivated by the question put to us by G. Buskes at Ord05: what maps are o-extendable; i.e., extend over the orthomorphism rings? (The orthomorphism ring oA is a unital extension of uA, and any o-extendable map lies in U.) While a complete answer seems quite complicated (if not hopelessly out of reach), here we shall identify a class of objects D for which oD = vuD and all maps from D lie in U, hence any map from D to a reduced archimedean f-algebra is o-extendable.     

The new methods for constructing matching-equivalence graphs

Two graphs G and H with order n are said to be matching-equivalent if and only if the number of r-matchings (i.e., the number of ways in which r disjoint edges can be chosen) is the same for each of the graphs G and H for each r, where 0?r?n. In this paper, the new methods for constructing ‘matching-equivalent’ graphs are given, and some families of non-matching unique graphs are also obtained.     

Historical evolution and mathematical models: A sociocultural algorithm

Though there are a lot of approaches to the problem of sociocultural evolution most of them are only one-sided, i.e., they deal only with either social or cultural processes. With few exceptions they are also only informal theories with no formal rigour. In this article we propose a theoretical model which considers both sides of the problem, that is the mutual interdependence of the evolution of social structures and of the culture of a society. A mathematical model, the sociocultural algorithm (SCA), based on these theoretical considerations maps several of the dynamic characteristics of sociocultural evolution, suggesting that universal principles underlie the dynamics of historical evolution.     

Generalized M-Matrices

Let ρ?Rⁿ be a proper cone. From the theory of M-matrices (see e.g. [1]) it is known that if there exist α > 0 and a matrix B: ρ→ρ such that A = B?αI, then the following conditions are equivalent: (i) ? A is ρ-monotone,(ii) A is ρ-seminegative, (iii) Re[Spectrum(A)]<0. In this paper we show that while the condition (e) e^tAρ?ρ ?t≥0 is more general than the structural assumption A = B?αI, conditions (i)-(iii) are nevertheless all equivalent to (iv) {x∈ρ: Ax∈ρ}={0} when (e) holds.