Game-theoretic Version Research Articles

Cardinal inequalities involving the weak Rothberger and cellularity games

We prove several results in the theory of topological cardinal invariants involving the game-theoretic versions of the weak Lindelöf degree and of cellularity. One of them is related to Bell, Ginsburg and Woods’s 1978 question of whether every weakly Lindelöf regular first-countable space has cardinality at most continuum and another one is connected with Arhangel’skii’s 1970 question on the weak Lindelöf degree of the Gδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_\\delta $$\\end{document} topology on a compact space. We provide a few application of our results, including some bounds on the cardinality of sequential and radial spaces. We finish with a series of counterexamples, which show the sharpness of our results and disprove a few natural conjectures about the impact of infinite games on topological cardinal invariants.

Treatment outcome in an SI model with evolutionary resistance: a Darwinian model for the evolution of resistance

We consider a Darwinian (evolutionary game theoretic) version of a standard susceptible-infectious SI model in which the resistance of the disease causing pathogen to a treatment that prevents death to infected individuals is subject to evolutionary adaptation. We determine the existence and stability of all equilibria, both disease-free and endemic, and use the results to determine conditions under which the treatment will succeed or fail. Of particular interest are conditions under which a successful treatment in the absence of resistance adaptation (i.e. one that leads to a stable disease-free equilibrium) will succeed or fail when pathogen resistance is adaptive. These conditions are determined by the relative breadths of treatment effectiveness and infection transmission rate distributions as functions of pathogen resistance.

Introducing selective d-separability in bitopological spaces

We introduce $\sf D$-separability and its game-theoretic version, $\sf D^+$-separability in bitopological spaces, and investigate their relationships with $d$-separability and a weaker form of $\sf H$-separability which will be called ${\sf DH}$-separability. Further we give the connection of these notions with the selective versions of separability-types properties under the bitopological context. We also obtain some results about the $d$-separability properties of bitopological spaces which are slightly different from those one expects for the classical case

МОДЕЛИРОВАНИЕ РАЗВИТИЯ ЭКОНОМИКИ В ФОРМЕ ПОЗИЦИОННОЙ ИГРЫ

In this paper, the authors consider the simplest generalization of the dynamic growth model of a single-sector closed economy to a competitive case with discrete time, for which the simplest illustrative example is compiled. The authors summarize the information from game theory necessary to describe the game-theoretic version of the dynamic growth model of a single-sector closed economy. The developed model is considered as a dynamic positional game with complete information. The dynamics of the conflict in the game is modeled using priority sets, and families of information sets describe the informativeness of the player. The player knows in which information set he is, but does not know in which position of this set in a particular period of the game. The formal description of the model is that the number of participants in the game is determined and their behavior is detailed. At the last step, each participant of the game evaluates its outcome with the value of the utility function. The paper presents a game-theoretic model of economic development in the form of a positional game. The participants of the game are entrepreneurs, the state and the population. At the first step, entrepreneurs choose the share of production output in the form of shadow capital. At the second step, the state chooses the tax rate, and allocates part of this tax to support social programs. At the third step, the population chooses, depending on the allocated amounts for social development, the demographic growth coefficient. For this game, based on the compiled algorithm, it is possible to automate the process of finding an equilibrium situation.

Countable dimensionality, a game and the Haver property

We characterize the countable dimensionality of metric spaces in terms of a game-theoretic version of a covering property of Haver, and conjecture a game-theoretic equivalent of Haver’s covering property for metric spaces.

A bifurcation theorem for Darwinian matrix models and an application to the evolution of reproductive life-history strategies

We prove bifurcation theorems for evolutionary game theoretic (Darwinian dynamic) versions of nonlinear matrix equations for structured population dynamics. These theorems generalize existing theorems concerning the bifurcation and stability of equilibrium solutions when an extinction equilibrium destabilizes by allowing for the general appearance of the bifurcation parameter. We apply the theorems to a Darwinian model designed to investigate the evolutionary selection of reproductive strategies that involve either low or high post-reproductive survival (semelparity or iteroparity). The model incorporates the phenotypic trait dependence of two features: population density effects on fertility and a trade-off between inherent fertility and post-reproductive survival. Our analysis of the model determines conditions under which evolution selects for low or for high reproductive survival. In some cases (notably an Allee component effect on newborn survival), the model predicts multiple attractor scenarios in which low or high reproductive survival is initial condition dependent.

Coordination mechanisms for scheduling selfish jobs with favorite machines

This paper studies the favorite machine model, where each machine has different speed for different types of jobs. The model is a natural generalization of the two related machines model and captures the features of some real life problems, such as the CPU–GPU task scheduling, the two products scheduling and the cloud computing task scheduling. We are interested in the game-theoretic version of the scheduling problem in which jobs correspond to self-interested users and machines correspond to resources. The goal is to design coordination mechanisms (local policies) with a small price of anarchy (PoA) for the scheduling game of favorite machines. We first analyze the well known Makespan policy for our problem, and provide exact bounds on both the PoA and the strong PoA (SPoA). We also propose a new local policy, called FF-LPT, which outperforms several classical policies (e.g., LPT, SPT, FF-SPT and Makespan) in terms of the PoA, and guarantees fast convergence to a pure Nash equilibrium. Moreover, computational results show that the FF-LPT policy also dominates other policies for random instances, and reveal some insights for practical applications.

Learn-As-You-Fly: A Distributed Algorithm for Joint 3D Placement and User Association in Multi-UAVs Networks

In this paper, we propose a distributed algorithm that allows unmanned aerial vehicles (UAVs) to dynamically learn their optimal 3D locations and associate with ground users while maximizing the network’s sum-rate. Our approach is referred to as ’Learn-As-You-Fly’ (LAYF) algorithm. LAYF is based on a decomposition process that iteratively breaks the underlying optimization into three subproblems. First, given fixed 3D positions of UAVs, LAYF proposes a distributed matching-based association that alleviates the bottlenecks of bandwidth allocation and guarantees the required quality of service. Next, to address the 2D positions of UAVs, a modified version of K-means algorithm, with a distributed implementation, is adopted. Finally, in order to optimize the UAVs altitudes, we study a naturally defined game-theoretic version of the problem and show that under fixed UAVs 2D coordinates, a predefined association scheme, and limited interference, the UAVs altitudes game is a potential game where UAVs can maximize the limited interference sum-rate by only optimizing a local utility function. Our simulation results show that the network’s sum-rate is improved as compared to both a centralized suboptimal solution and a distributed approach that is based on closest UAVs association.

Non-Islamist parties in post-2011 Egypt: winners in an MB-free political sphere

Purpose Years after the 2011 uprising Egypt, it seems that the country’s non-Islamist parties are still included in the political game. After significant alterations in their political sphere by mid-2013 at the advent of the Muslim Brother exclusion and the subsequent discrediting of Salafi al-Nour party, non-Islamist parties took clear part in the mobilization for presidential elections (2014, 2018) and competed for legislative seats in 2015. Nonetheless, it is difficult to expect them to turn into long-term key political players with clear-cut ideological postures, unique platforms and strong grass root mobilization. With the exception of the electoral gains scored by numbered parties like Free Egyptians’ party and Nation’s Future in 2015 legislative elections, these parties seem to be lagging behind esp. in terms of their popular base; who became winners at the advent of the radical exclusion of the MB from July 2013 onwards. Design/methodology/approach This paper is based on archival research and guided by basic assumptions of rational choice institutionalism, mainly game-theoretic versions of the approach. It is divided into four sections, three of them are chronological and the last one is thematic. Findings Egypt’s non-Islamists engaged in the post-2011 political sphere, with strong Islamist rivals crippling their political chances in the first two years following the 2011 uprising. They surely capitalized on the exclusion and discrediting of the latter, but they suffered lack of ideological clarity and fragmentation from 2011 onwards with no enough evidence these weaknesses were surpassed after Islamists were “out of their way”. The only strand of non-Islamist parties which came out as “game winners” were those possessing the resources and enjoying overt “friendly” relations with al-Sisi regime. Nonetheless, internal conflicts inside key secularist parties shed light on their capacity to turn into long-term players in Egypt’s political sphere. Originality/value Very few papers were published on Egypt’s secularists parties after the 2011 uprising from the perspective of the alteration that occurred in their political environment affecting their political weight and gains. More generally, literature on non-ruling parties in authoritarian contexts mostly reduce these parties to secondary roles allocated by ruling regimes. The paper seeks to overcome both shortages.

Usefulness Drives Representations to Truth

An important objection to signaling approaches to representation is that, if signaling behavior is driven by the maximization of usefulness (as is arguably the case for cognitive systems evolved under regimes of natural selection), then signals will typically carry much more information about agent-dependent usefulness than about objective features of the world. This sort of considerations are sometimes taken to provide support for an anti-realist stance on representation itself. The author examines the game-theoretic version of this skeptical line of argument developed by Donald Hoffman and his colleagues. It is shown that their argument only works under an extremely impoverished picture of the informational connections that hold between agent and world. In particular, it only works for cue-driven agents, in Kim Sterelny’s sense. In cases in which the agents’ understanding of what is useful results from combining pieces of information that reach them in different ways, and that complement one another (i.e., that are synergistic), maximizing usefulness involves construing first a picture of agent-independent, objective matters of fact.

Characterization and uniqueness of equilibrium in competitive insurance

This paper provides a complete characterization of equilibria in a game-theoretic version of Rothschild and Stiglitz's (1976) model of competitive insurance. I allow for stochastic contract offers by insurance firms and show that a unique symmetric equilibrium always exists. Exact conditions under which the equilibrium involves mixed strategies are provided. The mixed equilibrium features (i) cross-subsidization across risk levels, (ii) dependence of offers on the risk distribution, and (iii) price dispersion generated by firm randomization over offers.

Relating high dimensional stochastic complex systems to low-dimensional intermittency

We evaluate the implication and outlook of an unanticipated simplification in the macroscopic behavior of two high-dimensional sto-chastic models: the Replicator Model with Mutations and the Tangled Nature Model (TaNa) of evolutionary ecology. This simplification consists of the apparent display of low-dimensional dynamics in the non-stationary intermittent time evolution of the model on a coarse-grained scale. Evolution on this time scale spans generations of individuals, rather than single reproduction, death or mutation events. While a local one-dimensional map close to a tangent bifurcation can be derived from a mean-field version of the TaNa model, a nonlinear dynamical model consisting of successive tangent bifurcations generates time evolution patterns resembling those of the full TaNa model. To advance the interpretation of this finding, here we consider parallel results on a game-theoretic version of the TaNa model that in discrete time yields a coupled map lattice. This in turn is represented, a la Langevin, by a one-dimensional nonlinear map. Among various kinds of behaviours we obtain intermittent evolution associated with tangent bifurcations. We discuss our results.

A bifurcation theorem for evolutionary matrix models with multiple traits.

One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1. In this paper we consider an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. We extend the fundamental bifurcation theorem to this evolutionary model. We apply the results to an evolutionary version of a Ricker model with an added Allee component. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena, such as backward bifurcation induced strong Allee effects.

Game theoretical modelling of a dynamically evolving network Ⅰ: General target sequences

Animal (and human) populations contain a finite number of individuals with social and geographical relationships which evolve over time, at least in part dependent upon the actions of members of the population. These actions are often not random, but chosen strategically. In this paper we introduce a game-theoretical model of a population where the individuals have an optimal level of social engagement, and form or break social relationships strategically to obtain the correct level. This builds on previous work where individuals tried to optimise their number of connections by forming or breaking random links; the difference being that here we introduce a truly game-theoretic version where they can choose which specific links to form/break. This is more realistic and makes a significant difference to the model, one consequence of which is that the analysis is much more complicated. We prove some general results and then consider a single example in depth.

Imprecise stochastic processes in discrete time: global models, imprecise Markov chains, and ergodic theorems

We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as discrete-time stochastic processes with finite state sets and transition probabilities that are imprecise, in the sense that they are only known to belong to some convex closed set of probability measures. We derive various properties for their joint lower and upper expectations, and in particular a law of iterated expectations. We then focus on the special case of imprecise Markov chains, investigate their Markov and stationarity properties, and use these, by way of an example, to derive a system of non-linear equations for lower and upper expected transition and return times. Most importantly, we prove a game-theoretic version of the strong law of large numbers for submartingale differences in imprecise probability trees, and use this to derive point-wise ergodic theorems for imprecise Markov chains.

Infinite games and chain conditions

We apply the theory of infinite two-person games to two well-known problems in topology: Suslin's Problem and Arhangel'skii's problem on $G_\delta$ covers of compact spaces. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable and 2) in every compact space satisfying the game-theoretic version of the weak Lindel\of property, every cover by $G_\delta$ sets has a continuum-sized subcollection whose union is $G_\delta$-dense.

Selective versions of chain condition-type properties

We study selective and game-theoretic versions of properties like the ccc, weak Lindelofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal invariants of the continuum.

Evolutionary dynamics of a multi-trait semelparous model

We consider a multi-trait evolutionary (game theoretic) version of a two class (juvenile-adult) semelparous Leslie model. We prove the existence of both a continuum of positive equilibria and a continuum of synchronous 2-cycles as the result of a bifurcation that occurs from the extinction equilibrium when the net reproductive number $R_{0}$ increases through $1$. We give criteria for the direction of bifurcation and for the stability or instability of each bifurcating branch. Semelparous Leslie models have imprimitive projection matrices. As a result (unlike matrix models with primitive projection matrices) the direction of bifurcation does not solely determine the stability of a bifurcating continuum. Only forward bifurcating branches can be stable and which of the two is stable depends on the intensity of between-class competitive interactions. These results generalize earlier results for single trait models. We give an example that illustrates how the dynamic alternative can change when the number of evolving traits changes from one to two.

Socially efficient detection of terror plots

How many good guys are needed to find the bad guys? To answer this question, a staffing model is developed to determine the number of agents required to detect a specified fraction of terror attacks assuming that the hazard functions governing attack and plot detection are proportional. Given estimates of the benefit of preventing a terror attack and the cost of counterterror agents, the staffing model can be employed to determine both the socially efficient terror plot detection level and the implied number of counterterror agents. A game-theoretic version of the model emerges if strategic terrorists select their attack rate presuming that the state will respond optimally. Numerical examples are presented to illustrate potential applications using empirical estimates of the benefit of preventing attacks and the cost of counterterror agents.

Parametric Packing of Selfish Items and the Subset Sum Algorithm

The subset sum algorithm is a natural heuristic for the classical Bin Packing problem: In each iteration, the algorithm finds among the unpacked items, a maximum size set of items that fits into a new bin. More than 35 years after its first mention in the literature, establishing the worst-case performance of this heuristic remains, surprisingly, an open problem. Due to their simplicity and intuitive appeal, greedy algorithms are the heuristics of choice of many practitioners. Therefore, better understanding simple greedy heuristics is, in general, an interesting topic in its own right. Very recently, Epstein and Kleiman (Proc. ESA 2008, pp. 368–380) provided another incentive to study the subset sum algorithm by showing that the Strong Price of Anarchy of the game theoretic version of the Bin Packing problem is precisely the approximation ratio of this heuristic. In this paper we establish the exact approximation ratio of the subset sum algorithm, thus settling a long standing open problem. We generalize this result to the parametric variant of the Bin Packing problem where item sizes lie on the interval \((0, \alpha ]\) for some \(\alpha \le 1\), yielding tight bounds for the Strong Price of Anarchy for all \(\alpha \le 1\). Finally, we study the pure Price of Anarchy of the parametric Bin Packing game for which we show nearly tight upper and lower bounds for all \(\alpha \le 1\).