Stochastic Evolutionary Dynamics of Trust Games with Asymmetric Parameters

Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The Trust Game has been widely used to quantitatively study trust and trustworthiness, involving a sequential exchange between an investor and a trustee. The deterministic evolutionary game theory predicts no trust and no trustworthiness whereas the behavioural experiments with the one-shot anonymous Trust Game show that people substantially trust and respond trustworthily. To explain these discrepancies, previous works often turn to additional mechanisms, which are borrowed from other games such as Prisoner's Dilemma. Although these mechanisms lead to the evolution of trust and trustworthiness to an extent, the optimal or the most common strategy often involves no trustworthiness. In this paper, we study the impact of asymmetric demographic parameters (e.g. different population sizes) on game dynamics of the Trust Game. We show that, in weak-mutation limit, stochastic evolutionary dynamics with the asymmetric parameters can lead to the evolution of high trust and high trustworthiness without any additional mechanisms in well-mixed finite populations. Even full trust and near full trustworthiness can be the most common strategy. These results are qualitatively different from those of the previous works. Our results thereby demonstrate rich evolutionary dynamics of the asymmetric Trust Game.Comment: 17 pages, 15 figure

On the Origin of Risk Sensitivity: the Energy Budget Rule Revisited

The risk-sensitive foraging theory formulated in terms of the (daily) energy budget rule has been influential in behavioural ecology as well as other disciplines. Predicting risk-aversion on positive budgets and risk-proneness on negative budgets, however, the budget rule has recently been challenged both empirically and theoretically. In this paper, we critically review these challenges as well as the original derivation of the budget rule and propose a `gradual' budget rule, which is normatively derived from a gradual nature of risk sensitivity and encompasses the conventional budget rule as a special case. The gradual budget rule shows that the conventional budget rule holds when the expected reserve is close enough to a threshold for overnight survival, selection pressure being significant. The gradual view also reveals that the conventional budget rule does not need to hold when the expected reserve is not close enough to the threshold, selection pressure being insignificant. The proposed gradual budget rule better fits the empirical findings including those that used to challenge the conventional budget rule.Comment: 13 pages, 4 figure

Satisfied-defect, unsatisfied-cooperate: An evolutionary dynamics of cooperation led by aspiration

Evolutionary game theory has been widely used to study the evolution of cooperation in social dilemmas where imitation-led strategy updates are typically assumed. However, results of recent behavioral experiments are not compatible with the predictions based on the imitation dynamics, casting doubts on the assumption of the imitation-led updates and calling for alternative mechanisms of strategy updates. An aspiration-led update is often considered as an alternative to the imitation-led one. While details of update rules can have significant impacts on the evolutionary outcomes and many variations in imitation-led updates are thus studied, however, few variations exist in aspiration-led updates. We introduce an aspiration-led update mechanism ("Satisfied-Defect, Unsatisfied-Cooperate") that is psychologically intuitive and can yield a behavior richer than the conventional aspiration-led update does in Prisoner's Dilemma games. Using analytical and numerical methods, we study and link the stochastic dynamics of it in well-mixed finite populations and the deterministic dynamics of infinite populations.Comment: 13 pages, 10 figures, and 3 table

Somoclu: An Efficient Parallel Library for Self-Organizing Maps

Somoclu is a massively parallel tool for training self-organizing maps on large data sets written in C++. It builds on OpenMP for multicore execution, and on MPI for distributing the workload across the nodes in a cluster. It is also able to boost training by using CUDA if graphics processing units are available. A sparse kernel is included, which is useful for high-dimensional but sparse data, such as the vector spaces common in text mining workflows. Python, R and MATLAB interfaces facilitate interactive use. Apart from fast execution, memory use is highly optimized, enabling training large emergent maps even on a single computer.Comment: 26 pages, 9 figures. The code is available at https://peterwittek.github.io/somoclu

A Vector-Space Representation of Motion Data for Example-Based Motion Synthesis

Wearing a hat, tie, and dark skirt and jacket Willa Cather stands in front of evergreens on Grand Manan. She is turning and grasping a branch. Edith Lewis may have taken this photograph

To trust or not to trust: evolutionary dynamics of an asymmetric N-player trust game

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction between two players, an investor and a trustee. It requires at least two strategies or options for an investor (e.g.to trust versus not to trust a trustee). According to the evolutionary game theory, the antisocial strategies (e.g.not to trust) evolve such that the investor and trustee end up with lower payoffs than those that they would get with the prosocial strategies (e.g.to trust). A generalisation of the TG to a multiplayer (i.e.more than two players) TG was recently proposed. However, its outcomes hinge upon two assumptions that various real situations may substantially deviate from: (i) investors are forced to trust trustees and (ii) investors can turn into trustees by imitation and vice versa. We propose an asymmetric multiplayer TG that allows investors not to trust and prohibits the imitation between players of different roles; instead, investors learn from other investors and the same for trustees. We show that the evolutionary game dynamics of the proposed TG qualitatively depends on the nonlinearity of the payoff function and the amount of incentives collected from and distributed to players through an institution. We also show that incentives given to trustees can be useful and sufficient to cost-effectively promote trust and trustworthiness among self-interested players

An 8 x 8 nRERL serial multiplier for ultra-low-power applications

An 8 x 8-b nRERL serial multiplier is implemented in a 0.6- m n-well 3-metal CMOS pro- cess. nRERL (nMOS Reversible Energy Recov ery Logic) is a new reversible adiabatic logic circuit, which can be operated at the leakage-current lev el for ultra- low-energy applications. Measurement results show ed that the nRERL serial multiplier consumed only 0.9 % of the energy dissipation of the static CMOS one at the operating frequency 100 kHz at 5V, where its adiabatic and leakage losses were about equal.The test chip was fabricated with the help of IDEC program of KAIST, Taejon, Korea. This paper was sup- ported by NON DIRECTED RESEARCH FUND, Korea Research Foundation,throught Inter-university Semicon- ductor Research Center, Seoul National University, Seoul, Korea, from 1996 to 1999

Risk and Ambiguity in Information Seeking:Eye Gaze Patterns Reveal Contextual Behavior in Dealing with Uncertainty

Information foraging connects optimal foraging theory in ecology with how humans search for information. The theory suggests that, following an information scent, the information seeker must optimize the tradeoff between exploration by repeated steps in the search space vs. exploitation, using the resources encountered. We conjecture that this tradeoff characterizes how a user deals with uncertainty and its two aspects, risk and ambiguity in economic theory. Risk is related to the perceived quality of the actually visited patch of information, and can be reduced by exploiting and understanding the patch to a better extent. Ambiguity, on the other hand, is the opportunity cost of having higher quality patches elsewhere in the search space. The aforementioned tradeoff depends on many attributes, including traits of the user: at the two extreme ends of the spectrum, analytic and wholistic searchers employ entirely different strategies. The former type focuses on exploitation first, interspersed with bouts of exploration, whereas the latter type prefers to explore the search space first and consume later. Based on an eye-tracking study of experts' interactions with novel search interfaces in the biomedical domain, we demonstrate that perceived risk shifts the balance between exploration and exploitation in either type of users, tilting it against vs. in favour of ambiguity minimization. Since the pattern of behaviour in information foraging is quintessentially sequential, risk and ambiguity minimization cannot happen simultaneously, leading to a fundamental limit on how good such a tradeoff can be. This in turn connects information seeking with the emergent field of quantum decision theory.Comment: 20 pages, 3 figure