The Robust Weighted Multi-Objective Game

This paper studies a class of multi-objective n-person non-zero sum games through a robust weighted approach where each player has more than one competing objective. This robust weighted multi-objective game model assumes that each player attaches a set of weights to its objectives instead of accessing accurate weights. Each player wishes to minimize its maximum weighted sum objective where the maximization is pointing to the set of weights. To address this new model, a new equilibrium concept-robust weighted Nash equilibrium is obtained. The existence of this new concept is proven on suitable assumptions about the multi-objective payoffs.     

Leading the Game,Losing the Competition: Identifying Leaders and Followers in a Repeated Game

We explore a new method for identifying leaders and followers, LF, in repeated games by analyzing an experimental, repeated (50 rounds) game where Row player shifts the payoff between small and large values–a type of “investor” and Column player determines who gets the payoff–a type of “manager”. We found that i) the Investor (Row) most often is a leading player and the manager (Column) a follower. The longer the Investor leads the game, the higher is both player’s payoff. Surprisingly however, it is always the Manager that achieves the largest payoff. ii) The game has an efficient cooperative strategy where the players alternate in receiving a high payoff, but the players never identify, or accept, that strategy. iii) Under the assumption that the information used by the players is closely associated with the leader- follower sequence, and that information is available before the player’s decisions are made, the players switched LF- strategy primarily as a function of information on the Investor’s investment and moves and secondly as a function of the Manager’s payoff.     

Stability in negotiation games and the emergence of cooperation

Consider a two-player game in which each player contributes a costly resource to the common good of the pair. For such contests, the Nash equilibrium contribution, x*, is one for which neither player can increase its pay-off by unilaterally altering its contribution from x*. We study an elaboration of this game, which allows the players to exchange x-offers back and forth in a negotiation phase until they converge to a final pair of contributions, x1 and x2. A significant feature of such negotiation games, hitherto unrecognized, is the existence of a set of neutrally stable equilibrium points in negotiation phase space. To explore the long-term evolutionary outcome of such games, we simulate populations containing various mixtures of negotiation strategies and, contrary to previous results, we often find convergence to a contribution that is more cooperative than the Nash equilibrium. Mathematical analysis suggests why this might be happening, and provides a novel and robust explanation for cooperation, that negotiation can facilitate the evolution of cooperative behaviour.     

Evolution of Conformity in Social Dilemmas

People often deviate from their individual Nash equilibrium strategy in game experiments based on the prisoner’s dilemma (PD) game and the public goods game (PGG), whereas conditional cooperation, or conformity, is supported by the data from these experiments. In a complicated environment with no obvious “dominant” strategy, conformists who choose the average strategy of the other players in their group could be able to avoid risk by guaranteeing their income will be close to the group average. In this paper, we study the repeated PD game and the repeated m-person PGG, where individuals’ strategies are restricted to the set of conforming strategies. We define a conforming strategy by two parameters, initial action in the game and the influence of the other players’ choices in the previous round. We are particularly interested in the tit-for-tat (TFT) strategy, which is the well-known conforming strategy in theoretical and empirical studies. In both the PD game and the PGG, TFT can prevent the invasion of non-cooperative strategy if the expected number of rounds exceeds a critical value. The stability analysis of adaptive dynamics shows that conformity in general promotes the evolution of cooperation, and that a regime of cooperation can be established in an AllD population through TFT-like strategies. These results provide insight into the emergence of cooperation in social dilemma games.     

Evolution of Cooperation in Spatial Traveler's Dilemma Game

Traveler''s dilemma (TD) is one of social dilemmas which has been well studied in the economics community, but it is attracted little attention in the physics community. The TD game is a two-person game. Each player can select an integer value between and () as a pure strategy. If both of them select the same value, the payoff to them will be that value. If the players select different values, say and (), then the payoff to the player who chooses the small value will be and the payoff to the other player will be . We term the player who selects a large value as the cooperator, and the one who chooses a small value as the defector. The reason is that if both of them select large values, it will result in a large total payoff. The Nash equilibrium of the TD game is to choose the smallest value . However, in previous behavioral studies, players in TD game typically select values that are much larger than , and the average selected value exhibits an inverse relationship with . To explain such anomalous behavior, in this paper, we study the evolution of cooperation in spatial traveler''s dilemma game where the players are located on a square lattice and each player plays TD games with his neighbors. Players in our model can adopt their neighbors'' strategies following two standard models of spatial game dynamics. Monte-Carlo simulation is applied to our model, and the results show that the cooperation level of the system, which is proportional to the average value of the strategies, decreases with increasing until is greater than the critical value where cooperation vanishes. Our findings indicate that spatial reciprocity promotes the evolution of cooperation in TD game and the spatial TD game model can interpret the anomalous behavior observed in previous behavioral experiments.     

Cyclic Game Dynamics Driven by Iterated Reasoning

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a “hopping” behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.     

People Bouncing on Trampolines: Dramatic Energy Transfer,a Table-Top Demonstration,Complex Dynamics and a Zero Sum Game

Jumping on trampolines is a popular backyard recreation. In some trampoline games (e.g., “seat drop war”), when two people land on the trampoline with only a small time-lag, one person bounces much higher than the other, as if energy has been transferred from one to the other. First, we illustrate this energy-transfer in a table-top demonstration, consisting of two balls dropped onto a mini-trampoline, landing almost simultaneously, sometimes resulting in one ball bouncing much higher than the other. Next, using a simple mathematical model of two masses bouncing passively on a massless trampoline with no dissipation, we show that with specific landing conditions, it is possible to transfer all the kinetic energy of one mass to the other through the trampoline – in a single bounce. For human-like parameters, starting with equal energy, the energy transfer is maximal when one person lands approximately when the other is at the bottom of her bounce. The energy transfer persists even for very stiff surfaces. The energy-conservative mathematical model exhibits complex non-periodic long-term motions. To complement this passive bouncing model, we also performed a game-theoretic analysis, appropriate when both players are acting strategically to steal the other player''s energy. We consider a zero-sum game in which each player''s goal is to gain the other player''s kinetic energy during a single bounce, by extending her leg during flight. For high initial energy and a symmetric situation, the best strategy for both subjects (minimax strategy and Nash equilibrium) is to use the shortest available leg length and not extend their legs. On the other hand, an asymmetry in initial heights allows the player with more energy to gain even more energy in the next bounce. Thus synchronous bouncing unstable is unstable both for passive bouncing and when leg lengths are controlled as in game-theoretic equilibria.     

Evolutionary Stability in the Asymmetric Volunteer's Dilemma

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer''s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten''s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.     

Beauty Matters: Social Preferences in a Three-Person Ultimatum Game

Preference for beauty is human nature, as previous behavior studies have supported the notion of “beauty premium” in which attractive people were more easily to get promoted and receive higher salaries. In the present study, 29 males were recruited to participate in a three-person ultimatum game (UG) including a proposer, a responder and a powerless third player. Each subject, playing as the responder, had to decide whether to accept an offer from the allocator both for himself and a female third person. We aimed to elucidate how the facial attractiveness of the female subject affected the male subjects’ fairness and decision-making in social exchanges. Frontal feedback-related negativity (FRN) in response to four offers in an attractive-face condition revealed no significant differences between offers; however, when the companion was an unattractive female, an “unfair/fair” offer, which assigned a lower share to the responder and a fair share to the third player, elicited the largest FRN. Furthermore, when the third player was offered the smallest amount (“fair/unfair” offer), a larger FRN was generated in an attractive-face condition than unattractive-face condition. In the “unfair/fair” offer condition in which subjects received a smaller allocation than the third person, the beauty of their female counterparts attenuated subjects’ aversion to inequality, resulting in a less negative FRN in the frontal region and an increased acceptance ratio. However, the influence of the third player’s facial attractiveness only affected the early evaluation stage: late P300 was found to be immune to the “beauty premium”. Under the two face conditions, P300 was smallest following an “unfair/fair” offer, whereas the amplitudes in the other three offer conditions exhibited no significant differences. In addition, the differentiated neural features of processing facial attractiveness were also determined and indexed by four event-related potentials (ERP) components: N170, frontal N1, N2 and late positive potentials (LPPs).     

Genome scan meta-analysis of schizophrenia and bipolar disorder,part III: Bipolar disorder

Genome scans of bipolar disorder (BPD) have not produced consistent evidence for linkage. The rank-based genome scan meta-analysis (GSMA) method was applied to 18 BPD genome scan data sets in an effort to identify regions with significant support for linkage in the combined data. The two primary analyses considered available linkage data for “very narrow” (i.e., BP-I and schizoaffective disorder–BP) and “narrow” (i.e., adding BP-II disorder) disease models, with the ranks weighted for sample size. A “broad” model (i.e., adding recurrent major depression) and unweighted analyses were also performed. No region achieved genomewide statistical significance by several simulation-based criteria. The most significant P values (<.01) were observed on chromosomes 9p22.3-21.1 (very narrow), 10q11.21-22.1 (very narrow), and 14q24.1-32.12 (narrow). Nominally significant P values were observed in adjacent bins on chromosomes 9p and 18p-q, across all three disease models on chromosomes 14q and 18p-q, and across two models on chromosome 8q. Relatively few BPD pedigrees have been studied under narrow disease models relative to the schizophrenia GSMA data set, which produced more significant results. There was no overlap of the highest-ranked regions for the two disorders. The present results for the very narrow model are promising but suggest that more and larger data sets are needed. Alternatively, linkage might be detected in certain populations or subsets of pedigrees. The narrow and broad data sets had considerable power, according to simulation studies, but did not produce more highly significant evidence for linkage. We note that meta-analysis can sometimes provide support for linkage but cannot disprove linkage in any candidate region.     

The gradient clusteron: A model neuron that learns to solve classification tasks via dendritic nonlinearities,structural plasticity,and gradient descent

Synaptic clustering on neuronal dendrites has been hypothesized to play an important role in implementing pattern recognition. Neighboring synapses on a dendritic branch can interact in a synergistic, cooperative manner via nonlinear voltage-dependent mechanisms, such as NMDA receptors. Inspired by the NMDA receptor, the single-branch clusteron learning algorithm takes advantage of location-dependent multiplicative nonlinearities to solve classification tasks by randomly shuffling the locations of “under-performing” synapses on a model dendrite during learning (“structural plasticity”), eventually resulting in synapses with correlated activity being placed next to each other on the dendrite. We propose an alternative model, the gradient clusteron, or G-clusteron, which uses an analytically-derived gradient descent rule where synapses are "attracted to" or "repelled from" each other in an input- and location-dependent manner. We demonstrate the classification ability of this algorithm by testing it on the MNIST handwritten digit dataset and show that, when using a softmax activation function, the accuracy of the G-clusteron on the all-versus-all MNIST task (~85%) approaches that of logistic regression (~93%). In addition to the location update rule, we also derive a learning rule for the synaptic weights of the G-clusteron (“functional plasticity”) and show that a G-clusteron that utilizes the weight update rule can achieve ~89% accuracy on the MNIST task. We also show that a G-clusteron with both the weight and location update rules can learn to solve the XOR problem from arbitrary initial conditions.     

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.     

Exacerbating the Tragedy of the Commons: Private Inefficient Outcomes and Peer Effect in Experimental Games with Fishing Communities

Economic Experimental Games have shown that individuals make decisions that deviate down from the suboptimal Nash equilibrium. However, few studies have analyzed the case when deviation is above the Nash equilibrium. Extracting from above the Nash equilibrium is inefficient not only socially but also privately and it would exacerbate the tragedy of the commons. That would be the case of a race to the fish when stocks are becoming depleted or driver behavior on a highly congested road. The objective of this study is to analyze private inefficient extraction behavior in experimental games and to associate the type of player and the type of player group with such inefficient outcomes. To do this, we carried out economic experimental games with local coastal fishermen in Colombia, using a setting where the scarcity of the resource allows for an interior Nash equilibrium and inefficient over-extraction is possible. The state of the resource, the type of player and the composition of the group explain, in part, this inefficient behavior.     

Reciprocity on the Hardwood: Passing Patterns among Professional Basketball Players

Past theory and research view reciprocal resource sharing as a fundamental building block of human societies. Most studies of reciprocity dynamics have focused on trading among individuals in laboratory settings. But if motivations to engage in these patterns of resource sharing are powerful, then we should observe forms of reciprocity even in highly structured group environments in which reciprocity does not clearly serve individual or group interests. To this end, we investigated whether patterns of reciprocity might emerge among teammates in professional basketball games. Using data from logs of National Basketball Association (NBA) games of the 2008–9 season, we estimated a series of conditional logistic regression models to test the impact of different factors on the probability that a given player would assist another player in scoring a basket. Our analysis found evidence for a direct reciprocity effect in which players who had “received” assists in the past tended to subsequently reciprocate their benefactors. Further, this tendency was time-dependent, with the probability of repayment highest soon after receiving an assist and declining as game time passed. We found no evidence for generalized reciprocity – a tendency to “pay forward” assists – and only very limited evidence for indirect reciprocity – a tendency to reward players who had sent others many assists. These findings highlight the power of reciprocity to shape human behavior, even in a setting characterized by extensive planning, division of labor, quick decision-making, and a focus on inter-group competition.     

Inferring on the Intentions of Others by Hierarchical Bayesian Learning

Inferring on others'' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser''s incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players'' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers'' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser''s intentions were presently stable. Finally, our model of the players'' inference predicted the players'' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers'' helpfulness and the advisers'' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition.     

Algorithmic Mechanisms for Reliable Crowdsourcing Computation under Collusion

We consider a computing system where a master processor assigns a task for execution to worker processors that may collude. We model the workers’ decision of whether to comply (compute the task) or not (return a bogus result to save the computation cost) as a game among workers. That is, we assume that workers are rational in a game-theoretic sense. We identify analytically the parameter conditions for a unique Nash Equilibrium where the master obtains the correct result. We also evaluate experimentally mixed equilibria aiming to attain better reliability-profit trade-offs. For a wide range of parameter values that may be used in practice, our simulations show that, in fact, both master and workers are better off using a pure equilibrium where no worker cheats, even under collusion, and even for colluding behaviors that involve deviating from the game.     

Some game-theoretical aspects of parasitism and symbiosis

Given a two-person continuous non-constant sum game, a “solution” can be arrived at even in ignorance of the pay-off functions as each player tries to maximize his own pay-off by trial and error. The solution of the game considered here is either the intersection of two “optimal lines” (the case of the stable equilibrium) or parasitism of one player upon the other (the case of unstable equilibrium). The introduction of secondary satisfactions (linear combinations of the pay-offs) affects both the position and the stability of the equilibrium and thus the resulting primary satisfactions (the pay-offs). These effects of the matrix of transformation are investigated. In particular, it is shown that the social optimum, which is also the solution of the game where collusion is allowed, is attained if and only if the columns of the matrix are identical, and that this solution is generally stable. Some suggested connections with biological situations are discussed.     

Games of age-dependent prevention of chronic infections by social distancing

Epidemiological games combine epidemic modelling with game theory to assess strategic choices in response to risks from infectious diseases. In most epidemiological games studied thus-far, the strategies of an individual are represented with a single choice parameter. There are many natural situations where strategies can not be represented by a single dimension, including situations where individuals can change their behavior as they age. To better understand how age-dependent variations in behavior can help individuals deal with infection risks, we study an epidemiological game in an SI model with two life-history stages where social distancing behaviors that reduce exposure rates are age-dependent. When considering a special case of the general model, we show that there is a unique Nash equilibrium when the infection pressure is a monotone function of aggregate exposure rates, but non-monotone effects can appear even in our special case. The non-monotone effects sometimes result in three Nash equilibria, two of which have local invasion potential simultaneously. Returning to a general case, we also describe a game with continuous age-structure using partial-differential equations, numerically identify some Nash equilibria, and conjecture about uniqueness.     

Use of artificial genomes in assessing methods for atypical gene detection

Parametric methods for identifying laterally transferred genes exploit the directional mutational biases unique to each genome. Yet the development of new, more robust methods—as well as the evaluation and proper implementation of existing methods—relies on an arbitrary assessment of performance using real genomes, where the evolutionary histories of genes are not known. We have used the framework of a generalized hidden Markov model to create artificial genomes modeled after genuine genomes. To model a genome, “core” genes—those displaying patterns of mutational biases shared among large numbers of genes—are identified by a novel gene clustering approach based on the Akaike information criterion. Gene models derived from multiple “core” gene clusters are used to generate an artificial genome that models the properties of a genuine genome. Chimeric artificial genomes—representing those having experienced lateral gene transfer—were created by combining genes from multiple artificial genomes, and the performance of the parametric methods for identifying “atypical” genes was assessed directly. We found that a hidden Markov model that included multiple gene models, each trained on sets of genes representing the range of genotypic variability within a genome, could produce artificial genomes that mimicked the properties of genuine genomes. Moreover, different methods for detecting foreign genes performed differently—i.e., they had different sets of strengths and weaknesses—when identifying atypical genes within chimeric artificial genomes.     

Short and Long Term Investor Synchronization Caused by Decoupling

The dynamics of collective decision making is not yet well understood. Its practical relevance however can be of utmost importance, as experienced by people who lost their fortunes in turbulent moments of financial markets. In this paper we show how spontaneous collective “moods” or “biases” emerge dynamically among human participants playing a trading game in a simple model of the stock market. Applying theory and computer simulations to the experimental data generated by humans, we are able to predict the onset of such moments before they actually happen.