Quantal Response Equilibrium

In the lowest unique positive integer (LUPI) game, players pick positive integers and the player who chose the lowest unique number (not chosen by anyone else) wins a …xed prize. We derive theoretical equilibrium predictions, assuming fully rational players with Poisson-distributed uncertainty about the number of players. We also derive predictions for boundedly rational players using quantal response equilibrium and a cognitive hierarchy of rationality steps with quantal responses. The theoretical predictions are tested using both …eld data from a Swedish gambling company, and laboratory data from a scaled-down version of the …eld game. The …eld and lab data show similar patterns: in early rounds, players choose very low and very high numbers too often, and avoid focal ("round") numbers. However, there is some learning and a surprising degree of convergence toward equilibrium. The cognitive hierarchy model with quantal responses can account for the basic discrepancies between the equilibrium prediction and the data.

3 Some Simple Games 11 3.1 Myerson’s Exercise 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 The Lover-Hater Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2.1 Solution: Conversion to Strategic Form . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.2 Solution: Best Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 The Market for Lemons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 The Game of Chicken with Two Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5 Study Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Influence models enable the modelling of the spread of ideas, opinions and behaviours in social networks. Bounded rationality in social networks suggests that players make non-optimum decisions due to the limitations of access to information. Based on the premise that adopting a state or an idea can be regarded as being 'rational', we propose an influence model based on the heterogeneous bounded rationality of players in a social network. We employ the quantal response equilibrium model to incorporate the bounded rationality in the context of social influence. We hypothesise that bounded rationality of following a seed or adopting the strategy of a seed is negatively proportional to the distance from that node, and it follows that closeness centrality is the appropriate measure to place influencers in a social network. We argue that this model can be used in scenarios where there are multiple types of influencers and varying pay-offs of adopting a state. We compare different seed placement mechanisms to compare and contrast the optimum method to minimise the existing social influence in a network when there are multiple and conflicting seeds. We ascertain that placing of opposing seeds according to a measure derived from a combination of the betweenness centrality values from the seeds, and the closeness centrality of the network provide the maximum negative influence. Further, we extend this model to a strategic decision-making scenario where each seed operates a strategy in a strategic game.

Influence models enable the modelling of the spread of ideas, opinions and behaviours in social networks. Bounded rationality in social networks suggests that players make non-optimum decisions due to the limitations of access to information. Based on the premise that adopting a state or an idea can be regarded as being 'rational', we propose an influence model based on the heterogeneous bounded rationality of players in a social network. We employ the quantal response equilibrium model to incorporate the bounded rationality in the context of social influence. We hypothesise that bounded rationality of following a seed or adopting the strategy of a seed is negatively proportional to the distance from that node, and it follows that closeness centrality is the appropriate measure to place influencers in a social network. We argue that this model can be used in scenarios where there are multiple types of influencers and varying pay-offs of adopting a state. We compare different seed placement mechanisms to compare and contrast the optimum method to minimise the existing social influence in a network when there are multiple and conflicting seeds. We ascertain that placing of opposing seeds according to a measure derived from a combination of the betweenness centrality values from the seeds, and the closeness centrality of the network provide the maximum negative influence. Further, we extend this model to a strategic decision-making scenario where each seed operates a strategy in a strategic game.

Socio-ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback--Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where multiple equilibria are possible, the correlation between the scale-freeness of the system and the fraction of links with multiple equilibria goes through a rapid transition when the average system rationality increases. Our results explain the influence of the topological structure of socio-ecological systems in shaping their collective cognitive behaviour, and provide an explanation for the prevalence of scale-free and small-world characteristics in such systems. Game theory is widely used to study and model strategic decision making scenarios, ranging from politics and market economics to ecosystems and information routing . Network based games are increasingly used to understand critical phenomena in socio-ecological systems . The concept of Nash equilibrium has been an important cornerstone in understanding the dynamics of such systems 12 . While Nash equilibrium assumes that all players in a system are fully rational, most real-world strategic decision making scenarios involve players with non-optimal or bounded rationality, resulting in their strategies and behaviour deviating from those predicted by the Nash equilibrium 13 . The possible limitations, such as the amount of information at hand, cognitive capacity, and the computational time available, may force a self-interested autonomous player or agent to have bounded rationality and therefore to make non-optimal decisions 14 . Numerous theories have been presented to model the non-optimal rationality of players in strategic games, including the concepts of the near-rationality equilibrium and the quantal response equilibrium . However, these models do not attempt to quantify, in a predictive manner, the levels of rationality prevalent in individual players based on their observable characteristics. Meanwhile, studies in psychology and cognitive science have conjectured that the rationality of individuals is correlated to the level of their social interactions . In this paper, therefore, we propose a topological model of bounded rationality in socio-ecological systems, based on this conjecture. Using this model, we investigate how such systems could topologically evolve to have higher system rationality, given a heterogeneous bounded rationality distribution. Since the calculation of Nash equilibrium assumes perfect rationality of all players, we use

Socio–ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback–-Leibler divergence between Nash and Quantal Response Equilibria and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where...

This paper presents a Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) for the optimal operation of a complex multipurpose and multi-reservoir system. Firstly, MOEA/D decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems and optimizes them simultaneously. It uses information of its several neighboring sub-problems for optimizing each sub-problem. This simple procedure makes MOEA/D have lower computational complexity compared with nondominated sorting genetic algorithm II (NSGA-II). The algorithm (MOEA/D) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the realworld Zohre reservoir system in southern Iran. The objectives of the case study include water supply of minimum flow and agriculture demands over a long-term simulation period. Experimental results have demonstrated that MOEA/D can improve system performance to reduce the effect of drought compared with NSGA-II superiority. Therefore, MOEA/D is highly competitive and recommended to solve multi-objective optimization problems for water resources planning and management.

To deal with severe drought when water supply is insufficient hedging rule, based on hedging rule curve, is proposed. In general, in discrete hedging rules, the rationing factors have changed from a zone to another zone at once. Accordingly, this paper is an attempt to improve the conventional hedging rule to control the changes of rationing factors. In this regard, the simulation model has employed a fuzzy approach, and this causes rationing factor changing during a long term simulation gradually. To optimize different parameters of the purposed hedging a Multi-objective Particle Swarm Optimization (MOPSO) algorithm has been considered. The minimum of two objectives Modified Shortage Index (MSI) involving water supply of minimum flow and agriculture demands can be taken as the optimization objectives. The results of the proposed hedging rule indicate long term and annual MSI values have considerably improved compared to the conventional hedging rule. This determines that the propos...

Influence models enable the modelling of the spread of ideas, opinions and behaviours in social networks. Bounded rationality in social networks suggests that players make non-optimum decisions due to the limitations of access to information. Based on the premise that adopting a state or an idea can be regarded as being 'rational', we propose an influence model based on the heterogeneous bounded rationality of players in a social network. We employ the quantal response equilibrium model to incorporate the bounded rationality in the context of social influence. We hypothesise that bounded rationality of following a seed or adopting the strategy of a seed is negatively proportional to the distance from that node, and it follows that closeness centrality is the appropriate measure to place influencers in a social network. We argue that this model can be used in scenarios where there are multiple types of influencers and varying pay-offs of adopting a state. We compare different seed placement mechanisms to compare and contrast the optimum method to minimise the existing social influence in a network when there are multiple and conflicting seeds. We ascertain that placing of opposing seeds according to a measure derived from a combination of the betweenness centrality values from the seeds, and the closeness centrality of the network provide the maximum negative influence. Further, we extend this model to a strategic decision-making scenario where each seed operates a strategy in a strategic game.

This text may be downloaded for personal research purposes only. Any additional reproduction for other purposes, whether in hard copy or electronically, requires the consent of the author(s), editor(s). If cited or quoted, reference should be made to the full name of the author(s), editor(s), the title, the working paper or other series, the year, and the publisher. The author(s)/editor(s) should inform the Economics Department of the EUI if the paper is to be published elsewhere, and should also assume responsibility for any consequent obligation(s).

We examine individual behavior in generalized games of matching pennies. Our findings are twofold. First, individuals cooperate in these games; i.e., they systematically select strategies that lead both players to obtain higher expected payoffs than Nash. Second, among the main models in the extant literature (some of which were explicitly designed to induce cooperative behavior) the only one that predicts the observed behavior is the quantal response equilibrium.

Allocation is the number-one cause of conflict in water resources, whether betweensovereign nations, different user groups or neighboring basins. The inter-basin watertransfer is a remedy to the negative issues of water shortage in drought-stricken regions. Ina water transfer project, the receiving basin always benefits while the donor basin maysuffer. In this work, to define an operating policy, a multi-reservoir multi-purpose system issimulated and optimized for a set of long-term historical records. A multi-objectiveoptimization model is developed based on Non-Dominated Sorting Genetic Algorithm(NSGA-II). The optimization results define the best possible performance set for a twobasinsystem with the objectives of supplied water shortage minimization during droughts.In a multi-objective optimization problem, there is not a single solution that simultaneouslyoptimizes all objectives. However, decision makers are concerned with finding a uniquecompromise solution that balances confl...

This paper challenges Morris and Shin’s (1998) argument that the outcome of a speculative attack is uniquely determined by macroeconomic fundamentals. We generalize Morris and Shin’s model, and the experiment of Heinemann, Nagel, and Ockenfels (2004), by making decisions sequential and allowing some previous actions to be observed. We show sufficient conditions that guarantee the existence of a range of fundamentals where multiple outcomes occur. The main requirement is simply that most players must observe a sufficiently large number of previous choices. In our experimental sessions, eight to twelve players observe signals about the aggregate state and may also observe a random subset of previous actions. Our subjects display herding behavior consistent with the unique logit equilibrium of a boundedly rational version of our game. These strategies imply a unique mapping between fundamentals and the fraction of players attacking if previous actions are unobserved. But when most prev...

Wireless sensor network has large number of low-cost tiny nodes with sensing capability.  These provide low cost solutions to many real world problems such as such as defence, Internet of things, healthcare, environment monitoring and so on. The sensor nodes of these networks are placed in vulnerable environment. Hence, the security of these networks is very important. Intrusion Detection System (IDS) plays an important role in providing a security to such type of networks. The sensor nodes of the network have limited power and, traditional security mechanisms such as key-management, encryption decryption and authentication techniques cannot be installed on the nodes. Hence, there is a need of special security mechanism to handle the intrusions. In this paper, intrusion detection system is designed and implemented using game theory and machine learning to identify multiple attacks. Game theory is designed and used to apply the IDS optimally in WSN. The game model is designed by defi...

We experimentally study procurement auctions when both quality and price matter. We compare two treatments where sellers compete on one dimension only (price or quality), with three treatments where sellers submit a price-quality bid and the winner is determined by a scoring rule that combines the two offers. We find that, in the scoring rule treatments, efficiency and buyer's utility are lower than predicted. Estimates from a Quantal Response Equilibrium model suggest that increasing the dimension of the strategy space imposes a complexity burden on sellers, so that a simpler mechanism like a quality-only auction may be preferable.

We run an experiment on procurement auctions in a setting where both quality and price matter. We compare two unidimensional treatments in which the buyer fixes one dimension (quality or price) and sellers compete on the other, with three bidimensional treatments (with different strategy spaces) in which sellers submit a price-quality bid and the winner is determined by a score that linearly combines the two offers. We find that, with respect to the theoretical predictions, the bidimensional treatments significantly underperform, both in terms of efficiency and buyer's utility. We attribute this result to the higher strategic complexity of these treatments and test this intuition by fitting a structural Quantal Response Equilibrium model with risk aversion to our experimental data. We find very similar estimates for the risk aversion parameter across all treatments; instead, the error parameter, which captures deviations between the observed bids and the payoff-maximizing ones, ...

In a two-stage investment-effort game, we model altruistic investment in another agent's capacity to benefit from synergies between the two agents' efforts. Contrary to most models in the literature on altruism, we assume that agents who invest in others have no direct utility from their giving behavior, ruling out any genuinely altruistic component in their utility function, i.e., stemming from other-regarding preferences. Furthermore, we disentangle this "strategic ethics" from reputational effects yielding incentives for a more pro-social action in the present in order to favor Pareto-superior outcomes in the future. Isolated consumption of one's own benefits from own efforts is the worst equilibrium, which is globally stable and is shown to exist independently of the investment cost. However, for a low enough investment cost, there exist two alternative equilibria: an unstable intermediate equilibrium in which both agents make positive complementarity-building investments, and a stable one in which both agents invest all they can to complementarity building. Both equilibria Pareto-dominate the aforementioned no-investment equilibrium. Results of a laboratory experiment confirm our behavioral prediction that, for a low enough investment cost, subjects coordinate on positive complementarity-building investment, which in turn boosts their effort in the second stage. The latter increases in both own and others' complementarity-building investment, as predicted by our model. All this holds independently of subjects' risk and inequity aversion. The latter suggests that complementarity-building investment is not motivated by altruism. Rather, it is purely strategic.

Wireless sensor network has large number of low-cost tiny nodes with sensing capability.  These provide low cost solutions to many real world problems such as such as defence, Internet of things, healthcare, environment monitoring and so on. The sensor nodes of these networks are placed in vulnerable environment. Hence, the security of these networks is very important. Intrusion Detection System (IDS) plays an important role in providing a security to such type of networks. The sensor nodes of the network have limited power and, traditional security mechanisms such as key-management, encryption decryption and authentication techniques cannot be installed on the nodes. Hence, there is a need of special security mechanism to handle the intrusions. In this paper, intrusion detection system is designed and implemented using game theory and machine learning to identify multiple attacks. Game theory is designed and used to apply the IDS optimally in WSN. The game model is designed by defi...

Static and dynamic equilibria in noisy binary choice games on graphs are considered. Equations defining static quantal response equilibria (QRE) for binary choice games on graphs with arbitrary topology and noise distribution are written. It is shown that in the special cases of complete graph and arbitrary noise distribution, and circular and star topology and logistic noise distribution the resulting equations can be cast in the form coinciding with that derived in the earlier literature. Explicit equations QRE for non-directed graphs in the annealed approximation are derived. It is shown that the resulting effect on the phase transition is the same as found in the literature on phase transition in the Ising model on graphs in the same approximation.Evolutionary noisy binary choice game having the earlier described QRE as its stationary equilibria in the mean field approximation is constructed using the formalism of master equation.

Economic modeling struggles often with a lack of realism. The reason for that is that economic theory for the last 100 years has focused on simplifying assumptions which reduced important aspects of the economic reality. Concentrating on fix-point solutions and external statistical shocks prevented the profession from accurately describing the economy as a complex system with characteristics like feedback mechanism, evolution, and emergence. We propose a re-evaluation of major findings in the Classical economic literature. The classical literature described the economic system as inherently probabilistic. In this spirit, we discuss the importance of statistical equilibrium models as one way to model complex economic systems in a probabilistic way.

Background: Subtle lead malposition is an overlooked cause in patients who failed to respond to cardiac resynchronization therapy (CRT). Here, we demonstrate the voltage-dependent capture of the right ventricle (RV) by a subtly malpositioned right atrial (RA) lead. Case: An 80-year-old woman with severe non-ischemic cardiomyopathy (ejection fraction of 20%) underwent CRT with defibrillator implantation. Three months later, she continued to have New York Heart Association (NYHA) class III-IV heart failure symptoms. Device interrogation showed 74% bi-ventricular pacing and 74% RA pacing. Lead impedances were stable since implant. Pacing thresholds of the RV and left ventricular (LV) leads were 0.9 volts (V) @ 0.5 milliseconds (ms) and 0.75 V @ 0.5 ms, respectively. No significant atrial fibrillation or premature ventricular contraction detected. Decision-Making: During atrial lead threshold testing with continuous 12-lead electrocardiography monitoring, we noted RV capture starting at 5

Within the studies of human cooperation, there are gaps that require further investigation. One possible area for growth is developing theoretical concepts which describe high levels of cooperation. In this paper, we present a symmetrical quantal response equilibrium (QRE) in Prisoner’s Dilemma game (PD) constructed in Markov strategies (tolerance to defection and mutual cooperation). To prove the adequacy of the resulting equilibrium, we compare it with the previously found Nash equilibrium in PD in Markov strategies: the QRE converges with the Nash equilibrium that corresponds with the theory. Next, we investigate the properties of QRE in PD in Markov strategies by testing it against experimental data. For low levels of rationality, the found equilibrium manages to describe high cooperation. We derive the levels of rationality under which the intersection between Nash and QRE occurs. Lastly, our experimental data suggest that QRE serves as a dividing line between behavior with low...

This text may be downloaded for personal research purposes only. Any additional reproduction for other purposes, whether in hard copy or electronically, requires the consent of the author(s), editor(s). If cited or quoted, reference should be made to the full name of the author(s), editor(s), the title, the working paper or other series, the year, and the publisher. The author(s)/editor(s) should inform the Economics Department of the EUI if the paper is to be published elsewhere, and should also assume responsibility for any consequent obligation(s).

This paper surveys the theoretical work that has been done on majority rule and economic models of elections. Section I provides a n overview of the topic. Section 2 reviews the most important results that have been obtained about majority rule as an abstract collective choice rule. Section 3 identifies some alternative inferences that can be made from those results. Section 4 covers some models that include additional features that are present in political institutions where majority rule is used. Section 5 concentrates on some alternative election models and equilibrium concepts. Section 6 focuses on election models with abstentions and/or candidate uncertainty about voter behaviour. Section 7 compares and contrasts models where candidates are certain about what the voters' choices will be (contingent upon about the choices made by the candidates) and models where they are uncertain about those choices. Section 8 closes the survey by identifying some emerging areas of research.

We propose a novel approach to check whether individual behaviour in binary-choice participation games is consistent with the restrictions imposed by symmetric models. This approach allows in particular an assessment of how much cluster-heterogeneity a symmetric model can tolerate to remain consistent with its behavioural restrictions. We assess our approach with data from market-entry experiments which we analyse through the lens of ‘Exploration versus Exploration’ (EvE, which is equivalent to Logit-QRE) or of Impulse Balance Equilibrium (IBE). We find that when the symmetry assumption is imposed, both models are typically rejected when assuming pooled data and IBE yields more data-consistent estimates than EvE, i.e., IBE’s estimates of session and pooled data are more consistent than those of EvE. When relaxing symmetry, EvE (IBE) is rejected for 17% (42%) of the time. Although both models support cluster-heterogeneity, IBE is much less likely to yield over-parametrised specificat...

We propose a novel approach to check whether individual behaviour in binary-choice participation games is consistent with the restrictions imposed by symmetric models. This approach allows in particular an assessment of how much cluster-heterogeneity a symmetric model can tolerate to remain consistent with its behavioural restrictions. We assess our approach with data from market-entry experiments which we analyse through the lens of ‘Exploration versus Exploration’ (EvE, which is equivalent to Logit-QRE) or of Impulse Balance Equilibrium (IBE). We find that when the symmetry assumption is imposed, both models are typically rejected when assuming pooled data and IBE yields more data-consistent estimates than EvE, i.e., IBE’s estimates of session and pooled data are more consistent than those of EvE. When relaxing symmetry, EvE (IBE) is rejected for 17% (42%) of the time. Although both models support cluster-heterogeneity, IBE is much less likely to yield over-parametrised specificat...

We propose a novel approach to check whether individual behaviour in binary-choice participation games is consistent with the restrictions imposed by symmetric models. This approach allows in particular an assessment of how much cluster-heterogeneity a symmetric model can tolerate to remain consistent with its behavioural restrictions. We assess our approach with data from market-entry experiments which we analyse through the lens of ‘Exploration versus Exploration’ (EvE, which is equivalent to Logit-QRE) or of Impulse Balance Equilibrium (IBE). We find that when the symmetry assumption is imposed, both models are typically rejected when assuming pooled data and IBE yields more data-consistent estimates than EvE, i.e., IBE’s estimates of session and pooled data are more consistent than those of EvE. When relaxing symmetry, EvE (IBE) is rejected for 17% (42%) of the time. Although both models support cluster-heterogeneity, IBE is much less likely to yield over-parametrised specificat...

We unify and extend much of the literature on probabilistic voting in two-candidate elections. We give existence results for mixed and pure strategy equilibria of the electoral game. We prove general results on optimality of pure strategy equilibria visa -vis a weighted utilitarian social welfare function, and we derive the well-known "mean voter" result as a special case. We establish broad conditions under which pure strategy equilibria exhibit "policy coincidence," in the sense that candidates pick identical platforms. We establish the robustness of equilibria with respect to variations in demographic and informational parameters. We show that mixed and pure strategy equilibria of the game must be close to being in the majority rule core when the core is close to non-empty and voters are close to deterministic. This contraverts the notion that the median (in a one-dimensional model) is a mere "artifact." Using an equivalence between a class of models including the binary Luce model and a class including additive utility shock models, we then derive a general result on optimality visa -vis the Nash social welfare function.

This paper is concerned with the public policies that occur in economies with elections when political candidates estimate voting behavior with log-concave probabilistic voting estimators (e.g., normal estimators). We establish that, for a vector of policies to be the outcome of an election, it is both necessary and sufficient that these policies maximize the society's mean (or social) log-likelihood function. This implies: First, the set of possible electoral outcomes is convex. Second, there is an electoral equilibrium whenever the set of social alternatives is compact. This property which holds for all multidimensionalpolicy spaces does not use any special symmetry requirements on voter preferences. Third, under "cardinal probabilistic voting," every electoral outcome is also a maximum of a Nash type Social Welfare function. Fourth, in a finite population of m voters with independent probabilistic voting density functions a vector of policies is an electoral outcome if and only if it has the maximum estimated likelihood of receiving unanimous support. n DI 1D~st Va ELECTORAL OUTCOMES AND SOCIAL LOG-LIKELIHOOD MAXIMA*

This paper studies the Pareto optimality properties of policy proposals that are made by k(k > 2) strategic candidates that face uncertainty about the choices that the voters will make. Our first theorem shows that, under very general conditions, any proposal that is a best reply for a candidate is necessarily Pareto optimal. This theorem, in turn, implies that, under slightly stronger conditions, all candidate proposals that are made in a Nash equilibrium or sequentially are necessarily Pareto optimal. Our second theorem shows that, when these conditions are themselves slightly strengthened, any proposal outside of the Pareto set is strictly dominated by at least one proposal inside the Pareto set.

This paper studies societies which have probabilistic voting that is smooth, scalable and unbiased. Its results establish that, in such societies, the decisions of vote-seeking candidates who start at a common location'(such as the status quo for the society's policies and/or the same allocation of campaign resources) contain implicit rationality properties. In particular, it shows that in every such society there exist social utility functions which simultaneously rationalize the directional Nash behavior of candidates, the stationary electoral equilibria, and the noadegenerate local electoral equilibria which can occur at these locations. This is shown to be true both for unconstrained and for constrained sets of possible candidate locations. An example of such a utility function (which occurs in every one of the societies under consideration) is also provided.

This paper studies the policy outcomes that can be expected to occur when candidates are uncertain about voter behavior. Its analysis begins with an example that illustrates how the ' Comaner-Hinich effect' (i.e., the possibility of non-median outcomes) can occur under such circumstances. This example is then modified in ways which restore a median outcome. After this is done, the method of restoration is generalized to obtain a unidimensional median voter result for probabilistic voting models.

This paper is about game-theoretic models of electoral competitionwith an emphasis on models where there is probabilistic voting. Section 1 has (i) an example in which the voters' choices are assumed to be deterministic and (ii) an example in which the voters' choices are assumed to have probabilities that satisfy Luce's axiom of "independence from irrelevant alternatives". Section 2 has a more general model, which includes the two examples as special cases. Section 3 discusses some work that has been done on deterministic voting models. Section 4 discusses some work that has been done on probabilistic voting models. Forthcoming in: Methods and Applications of Statistics in the Social and Behavioral Sciences, Wiley

Our society's diploma of reliance on IT and our online world is developing daily. Cyberspace, the call given to the worldwide and dynamic domain, composed of the infrastructure of the statistics era consisting of the net networks and statistics and telecommunications structures has supplied extraordinary globalization that gives new opportunities, but additionally includes new challenges, risks, and threats. Knowledge of its threats, dealing with the risks, and constructing suitable prevention, defense, detection, evaluation, investigation, and recuperation is essential. Given the present-day assessment of the statistics safety and intrusion detection, there's without a doubt a want for a choice and manipulation framework to cope with problems like assault modeling, evaluation of detected threats, and choice of reaction actions. We look at the goals of designing a mathematical version for gamified cybercrime tracking in a community environment.

Our society's diploma of reliance on IT and our online world is developing daily. Cyberspace, the call given to the worldwide and dynamic domain, composed of the infrastructure of the statistics era consisting of the net networks and statistics and telecommunications structures has supplied extraordinary globalization that gives new opportunities, but additionally includes new challenges, risks, and threats. Knowledge of its threats, dealing with the risks, and constructing suitable prevention, defense, detection, evaluation, investigation, and recuperation is essential. Given the present-day assessment of the statistics safety and intrusion detection, there's without a doubt a want for a choice and manipulation framework to cope with problems like assault modeling, evaluation of detected threats, and choice of reaction actions. We look at the goals of designing a mathematical version for gamified cybercrime tracking in a community environment.

We study the Markov perfect equilibria (MPEs) of an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain. Players who reach agreement are removed from the network without replacement. We establish the existence of MPEs and show that MPE payoffs are not necessarily unique. A method for constructing pure strategy MPEs for high discount factors is developed. For some networks, we find that all MPEs are asymptotically inefficient as players become patient.

How important are leaders' actions in facilitating coordination? In this paper, we investigate their signaling role in a global games framework. A perfectly informed leader and a team of followers face a coordination problem. Despite the endogenous information generated by the leader's action, we provide a necessary and sufficient condition that makes the monotone equilibrium strategy profile uniquely ∆-rationalizable and hence guarantees equilibrium uniqueness. Moreover, the unique equilibrium is fully efficient. This result remains valid when the leader observes a noisy signal about the true state except full efficiency may not be obtained. We discuss the implications of our results for a broad class of phenomena such as adoption of green technology, currency attacks and revolutions.

A mathematical method of decision-making in which a competitive or cooperative situation is analyzed to determine the optimal course of action for an interested "player" is often called game theory. Game theory has very broad application in different sciences. Team sports tactical performance is considered from the aspects of data processing theory and the phenomenon of selective attention, as well as from the game theory. Team sports tactical performance is an asymmetric, sequential (of imperfect information), non-zero-sum game. In decision making, predictability in team sports is in fact bargaining, and the player has to use a mixed strategy for choosing option with highest expected utility. Player could choose a trembling hand equilibrium, to eliminate imperfect equilibrium. Strategic dominance conceipt can explain that a player could choose strategy which dominates between other possible strategies, and/or could be led by "team reasoning", too. In this article, the level of predictability of the most frequent tactical performance of one player in a team sport game is considered, reflecting outcomes both for the same team's tactical performance (co-players in one player's team), as well as for the opponent team's tactical performance. Four different possible situations during team sport competition could lead to considering utilities of one player's specific decisions.

Recent work has established that, in general, median voter results do not hold when there is probabilistic voting. This has, quite naturally, led to the following question: When, under such circumstances, will median outcomes occur? In this paper, it is shown that directly generalizing certain conditions that have previously been shown to be sufficient for multidimensional median voter results in deterministic voting models leads to conditions that are, themselves, sufftcient for median outcomes in probabilistic voting models. This generalization includes both discrete and continuous distributions of voters. In addition, it also applies to both unidimensional and multidimensional policy spaces.

Network routing has a great impact on the efficiency and reliability of the traffic network system in a real-world scenario. To date, achieving network-consistent performance is the main goal of many traffic network research studies. In this research, a mixed strategy game-theory model for network routing is proposed that discovers the optimal strategies that can be adopted by network route players in a network graph. This model has been validated by measuring the model outcomes using quantal response equilibrium (QRE) technique, which explores the players' noisy decisions by comparing the utilized optimal strategies with Nash equilibrium. The experimental results demonstrate that there is an equilibrium with a mixed strategy of a given network.

This research studied the strategies that players use in sequential adversarial games. We took the Rock-Paper-Scissors (RPS) game as an example and ran players in two experiments. The first experiment involved two humans, who played the RPS together for 100 times. Importantly, our payoff design in the RPS allowed us to differentiate between participants who used a random strategy from those who used a Nash strategy. We found that participants did not play in agreement with the Nash strategy, but rather, their behavior was closer to random. Moreover, the analyses of the participants’ sequential actions indicated heterogeneous cycle-based behaviors: some participants’ actions were independent of their past outcomes, some followed a well-known win-stay/lose-change strategy, and others exhibited the win-change/lose-stay behavior. To understand the sequential patterns of outcome-dependent actions, we designed probabilistic computer algorithms involving specific change actions (i.e., to d...

This paper studies two widely used models of political competitioncitizen-candidate and probabilistic votingto investigate the impact that asymmetries in single-peaked preferences have on two-party electoral competition. In a two-candidate equilibrium of the citizencandidate model, asymmetries determine which candidate proposes a more moderate platform. In the probabilistic voting model, they induce both parties to move their platforms in the direction of the asymmetry, and affect the probabilities of victory of the contenders, sometimes in unexpected ways: under a restriction on party preferences, more overprovision avoidance increases the probability of victory of the party proposing a larger public sector and vice versa. The final part of the analysis shows that consumers' risk aversion, prudence and a decreasingly effective government induce overprovision avoidance asymmetries, whereas consumers' risk neutrality, a constant-effective government and a property we call decreasing satiation induce shortfall avoidance asymmetries.

Existing models of multicandidate spatial competition with probabilistic voting typically predict a high degree of policy convergence, yet in actual elections candidates advocate quite divergent sets of policies. What accounts for this disparity between theory and empirical observation? I introduce two variations on the basic probabilistic vote model which may account for candidate policy divergence: 1) a model which incorporates candidate-specific variables, so that candidates may enjoy nonpolicy-related electoral advantages (or disadvantages); 2) a model which allows nonzero correlations between the random terms associated with voters' candidate utilities, thereby capturing situations where voters view two or more candidates as similar on nonpolicy grounds. I report candidate equilibrium analyses for each model, which show far greater policy divergence than exists under the standard probabilistic vote model. I then analyze the strategic logic which underlies these results.

In this paper I analyze the equilibrium in a probabilistic voting model where the candidates have preferences other than the maximization of the expected number of votes or the probability of win maximization. I derive the comparative statics for two voters and one-dimensional policy space. Each voter cares about both the policy platform and the identity of the candidate. It is shown that an increase in the value of exactly one vote causes each candidate to choose a position closer to that of its partisan voter. Numeric computation of equilibria show that these results can be generalized to three or more voters.

Cyber security is among the most complex and rapidly evolving issues and has been the focus of present day organizations. Cyber security risk management is the process of managing or reducing potentially harmful and uncertain events that posse as threats to cyber security. It involves looking at what could go wrong on the cyber space and deciding on ways to prevent or minimize their occurrences or effects. One of the prominent cyber security risk management techniques is the Game Theoretic Approach (GTA), which focuses on the use of resources, internal controls, information sharing, technical improvements, behavioral or organizational scale-ups and cyber insurance for cyber risk management. This paper presents a review of game theoretic-based model for cyber security risk management. Specifically, issues on modeling, some related works and significance of game theoretic approach to cyber security risk management are presented. Findings from the review revealed the peculiarities and specificity of each model. It is also revealed that the models are just evolving and require much improvement.

Measuring centrality in a social network, especially in bipartite mode, poses many challenges, for example, the requirement of full knowledge of the network topology, and the lack of properly detecting top-k behavioral representative users. To overcome the above mentioned challenges, we propose HellRank, an accurate centrality measure for identifying central nodes in bipartite social networks. HellRank is based on the Hellinger distance between two nodes on the same side of a bipartite network. We theoretically analyze the impact of this distance on a bipartite network and find upper and lower bounds for it. The computation of the HellRank centrality measure can be distributed, by letting each node uses local information only on its immediate neighbors. Consequently, one does not need a central entity that has full knowledge of the network topological structure. We experimentally evaluate the performance of the HellRank measure in correlation with other centrality measures on real-world networks. The results show partial ranking similarity between the HellRank and the other conventional metrics according to the Kendall and Spearman rank correlation coefficient.