This paper includes a survey of decision theories directed toward exploring the adequacy of alternative approaches for application to game theoretic reasoning, a review of the classic results of von Neumann and Morgenstern and Nash about equilibrium solutions, an account of a recent challenge to the idea that solutions should be equilibria, and, finally, an explicit reconstruction and defense (using the resources of causal decision theory) of the classic indirect argument for equilibrium solutions.

New numerical solutions of 3+1D covariant kinetic theory are reported for nuclear collisions in the energy domain Ecm∼200 AGeV. They were obtained using the MPC 0.1.2 parton transport code employing high parton subdivision to retain Lorentz covariance. The solutions are compared to those of relativistic hydrodynamics employing Cooper–Frye isotherm freeze-out. The transport solutions follow a different dynamical path than hydrodynamics due to large dissipative effects when pQCD scattering rates and HIJING initial conditions are assumed. The transport freeze-out (...) four-volume is sensitive to the reaction rates. The final transverse momentum distributions are found to deviate by up to an order of magnitude from those of Cooper–Frye frozen hydrodynamics. (shrink)

A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant “historical time” τ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperangular variables. All the characteristic averages are calculated. Expressions for the pressure and the energy density are found, and the relativistic equation of state is obtained. Validity criteria are (...) defined. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles. Anti-events are introduced; for an event-anti-event system the equation of state p, ρ ∝ T 6 is found, which gives the value of the sound velocity c 2 = 0.20, in agreement with the “realistic” equation of state suggested by Shuryak for hot hadronic matter. (shrink)

The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production.Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to which he (...) has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary.General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field. (shrink)

A mistake in “Five legitimate definitions of correlated equilibrium (CE) in games with incomplete information” motivates a re-examination of some extensions of the solution concept that Aumann introduced.

This paper studies an economy whose agents perceive their consumption possibilities subjectively, and whose preferences are defined on what they subjectively experience, rather than on those alternatives that are objectively present. The model of agents' perceptions is based on intuitionistic logic. Roughly, this means that agents reason constructively: a solution to a problem exists only if there is a construction by which the problem can be solved. The theorems that can be proved determine how an agent perceives a set of (...) alternatives. A dual model relates perceived alternatives to a shared language, which the agents use in trading. So perceptions relate objective alternatives to an agent's subjective view of them, and reporting dually relates an agent's subjective world to a shared language. It turns out that an appropriately modified notion of competitive equilibrium always exists. However, in contrast with standard results in economic theory, competitive equilibrium need not be efficient. (shrink)

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show (...) how the equilibrium concepts differ, computing necessary and sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (shrink)

This paper develops a philosophical investigation of the merits and faults of a theorem by Lanford , Lanford , Lanford for the problem of the approach towards equilibrium in statistical mechanics. Lanford’s result shows that, under precise initial conditions, the Boltzmann equation can be rigorously derived from the Hamiltonian equations of motion for a hard spheres gas in the Boltzmann-Grad limit, thereby proving the existence of a unique solution of the Boltzmann equation, at least for a very short amount (...) of time. We argue that, by establishing a statistical H-theorem, it offers a prospect to complete Boltzmann’s combinatorial argument, without running against the objections which plug other typicality-based approaches. However, we submit that, while recovering the irreversible approach towards equilibrium for positive times, it fails to predict a monotonic increase of entropy for negative times, and hence it yields the wrong retrodictions about the past evolution of a gas. (shrink)

Reflective equilibrium is overdue a twenty-first century update. Despite its apparent popularity, there is scant evidence that theorists ever thoroughly implement the method, and fewer still openly and transparently publish their attempts to do so in print—stymying its supposed justificatory value. This paper proposes digitising reflective equilibrium as a solution. Inspired by the global open science movement, it advocates for coupling a novel, digital implementation of the equilibrating process with new publication norms that can capitalise on the inherent (...) reproducibility of digital data. The argument is structured around three main claims: that digitising will make it easier to (a) methodically construct, (b) widely disseminate, and (c) thoroughly critique reflective equilibria. Practical guidance is also provided throughout. Altogether, it is argued that digitisation will not only help theorists to better realise reflective equilibrium’s latent theoretical potential, but also greatly extend its value as a justificatory device in contemporary academic discourses. (shrink)

Groups of people perform acts that are subject to standards of rationality. A committee may sensibly award fellowships, or may irrationally award them in violation of its own policies. A theory of collective rationality defines collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the products of acts its members fully control. It also argues that such an act is collectively rational if (...) the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for joint action.The people engaged in a game of strategy form a group, and the combination of their acts yields a collective act. If their collective act is rational, it constitutes a solution to their game. A theory of collective rationality yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium standard for cooperative games requires that agents pursue only incentives that provide sufficient reasons to act. The book's theory of collective rationality supports an attainable equilibrium-standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts.By extending the theory of rationality to groups, this book reveals the characteristics that make an act evaluable for rationality and the way rationality's evaluation of an act responds to the type of control its agent exercises over the act. The book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions. (shrink)

We introduce a new solution concept, called correlated-belief equilibrium. The difference to Nash equilibrium is that, while each player has correct marginal conjectures about each opponent, it is not necessarily the case that these marginal conjectures are independent. Then, we provide an epistemic foundation and we relate correlated-belief equilibrium with standard solution concepts, such as rationalizability, correlated equilibrium and conjectural equilibrium.

Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash equilibria is discussed in detail. Finally, (...) for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing as their own confidence levels when players employ the optimistic value criterion. (shrink)

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (cf. Hansson [10]) studies (...) formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can “deconstruct” standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power.. (shrink)

In the theses published in Voprosy filosofii there is, in my view, one very important question: What changes have occurred in the relations between art and science? Inasmuch as I am a scholar of foreign cultures, permit me to express that question a bit more concretely for myself: What changes have occurred in the West in the interactions between art and science? The question is rather complex, for in responding to it one must always take into consideration the factor of (...) "compression of time" during the RST. Not only scientific discoveries and industrial equipment have begun to obsolesce rapidly but also the notion of the role of science in the social and cultural development of society. Regrettably, the authors of some works published in our country, even in the 1970s, analyzing the relationship between science and art that has come into being in the West, ignore this circumstance. The "ancient" debate between Snow and Leavis, now almost fifteen years in the past, is presented as the most recent stirring in contemporary bourgeois culture. Yet even at that time it was clear that these discussions were to no point and would not lead to a constructive solution of the conflict between the "two cultures": the contradictions had gone entirely too far. Even then the English poet Auden granted that when he encountered scientists he felt like a "shabby scribe who had accidentally entered a drawing room bulging with dukes." This was not any rank-and-file "lyricist," but the famous Auden himself'. (shrink)

This paper concerns periodic solutions of a class of equations that model gene regulatory networks. Unlike the vast majority of previous studies, it is not assumed that all decay rates are identical. To handle this more general situation, we rely on monotonicity properties of these systems. Under an alternative assumption, it is shown that a classical fixed point theorem for monotone, concave operators can be applied to these systems. The required assumption is expressed in geometrical terms as an alignment (...) condition on so-called focal points . As an application, we show the existence and uniqueness of a stable periodic orbit for negative feedback loop systems in dimension 3 or more, and of a unique stable equilibrium point in dimension 2. This extends a theorem of Snoussi, which showed the existence of these orbits only. (shrink)

Analytical models describing the motion of colloidal particles in given force fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker–Planck equations, a global description based on path integration is reviewed. A new result is presented, showing that under very broad conditions, during its evolution a dissipative system tends to minimize its energy dissipation in such a way to keep constant the Hamiltonian time rate, equal to the difference between (...) the flux-based and the force-based Rayleigh dissipation functions. In fact, the Fokker–Planck equation can be interpreted as the Hamilton–Jacobi equation resulting from such minumum principle. At steady state, the Hamiltonian time rate is maximized, leading to a minimum resistance principle. In the unsteady case, we consider the relaxation to equilibrium of harmonic oscillators and the motion of a Brownian particle in shear flow, obtaining results that coincide with the solution of the Fokker–Planck and the Langevin equations. (shrink)

In this paper, the nonsmooth compound transmission control protocol with the gentle random early detection system with the state-dependent round-trip delay is investigated in detail. Uniqueness of the positive equilibrium is proved firstly. Then, the closed approximate periodic solutions in this state-dependent delayed nonsmooth compound TCP with the GRED model are obtained by employing the harmonic balance and alternating frequency/time domain method. Then, we compare the results generated by numerical simulations with those of the closed approximate expressions obtained (...) by HB-AFT. It indicates that HB-AFT is simple, correct, and powerful for state-dependent delayed nonsmooth dynamical systems. Finally, we find the complicated dynamic: chaos. It is a grazing chaos with a hybrid property, i.e., where usually w oscillates at a very low frequency and q oscillates at a very high frequency. And, the route to chaos is a very rare route, i.e., the instantaneous and local transition of stable equilibrium to chaos. So, to the end of stability and good performance, we should adjust the parameters carefully to avoid the periodic and chaotic oscillations. (shrink)

It is usually assumed in game theory that agents who interact strategically with each other are rational, know the strategies open to other agents as well as their payoffs and, moreover, have common knowledge of all the above. In some games, that much information is sufficient for the players to identify a "solution" and play it. The most commonly adopted solution concept is that of Nash equilibrium. A Nash equilibrium is defined a combination of strategies, one for each (...) player, such that no player can profit from a deviation from his strategy if the opponents stick to their strategies. Nash equilibrium is taken to have predictive power, in the sense that in order to predict how rational agents will in fact behave, it is enough to identify the equilibrium patterns of actions. Barring the case in which players have dominant strategies, to play her part in a Nash equilibrium a player must believe that the other players play their part, too. But an intelligent player must immediately realize that she has no ground for this belief. Take the case of a one-shot, simultaneous game. Here all undominated strategies are possible choices, and the beliefs supporting them are possible beliefs, even if this game has a.. (shrink)

Several studies have lately revealed that social media conceal at least three dangerous pitfalls. Firstly, social media can negatively impact sociopolitical processes in advanced liberal democracies by becoming vehicles for the spread of false information that augments political polarization (Lee et al. 2017; Ostillio 2018). Secondly, as a result of the first point, social mediacan rapidly become a source of incorrect beliefs for those subjects with low digital literacy (Guess et al. 2019). Thirdly, because of the first and second points, (...) intentionally deceitful manipulations of social media content are potent generators of information cascades that increase group polarizations across groups of vulnerable social media users (Jang and Kim2018, Wang et al. 2018, Colliander 2019). These findings support the claim that the circulation of biased content on social media potentially threatens sociopolitical stability in liberal Western democracies (Duffy 2018; Sunstein 2018). Although this claim is far from being speculative, as shown by the FacebookFile investigations (Wall Street Journal 2019) and the center for humane technology’s recen tresearch, it introduces a thorny dilemma regarding the founding principles of liberal Western democracies. Namely, should Western legislators limit free speech by introducing severe penalties for those who spread fake news and the likes on social media? Or should they let the free market autonomously produce efficient technology allowing people to identify biased social media content?In other words, is a libertarian solution to the plight of online fake news and the like preferable to adequate legislation that punishes those who spread such content? Though appealing, it is unrealistic to believe that the free market can resolve this problem. On the other hand, it is realistic to suppose that Western governments should engage in a merciless battle against biased social media content. For instance, following the publication of the Report of the independent High level Group on fake news and online disinformation in 2018, the European Union introduced new directives to limit the spread of fake news online in 2021, when the Covid19 pandemic started fading. Although initiatives as such might look like limitations of free speech, there is solid philosophical ground to defend such initiatives. To prove this contention, we resort to Hobbes’s (1651, Part II, §18 and §29) argument that humans can avoid falling back into the Hobbesian state of war only if they stipulate a covenant. Specifically, we appeal to Hobbes’s (1651) argument in favor of bestowing the sovereign the right to ban those seditious doctrines that might undermine peace and sociopolitical stability in the Hobbesian Commonwealth. In this regard, we show that the Hobbesian covenant resolves conflict among humans in the same way a correlated equilibrium limits noncooperation in game theory. Namely, like game theory players, citizens enjoy greater welfare whenever they observe rules that mitigate conflict (Slomp 2010). Accordingly, we argue that citizens would be better off only if Western governments introduced severe penalties for those who intentionally spread fake news. Notably, we argue that effective regulation would create disincentives for spreading biased content and incentives for spreading truthful content. Furthermore, we argue that effective regulation against online fake news would assuage the polarizing effects of online availability cascades on social networks. Importantly, we provide empirical evidence supporting these claims by showing that the lack of effective regulation led the American government to miserably fail to contain the devasting effects of the online infodemic (i.e., the epidemic of false online information)that took place during the first two waves of the Covid19 pandemic (Evanega et al. 2020, Milosh et al. 2020). (shrink)

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in (...) terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)

Which moral judgments should one pay attention to in building a moral philosophy? Thomas Kelly and Sarah McGrath object to John Rawls’s suggestion to not rely on judgments heavily bound up with one’s own interests. I propose a solution in response to the objection.

This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement, called the Golden Rule of ethics (GR). This rule states, "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. The book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based (...) on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book of the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: a) a modification of N.N. Krasovskii's mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; b) the method of guiding control, proposed by N.N. Krasovskii; c) the Germeier convolution of the payoff functions of different players. Additionally, the book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2-4. The book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications. (shrink)

The cluster variation method has been applied to establish effective interaction potentials that describe both n '-Fe 4 N 1 m x - k -Fe 2 N 1 m z miscibility gaps in the Fe-N phase diagram. The calculated nitrogen distributions show that long-range order occurs in the n :'-Fe 4 N 1 m x phase and that short-range ordering as well as long-range ordering occurs in the k -Fe 2 N 1 m z phase. The calculated nitrogen distributions for (...) the k -Fe 2 N 1 m z , pertaining to temperatures and concentrations at the n '- k -phase boundaries, are compared with available data obtained by Mössbauer spectrometry. Preferential occupation of specific interstitial sites occurs from about 16 at.% N onwards; at the highest concentration considered, about 25 at.% N, the occupation is that of Fe 3 N as proposed in the literature on the basis of diffraction data. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a bargaining model based on the (...) benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

In this paper, I present an objection to the reflective equilibrium method based on land purchases and trespassing. I then propose a solution, which involves a change to how we regard the method.

Many normative theorists want to contribute to making the world a better place. In recent years, it has been suggested that to realise this ambition one must start with an adequate description of real-life practices. To determine what should be done, however, one must also fundamentally criticise existing moral beliefs. The method of reflective equilibrium offers a way of doing both. Yet, its practical usefulness has been doubted and it has been largely ignored in the recent practical turn of (...) normative theorising. This paper offers a complementary methodology to the method of reflective equilibrium, referred to as Rawlsian constructivism, which brings forth its practical merits. With the support of Rawlsian constructivism, the method of reflective equilibrium becomes a tool for public reasoning about practical problems which aims to facilitate shared solutions. The process of reflective scrutiny is used, not in the search of moral truth, but rather to highlight what stands in the way of solutions to problems agents face in different domains of social life. The practical value lies in scrutinising reasons for action that are taken for granted, explicating new rationales for action and highlighting neglected points of agreement. The paper exemplifies this approach with a process of justifying individual obligations to combat climate change. Normative theorists who share the practical agenda have correctly noted the importance of bottom-up investigations of subject domains. This paper argues that the next step should be to utilise this version of the method of reflective equilibrium to explore the potential for morally progressive solutions to these problems. (shrink)

A completely non-statistical non-linear non-unitary framework in which "God does not play dice..." that describes the physical foundations of consciousness is presented for the first time. At its core is the insight that the missing link between current physical descriptions of reality and a credible physical framework for consciousness is provided by post-quantum mechanics : the extension of statistical linear unitary quantum mechanics for closed systems to a locally-retrocausal[i] non-statistical non-linear non-unitary theory for open systems through the introduction of a (...) back-reaction potential and its implications. PQM is to orthodox QM as General Relativity is to Special Relativity. PQM and GR both share the same metaphysical organizing principle that one-way actions without a compensating reaction or back-reaction means an incompleteness in the theoretical model leaving out important physical phenomena. We gleaned the final piece in the puzzle of how consciousness arises from the material world from a result relating to long range collective excitations in microtubules described by Stuart Hameroff in a recent Fetzer Foundation conference in London. Herbert Fröhlich suggested that almost any many-particle system when properly pumped far off thermodynamic equilibrium can be put into a robust macro-quantum coherent state immune from environmental decoherence. Indeed, we suggest that all life forms are an example of Frohlich coherence that is intimately connected with locally-retrocausal PQM back-reaction's violation of the de Broglie guidance equation that was assumed by Bohm in his 1952 pilot wave theory. Using nature as a guide combined with nano-technology points the way to the construction of naturally conscious artificial intelligence machines capable of hacking into current-day quantum cryptographic networks. Furthermore, one can imagine attaining the transhumanist agenda. For example, the consciousness of a genius like Stephen Hawking could be uploaded to the post-quantum Cloud and then downloaded to a healthy body or android. (shrink)

This book presents the latest research on the challenges and solutions affecting the equilibrium between freedom of speech, freedom of information, information security, and the right to informational privacy. Given the complexity of the topics addressed, the book shows how old legal and ethical frameworks may need to be not only updated, but also supplemented and complemented by new conceptual solutions. Neither a conservative attitude (“more of the same”) nor a revolutionary zeal (“never seen before”) is likely (...) to lead to satisfactory solutions. Instead, more reflection and better conceptual design are needed, not least to harmonise different perspectives and legal frameworks internationally. The focus of the book is on how we may reconcile high levels of information security with robust degrees of informational privacy, also in connection with recent challenges presented by phenomena such as “big data” and security scandals, as well as new legislation initiatives, such as those concerning “the right to be forgotten” and the use of personal data in biomedical research. The book seeks to offer analyses and solutions of the new tensions, in order to build a fair, shareable, and sustainable balance in this vital area of human interactions. (shrink)

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly (...) explanation which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding. (shrink)

Political science and economic science . . . make use of the same language, the same mode of abstraction, the same instruments of thought and the same method of reasoning. (Black 1998, 354) Proponents as well as opponents of economics imperialism agree that imperialism is a matter of unification; providing a unified framework for social scientific analysis. Uskali Mäki distinguishes between derivational and ontological unification and argues that the latter should serve as a constraint for the former. We explore whether, (...) in the case of rational-choice political science, self-interested behavior can be seen as a common causal element and solution concepts as the common derivational element, and whether the former constraints the use of the latter. We find that this is not the case. Instead, what is common to economics and rational-choice political science is a set of research heuristics and a focus on institutions with similar structures and forms of organization. (shrink)

The fact of reasonable pluralism in liberal democracies threatens the stability of such societies. John Rawls proposed a solution to this problem: The different comprehensive moral doctrines endorsed by the citizens overlap on a shared political conception of justice, e.g. his justice as fairness. Optimally, accepting the political conception is for each citizen individually justified by the method of wide reflective equilibrium. If this holds, society is in full reflective equilibrium. Rawls does not in detail investigate the conditions (...) under which a full reflective equilibrium is possible or likely. This paper outlines a new strategy for addressing this open question by using the formal model of reflective equilibrium recently developed by Beisbart et al. First, it is argued that a bounded rationality perspective is appropriate which requires certain changes in the model. Second, the paper rephrases the open question about Rawlsian full reflective equilibrium in terms of the model. The question is narrowed down by focusing on the inferential connections between comprehensive doctrines and political conception. Rawls himself makes a demanding assumption about which connections are necessary for a full reflective equilibrium. Third, the paper presents a simulation study design that is focused on simplicity. The results are discussed, they fit with Rawls’s assumption. However, because of the strong idealisations, they provide a useful benchmark rather than a final answer. The paper presents suggestions for more elaborate study designs. (shrink)

In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of (...) equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations. (shrink)

This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system of (...) integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self-exciting attractors and a separatrix in a global domain. (shrink)

Data mining’s primary clustering method has several uses, including gene analysis. A set of unlabeled data is divided into clusters using data features in a clustering study, which is an unsupervised learning problem. Data in a cluster are more comparable to one another than to those in other groups. However, the number of clusters has a direct impact on how well the K-means algorithm performs. In order to find the best solutions for these real-world optimization issues, it is necessary (...) to use techniques that properly explore the search spaces. In this research, an enhancement of K-means clustering is proposed by applying an equilibrium optimization approach. The suggested approach adjusts the number of clusters while simultaneously choosing the best attributes to find the optimal answer. The findings establish the usefulness of the suggested method in comparison to existing algorithms in terms of intra-cluster distances and Rand index based on five datasets. Through the results shown and a comparison of the proposed method with the rest of the traditional methods, it was found that the proposal is better in terms of the internal dimension of the elements within the same cluster, as well as the Rand index. In conclusion, the suggested technique can be successfully employed for data clustering and can offer significant support. (shrink)

Miyagawa (Games and Economics Behavior 41(2), 292–308 [2002]) provides a simple extensive game form that implements a large class of two-agent bargaining solutions in subgame-perfect equilibrium. This class includes all of the Nash, Kalai–Smorodinsky, and relative utilitarian solutions. This note extends Miyagawa’s result to multi-agent bargaining problems.

In a pair of controversy provoking papers1, Kadane and Larkey argued that the normative or prescriptive understanding of expected utility theory recommended that participants in a game maximize expected utility given their assessments of the probabilities of the moves that other players would make. They observed that no prescription, norm or standard of Bayesian rationality recommends how they should come to make probability judgments about the choices of other players. For any given player, it is an empirical question as to (...) whether other players are Bayes rational, judge him to be Bayes rational, etc., just as it is an empirical question as to what the other players’ goals and beliefs are. Participants in the game should, of course, use all empirical information available to them about how other players have behaved and how they are likely to behave in the given context of choice. Kadane and Larkey pointed out that rational players could participate in a game meeting these requirements without the game’s terminating with a Nash equilibrium or a result satisfying any other particular solution concept. (shrink)

H.L.A. Hart objects to John Rawls’s liberty principle by drawing attention to how our legal system accepts the restriction of liberty to protect against other harms than liberty-deprivation, such as by laws against slander, libel, and publications which grossly infringe privacy. What is the solution for John Rawls, faced with this criticism? One solution is, by the reflective equilibrium method, to justify abandoning the judgment that these actions are immoral.

Skyrms has pointed out differences between the results of rational choice theory and evolutionary game theory. This commentary argues that there is a great deal of agreement on the Nash Bargaining Solution, which maximizes the product of player payoffs, in both rational-choice-based and evolution-based theories of equilibrium selection. While evolutionary game theory has the potential to explain how we arrive at the behavioural rules that govern what we do, realistic models will require calibration through laboratory experiments. Indeed, experimental evidence (...) strongly supports the Nash Bargaining Solution. (shrink)

Kant identifies what are in fact Free Riders as the most noxious species of polemicists. Kant thinks polemic reduces the stature and authority of reason to a method of squabbling that destabilizes social equilibrium and portends disintegration into the Hobessian state of nature. In the first Critique, Kant proposes two textually related solutions to the Free Rider problem.

It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification of the (...) Newtonian-force analogy, it can be suggested that a better metaphor for natural selection is that of an emergent force, similar in nature to entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or point of application. (shrink)

We consider a class of dynamic tournaments in which two contestants are faced with a choice between two courses of action. The first is a riskless option (“hold”) of maintaining the resources the contestant already has accumulated in her turn and ceding the initiative to her rival. The second is the bolder option (“roll”) of taking the initiative of accumulating additional resources, and thereby moving ahead of her rival, while at the same time sustaining a risk of temporary setback. We (...) study this tournament in the context of a jeopardy race game (JRG), extend the JRG to $N > 2$ contestants, and construct its equilibrium solution. Compared to the equilibrium solution, the results of three experiments reveal a dysfunctional bias in favor of the riskless option. This bias is substantially mitigated when the contestants are required to commit in advance how long to pursue the risky course of action. (shrink)

In this study, the authors utilize mountain pass lemma, variational methods, regularization technique, and the Lyapunov function method to derive the unique existence of the positive classical stationary solution of a single-species ecosystem. Particularly, the geometric characteristic of saddle point in the mountain pass lemma guarantees that the equilibrium point is the ground state stationary solution of the ecosystem. Based on the obtained uniqueness result, the authors use the Lyapunov function method to derive the globally exponential stability criterion, which (...) illuminates that under some suitable conditions, a certain internal competition is conducive to the global stability of the population, and a certain amount of family planning is conducive to the overall stability of the population. Most notably, the regularity technique of weak stationary solution employed in this study can also be applied to some existing literature related with time-delays reaction-diffusion systems for the purpose of regularization of weak solutions. Finally, an illuminative numerical example shows the effectiveness of the proposed methods. (shrink)

Reconsideration-proofness is a solution concept proposed by Kocherlakota :33–54, 1996) for infinite horizon single-player problems in which time inconsistency is important. Kocherlakota’s definition has a limitation: it is not applicable to environments with state variables. The limitation is important because many time-inconsistent problems have state variables. This paper displays a natural generalization of reconsideration-proofness to environments with state variables, and shows that it leads to nonexistence in three examples. Such nonexistence contrasts with the general existence theorem obtained in environments without (...) state variables in Kocherlakota. In the first two examples, existence can be recovered with a modification in the solution concept. In the last example, nonexistence occurs even with the modified solution concept. Insights about further research are derived from these nonexistence results. (shrink)

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above (...) two schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72. (shrink)

This online appendix has five main sections. 1) Simulation 2) Derivation of model a. Success biases b. Migration c. Five equilibrium solutions d. Why economic interactions () between groups is likely not near zero e. Derivation of total payoffs 3) Discussion of the limitation of time-scales 4) An ethnographic example of occupational specialization, Swat Valley. 5) The evolution of the division of labor in other species..

This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the (...) existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality. (shrink)