Battle of the Sexes

ecology n. 1. The division of biology that treats of the relations between organisms and their environment. 2. Sociol. The study of human populations in terms of physical environment, spatial distribution, and cultural characteristics. Funk & Wagnalls Canadian College Dictionary, 1986. Do experiments with a single Prisoner's Dilemma payoff matrix apply to all PDs? Do they ever apply to games that are not PDs? We describe a two-dimensional payoff space of the twelve 2 × 2 games that allows us to sample payoff matrices in a controlled fashion. Using examples from evolutionary tournament play and from reinforcement learning strategies, we show that resulting populations can vary significantly across the payoff plane and that the boundaries of the ordinal games are not the boundaries for behaviour, evolution or learning. 2 C and D are also used to identify the player's choices of Cooperate or Defect. We follow this convention when it is obvious the reference is to a move not a payoff. 3 If C = D, an alternative normalization is required. 4 To locate any symmetric game (c,d,t,s) on this plane, map c to C(= 3 in this case), d to D(= 1). Values of S and T are computed by linear transformations:

ecology n. 1. The division of biology that treats of the relations betwe en organisms and their environment. 2. Sociol. The study of human populations in terms of physical environ- ment, spatial distribution, and cultural characteristics . Funk & Wagnalls Canadian College Dictionary, 1986. Do experiments with a single Prisoner's Dilemma payoff matr ix apply to all PDs? Do they

Social situations can be modeled as games with payoff struc- tures. The complexity of the situation emerges from the pattern of pay- offs. Inferring the outcome of the game from the payoff matrix is the conventional approach to describing, predicting or prescribing behaviour of participants. This approach makes a strong assumption of rationality of the players and suffers from other drawbacks as well. While Nash (8) proved a mixed equilibrium always exists, this appealing universality comes at a price. Mixed equilibria are not a natural and credible model of decision-making behaviour. Indeed, it has been shown that efficient algorithms to compute mixed equilibria likely do not exist for all games. (3) The pure Nash equilibrium, a more appealing model of behaviour, fails on universality: a subset of games - and a growing proportion as the number of players and choices increases - do not possess a pure Nash equilibrium. Miller (5),(6) describes unpublished research in which he took a ...

As female primates carry and nurse the fetus, it naturally falls on them to rear the o¤spring. On the assumption that males are at least equally adept at obtaining food, it follows that they generate a surplus which they might either share with females or consume themselves. This choice lies at the heart of an evolutionary battle of the sexes. If females suceed in obtaining a large share of the surplus, there is little scope for size dimorphism between males and females; otherwise males can use the surplus to sustain larger and stronger bodies, which are advantageous in sexual competition with other males. Besides competing with males, females may compete with each other. Moreover, dependency may coincide with sexiness and such dependency can persist. This paper examines these ideas in a game-theoretic setting. The position of women in technologically advanced societies generates numerous questions. Is there a 'glass ceiling' ? Are women signi…cantly disad-¤ Part of this paper was presented at the World Congress of the Game Theory Society under the title of "Female Competition, Near-Monogamy and Sexual Dimorphism; An Evolutionary and Game-Theoretic Approach." The authors are grateful to an anonymous referee, Robin Dunbar, Mike Ball and participants of seminars at the First World Congress of the Game Theory Society and the University of Liverpool Department of Applied Mathematics. The authors are also grateful to Jolanda van den Berg and Dolores Holtz for editorial comments.

As female primates carry and nurse the fetus, it naturally falls on them to rear the o¤spring. On the assumption that males are at least equally adept at obtaining food, it follows that they generate a surplus which they might either share with females or consume themselves. This choice lies at the heart of an evolutionary battle of the sexes. If females suceed in obtaining a large share of the surplus, there is little scope for size dimorphism between males and females; otherwise males can use the surplus to sustain larger and stronger bodies, which are advantageous in sexual competition with other males. Besides competing with males, females may compete with each other. Moreover, dependency may coincide with sexiness and such dependency can persist. This paper examines these ideas in a game-theoretic setting

Female primates carry and nurse the fetus, and thus have the …rst responsibility for rearing the o¤spring. Assuming males are at least equally adept at obtaining food, males might either share surplus food with females or consume the food themselves. The distribution of this surplus is the subject of a battle of the sexes. If females succeed in obtaining a large share of the surplus, then there is little size dimorphism between males and females; otherwise males might use the surplus themselves to become larger and stronger, and to engage in sexual competition with other males. Besides competing with males, females may compete with each other. Dependency may coincide with sexual competitiveness (sexiness). This paper introduces these ideas in a game theoretic setting and derives a simple bound, called the '®-male condition, on the male 'sexiness' required for a nonsupportive strategy to be worthwhile.

Economic theories of legal compliance emphasize legal sanctions, while psychological and sociological theories stress the perceived legitimacy of law. Without disputing the importance of either mechanism, we test a third way that law affects behavior, an expressive theory that claims law influences behavior by creating a focal point around which individuals coordinate. The focal point theory makes three claims: (1) that the need for coordination is pervasive because "mixed motive" games involving coordination model common disputes; (2) that law, by publicly endorsing a particular equilibrium, tends to call the players' attention to that outcome; and (3) that, in such games, any third-party cheap talk that calls the players' attention to a particular equilibrium tends to produce that equilibrium. After explaining the first and second claim, we offer an experimental test of the third. Specifically, we investigated how various forms of third party cheap talk influence the behavior of subjects in a Hawk/Dove or Chicken game. Despite the players' conflicting interests, we found that messages highlighting an equilibrium tend to produce that outcome. Most striking, this result emerged even when the message was selected by an overtly random, mechanical process. We obtained a similar result when the message was delivered by a third-party subject; the latter effect was significantly stronger than the former only when the subject speaker was selected by a merit-based process. These results suggest that, in certain circumstances, law generates compliance not only by sanctions and legitimacy, but also by facilitating coordination around a focal outcome. For their comments on an earlier draft, the authors thank Rachel Croson, Dhammika Dharmapala, Shari Diamond, Tom Ginsburg, Tom Miles, Jeff Rachlinsky, Larry Ribstein, Tom Ulen, members of the research committees of the American Bar Foundation, and the participants at law faculty workshops at Connecticut, Florida State, Northwestern, and Virginia and at the law and economics workshop at Michigan and Southern California. We also thank Emily Solberg for research assistance. We thank the American Bar Foundation,

O traballo analiza con enfoque comparado un corpus de catro novelas sobre o exilio republicano de 1939 relacionadas coas mulleres de Galicia. Duas delas foron publicadas por escritoras que viviron o exilio uns vinte anos despois do inicio da diaspora. As outras duas foron editadas recentemente en galego por autores que crearon personaxes a partir de figuras de exiliadas galegas reais. Exponense as experiencias vitais e amosanse trazos e citas dos textos antes de chegar as conclusions.

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

Sexual conflict has been suggested to be important in the evolution of reproductive traits, with much recent theoretical and empirical evidence emphasizing its role in generating sexually antagonistic coevolution in the context of promiscuous mating. Here we shift attention to the role of sexual conflict in a monogamous mating context. Conflicts can arise, for example, when males are successful in imposing monandry at a cost to female fitness, or when females impose monogyny on males. Conflict over remating can also generate monogamy. For example, when males invest heavily in attempting to impose female monandry, the cost of their investment may prevent them from securing additional mates. We emphasize that sexual conflicts need not always generate sexually antagonistic coevolution, and that it is important to consider whether mating decisions are controlled primarily by males or females. Finally, we briefly discuss approaches to distinguish between conflict and classical modes of s...

Deriving advice that can in fact be utilized by boundedly rational decision makers is a central function of modeling choice making. We illustrate why this role is not being fulfilled well by standard models of full rationality and that theories of bounded rationality are needed not only for better predictions, but also for developing better advice. Our main point is that one cannot succeed here without studying how theories of bounded rationality causally influence the behavior of boundedly rational individuals. In view of such a causal role of theories we discuss how advice of a theory of boundedly rational behavior can become known, be followed among boundedly rational individuals and still be good advice. of explicating them an important one. Second, the actual use of the term "rational" varies so much that even the most careful description will not reveal a common conceptual core. Avoiding part of the challenge, traditional rational choice theorists have not paid much attention to the everyday or common use of the term "rational" or to actual behavior. They established their standards of rationality -thus fixing the meaning of the term "rational" -independently of or even counter to the facts. For instance, even if most individuals used the term "irrational" for characterizing polluting behavior in an n-person "public bads'" experiment, the typical rational choice theorist would tend to classify the participants' behavior as "rational". As a matter of fact, if many people should say that individuals who do not co-operate in a one-off classical two-person prisoners' dilemma situation are behaving "irrationally", this will not make the rational choice theorist think twice. If philosophers like Edward insist that "backward induction" in the finitely repeated prisoners' dilemma must be given up since it just cannot be rational not to co-operate at least to some extent in such situations, the adherent of theories of perfect rationality will remain unmoved. Her concept of "full rationality" is formed "deductively" rather than "inductively" and justified by a priori normative rather than a posteriori descriptive reasoning. Common usage of the terms "rational" and "irrational" as well as philosophical analyses starting from common intuitions seem simply misguided to the traditional rational choice theorist. She would claim that neither actual behavior nor actual usage of terms should determine the "proper" meaning of the term "rational" in a scientific or philosophical context. The "a priori" approach is clearly a possibility. But it must be noted, too, that by establishing standards of rationality independently of or counter to the facts, the rational choice theorist turns "rationality" into what may be called a "counterfactual concept". If we take such an approach to its extreme, we get a very refined rationality-concept that may be appealing to the theorist, in particular the decision and the game theorist. However, it neither relates directly to the understanding of real people, nor does it apply to their behavior, nor can it form

argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we contest this assertion by showing that a random strategy in a particular quantum (Hawk-Dove) game is unique to the quantum game. In other words, one cannot obtain the equilibrium solution of the quantum Hawk-Dove game in the classical Hawk-Dove game. Moreover, we provide an analytical solution to the quantum 2 × 2 strategic form Hawk-Dove game using randomly mixed strategies. The random strategy which we describe is Pareto optimal with their payoff classically unobtainable. We compare the quantum strategies to correlated strategies and find that the quantum Hawk-Dove game or quantum Prisoner's dilemma yields the Nash equilibrium solution.

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

Sexual conflict has been suggested to be important in the evolution of reproductive traits, with much recent theoretical and empirical evidence emphasizing its role in generating sexually antagonistic coevolution in the context of promiscuous mating. Here we shift attention to the role of sexual conflict in a monogamous mating context. Conflicts can arise, for example, when males are successful in imposing monandry at a cost to female fitness, or when females impose monogyny on males. Conflict over remating can also generate monogamy. For example, when males invest heavily in attempting to impose female monandry, the cost of their investment may prevent them from securing additional mates. We emphasize that sexual conflicts need not always generate sexually antagonistic coevolution, and that it is important to consider whether mating decisions are controlled primarily by males or females. Finally, we briefly discuss approaches to distinguish between conflict and classical modes of sexual selection, as this highlights difficulties associated with deciding whether monogamy is enforced by one sex or the other. We suggest that documenting the current fitness consequences of mate choice and mating patterns provides insight into the relative importance of classic and conflict modes of selection.

Sexual conflict has been suggested to be important in the evolution of reproductive traits, with much recent theoretical and empirical evidence emphasizing its role in generating sexually antagonistic coevolution in the context of promiscuous mating. Here we shift attention to the role of sexual conflict in a monogamous mating context. Conflicts can arise, for example, when males are successful in imposing monandry at a cost to female fitness, or when females impose monogyny on males. Conflict over remating can also generate monogamy. For example, when males invest heavily in attempting to impose female monandry, the cost of their investment may prevent them from securing additional mates. We emphasize that sexual conflicts need not always generate sexually antagonistic coevolution, and that it is important to consider whether mating decisions are controlled primarily by males or females. Finally, we briefly discuss approaches to distinguish between conflict and classical modes of s...

A genetic algorithm incorporating mutation and crossing-over was used to investigate the evolution of social behaviour in repeated Prisoner's Dilemma, Chicken (Hawk-Dove), Battle of the Sexes, and Leader games. The results show that the strategic structure of an interaction has a crucial determining effect on the type of social behaviour that evolves. In particular, simulations using repeated Prisoner's Dilemma and Chicken (Hawk-Dove) games lead to the emergence of genes coding for symmetric reciprocity and the evolution of mutual cooperation, whereas simulations using repeated Battle of the Sexes and Leader games lead to nearfixation of genes coding for asymmetric strategic choices and the evolution of coordinated alternating reciprocity. A mechanism is suggested whereby, in games with asymmetric equilibrium points, coordinated alternating reciprocity might evolve without insight or communication between players.

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

In situations where people have an incentive to coordinate their behavior, law can provide a framework for understanding and predicting what others are likely to do. According to the focal point theory of legal compliance, the law's articulation of a behavior can sometimes create self‐fulfilling expectations that it will occur. Existing theories of legal compliance emphasize the effect of sanctions or legitimacy; we argue that, in addition to sanctions and legitimacy, law can also influence compliance simply by making one outcome salient. We tested this claim in two experiments where sanctions and legitimacy were held constant. Experiment 1 demonstrated that a mandatory legal rule operating in a property dispute influenced compliance only when there was an element of coordination. Experiment 2 demonstrated that a default rule in a contract negotiation acted as a focal point for coordinating negotiation decisions. Both experiments confirm that legal rules can create a focal point...

Contrary to the widespread belief that game repetition induces conciliatory behavior, in a repeated battle of the sexes where player 1 values the future and player 2 is myopic, player 1 is more inclined through conflicting behavior to risk a conflict in the present when the future is important, and/or there are many periods left in the game. Should players choose conflict today to reap benefits tomorrow? The results in today's literature are mixed. Folk theorem arguments (Fudenberg and Maskin, 1986) exemplified by repeating the prisoner's dilemma (Axelrod, 1984) are often taken to imply cooperation in long-term relationships. This result is often applied uncritically out of context. Skaperdas and Syropoulos (1996) equip each agent with a resource, which can be allocated into production versus arms. They show that increased importance of the future may harm cooperation. This article considers neither the prisoner's dilemma nor resource division into production versus arms, but considers the repeated battle of the sexes in Table 1 where a 1 zb 1 zt 1 , b 2 za 2 zt 2 and where a 1 zd 1 , b 2 Nd 2 ,or a 1 Nd 1 , b 2 zd 2. Does increased importance of the future induce conciliatory

The article shows that in a game with multiple equilibria, where one player estimates that there is at least a minuscule probability that the other player acquiesces, then conflict is inevitable if both players value the future sufficiently highly.

Question: How can the evolution of turn-taking be explained in species without language? Features of model: Using a genetic algorithm incorporating mutation and crossover, we studied noisy decision making in three repeated two-player games in which we predicted on theoretical grounds that cooperative turn-taking would evolve and three games in which we expected synchronized cooperation to evolve. Ranges of key variables: We set population size to 20, number of rounds to be played by each pair in each generation to 200, and number of evolutionary generations to 2000, and we repeated each simulation 10 times to check the stability of the results. Results: Cooperative turn-taking and (unexpectedly) a form of double turn-taking evolved in the alternation games, and joint cooperation evolved in the synchronization games. We propose a mechanism to explain how cooperative turn-taking can evolve mechanically, even without communication or insight, as it did in our simulations.

En 2020 el autor Suso de Toro publicaba Un señor elegante, novela que narra la vida del doctor santiagués Ramón Baltar, una de las personas implicadas en la Operación Termópilas que intentó acabar con la vida del dictador Francisco Franco en la década de los 40. Con esta importante obra el novelista volvía a reclamar su lugar en las letras peninsulares tras un complicado periodo personal a causa de su imbricación política y social durante la primera década del presente siglo. En esta entrevista el autor reflexiona sobre el periodo transcurrido entre la publicación del libro-entrevista Conversas con Suso de Toro (Xerais, 2005), la literatura, así como sobre la evolución de varios de los temas que pueblan su ingente obra narrativa y ensayística. AP [Antonio Pedrós-Gascón]: ¿Cómo entiendes que ha evolucionado tu vida desde la publicación en 2005 del libro Conversas con Suso de Toro?

Resumo: Neste traballo faise un repaso á produción narrativa de Carvalho Calero constituída por nove pezas literarias. Faise unha clasificación abordando as crónicas e a narrativa infantil e tamén textos tan emblemáticos como Aos amores seródios. Facemos tamén unha aproximación á celebrada obra Scórpio deténdonos nas múltiples e diversas relacións que o protagonista da narración mantén con varias mulleres.

The paper models strategic monetary-…scal interactions in the aftermath of the global …nancial crisis-in a single country as well as a monetary union. It depicts both the shortterm (stabilization) perspective and the long-term (sustainability) perspective, and the link between them. This is done in a game theoretic framework that allows for revisions of actions, deterministic or stochastic. In addition, we consider incomplete information about economic conditions, and di¤erent types of government. We …nd that, under ambitious …scal policies, a legislated long-term monetary commitment may: (i) reduce the risk of a double-dip recession and de ‡ation in the short-term, and at the same time (ii) facilitate the 'exit strategy'of monetary policy, ie prevent sub-optimally high future in ‡ation caused by …scal spillovers. Our analysis thus implies that an explicit numerical target for average in ‡ation may play the role of a monetary 'credibility insurance'over all phases of the business cycle, and is bene…cial especially in countries facing …scal stress.

The authors examined how gender stereotypes affect negotiation performance. Men outperformed women when the negotiation was perceived as diagnostic of ability (Experiment 1) or the negotiation was linked to gender-specific traits (Experiment 2), suggesting the threat of negative stereotype confirmation hurt women's performance relative to men. The authors hypothesized that men and women confirm gender stereotypes when they are activated implicitly, but when stereotypes are explicitly activated, people exhibit stereotype reactance, or the tendency to behave in a manner inconsistent with a stereotype. Experiment 3 confirmed this hypothesis. In Experiment 4, the authors examined the cognitive processes involved in stereotype reactance and the conditions under which cooperative behaviors between men and women can be promoted at the bargaining table (by activating a shared identity that transcends gender).

Study of pattern formation in three species spatio-temporal food chain models with the help of amplitude equations within Turing domain is a much less explored area compared to that of two species prey-predator models. These models play a vital role in understanding the resource-consumer interactions at the successive trophic levels of respective ecosystems. In this work, we consider the spatio-temporal extension of a three species food chain model with Holling type-II functional response to describe the grazing pattern of both the intermediate and top predator populations. Conditions for Turing instability are derived. The thresholds for emergence and stability of various Turing patterns near the Turing bifurcation boundary are obtained with the help of amplitude equations using weakly nonlinear analysis. The analytical results are further verified with the help of extensive numerical simulations for the complete nonlinear model and both the results are compared for different sets of parameter values.

Simple game experiments of the reward allocation, dictator and ultimatum type are used to demonstrate that true explanations of social phenomena cannot conceivably be derived in terms of the perfect rationality concept underlying neo-classical economics. We explore in some depth, if speculatively, how experimental game theory might bring us closer to a new synthesis or at least the nucleus of a general theory of ‘games and boundedly rational economic behavior’ with enhanced explanatory power.

In this paper, the authors examine a phenomenon, which has been observed in the grocery channel recently, called ''guarantee of margins''. Guarantee of margins is a clause inserted in the contract between the manufacturer and the retailer that ensures a certain profit margin for the retailer irrespective of the retail price hershe is charging. In the wake of increasing retail level concentration and competition, the retailers' ability of extracting these guarantees from the manufacturers is a clear demonstration of retailer power. Our analysis provides new insights into the growing debate about the power shift to the retailers in the grocery channel. It shows how the retailers can and have utilized this power to maintain their margins by extracting these guarantees from the manufacturers. We specifically model the ability of the retailers to play one manufacturer against another and to use the private label brands as a lever to extract more profits.

The paper models strategic monetary-…scal interactions in the aftermath of the global …nancial crisis-in a single country as well as a monetary union. It depicts both the shortterm (stabilization) perspective and the long-term (sustainability) perspective, and the link between them. This is done in a game theoretic framework that allows for revisions of actions, deterministic or stochastic. In addition, we consider incomplete information about economic conditions, and di¤erent types of government. We …nd that, under ambitious …scal policies, a legislated long-term monetary commitment may: (i) reduce the risk of a double-dip recession and de ‡ation in the short-term, and at the same time (ii) facilitate the 'exit strategy'of monetary policy, ie prevent sub-optimally high future in ‡ation caused by …scal spillovers. Our analysis thus implies that an explicit numerical target for average in ‡ation may play the role of a monetary 'credibility insurance'over all phases of the business cycle, and is bene…cial especially in countries facing …scal stress.

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

Deriving advice that can in fact be utilized by boundedly rational decision makers is a central function of modeling choice making. We illustrate why this role is not being fulfilled well by standard models of full rationality and that theories of bounded rationality are needed not only for better predictions, but also for developing better advice. Our main point is that one cannot succeed here without studying how theories of bounded rationality causally influence the behavior of boundedly rational individuals. In view of such a causal role of theories we discuss how advice of a theory of boundedly rational behavior can become known, be followed among boundedly rational individuals and still be good advice.

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We use the self-tuning Experience Weighted Attraction model with repeated-game strategies as a computer testbed to examine the relative frequency, speed of convergence and progression of a set of repeated-game strategies in four symmetric 2 × 2 games: Prisoner's Dilemma, Battle of the Sexes, Stag-Hunt, and Chicken. In the Prisoner's Dilemma game, we find that the strategy with the most occurrences is the "Grim-Trigger." In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences. In the Stag-Hunt and Chicken games, the "Win-Stay, Lose-Shift" and "Grim-Trigger" strategies are the ones with the most occurrences. Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

This paper deals with the morphogenesis of spatialized cooperative relations and with the role of proximity in the evolution, persistence and coexistence of various local strategies. The first part is devoted to a presentation of the analysis of cooperative relations in the evolutionary game theory. In the second part of the paper are presented various simulations on the emergence and evolution of localized cooperative relations, based on endogenous mutations and genetic algorithms. They reveal that a cooperative behavior is a stable, even if complex strategy, and that its emergence and diffusion are favored by the spatial character of inter firms relations. In addition, the results confirm that various strategies can locally coexist and be maintained, generally temporarily.

We report an experiment that uses the strategy method (Selten 1967) to elicit subjects' general strategy for playing any 2-person 3x3-game with integer payoffs between 0 and 99. Each two subjects' strategies play 500000 games in each of the 5 tournaments. For games with pure strategy equilibria (ca. 80%), the frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, in which there is equilibrium play in 98% of all games with only one pure equilibrium. In games with more than one pure equilibrium, a tendency towards the selection of the one with the maximum joint payoff is observed. For games without pure equilibria, subjects' strategies do not search for mixed equilibria. The strategy programs are based on much simpler strategic concepts combined in various ways. The simplest one is MAP, maximal average payoff, the strategy which maximizes the sum of the three payoffs obtainable against the possible choices of the other player. BR-MAP, the best reply to MAP, and BR-BR-MAP, the best reply to BR-MAP, are also important ingredients of the strategy programs. Together these three form a hierarchy to which we refer to as the best-reply cascade.

We report the results of experiments designed to test the impact of social status on learning in a coordination game. In the experiment, all subjects observe the play of an agent who either has high status or low status. In one treatment the agent is another player in the game; in the other the agent is a simulated player. Status is assigned within the experiment based on answers to a trivia quiz. The coordination game has two equilibria: one is payoff-dominant but risky, and the other is risk-dominant. The latter is most commonly chosen in experiments where there is no coordination device. We find that a commonly observed agent enhances coordination on the payoff-dominant equilibrium more often when the agent has high status.

An evolutionary battle-of-the-sexes game is proposed to model the opinion formation on networks. The individuals of a network are partitioned into different classes according to their unaltered opinion preferences, and their factual opinions are considered as the evolutionary strategies, which are updated with the birth-death or death-birth rules to imitate the process of opinion formation. The individuals finally reach a consensus in the dominate opinion or fall into ͑quasi͒stationary fractions of coexisting mixed opinions, presenting a phase transition at the critical modularity of the multiclass individuals' partitions on networks. The stability analysis on the coexistence of mixed strategies among multiclass individuals is given, and the analytical predictions agree well with the numerical simulations, indicating that the individuals of a community ͑or modular͒ structured network are prone to form coexisting opinions, and the coexistence of mixed evolutionary strategies implies the modularity of networks.

Er zaten zo’n 25 docenten in de zaal. Ze waren afgereisd naar mijn inleiding over speltheorie. Ik gebruikte anderhalf uur van hun tijd. Het gevangenenprobleem kwam langs, ik had het over acties en strategieen, en the battle of the sexes liet zien dat niet ieder spel een oplossing in zuivere strategieen heeft. Na afloop hoorde ik geklap en werd mij een envelop van een boekhandel overhandigd. Ik vermoedde een boekenbon. Zonder de envelop open te maken riep ik: 'Deze gaan we veilen. De hoogste bieder wint!' Opgewonden bespraken de deelnemers hun biedingsstrategie. Bijna iedereen schreef een bod op een papiertje. Goed afgeschermd want niemand hoefde hun bod te zien. Toen wist ik al dat het hoogste bod de boekenbon zou overtreffen.

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

Several quantum versions of the battle of the sexes game are analyzed. Some of them are shown to reproduce the classical game. In some, there are no Nash quantum pure equilibria. In some others, the payoffs are always equal to each other. In others still, all equilibria favor Alice or Bob depending on a phase shift of the initial state of the system. Explicit detailed calculations are for the first time exhibited.

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

While the Supreme Court declined an early invitation to resolve challenges to the Patient Protection and Affordable Care Act (ACA or the Act), a split between the United States Courts of Appeals for the Sixth Circuit (sustaining the ACA's "individual mandate") and the Eleventh Circuit (striking it down) ultimately compelled the Court to grant certiorari in a series of cases challenging the constitutional validity of the new federal health care law. In addition to deciding the fate of this centerpiece of the Obama Administration's regulatory agenda, the Court's decision will likely affect Commerce Clause doctrine-and related doctrines-for years or even decades to come. Litigants, judges, and academic commentators have focused on whether the Court's "economic activity" test, as set forth in United States v. Lopez, permits the individual mandate. This Article approaches the constitutionality of that provision from a novel perspective, one that proves essential in applying past Commerce Clause decisions, including Lopez, to the ACA and in appreciating the real stakes involved in upending the individual mandate. By analyzing the Court's Commerce Clause jurisprudence through the lens of game theory, we expose common features of games that have resulted in limiting state powers on the dormant side of Commerce Clause doctrine, and in sustaining and restricting congressional powers on the affirmative side. Applying such games as "the prisoners' dilemma," "the driving game," and "the battle of the sexes" yields critical insights about the nature and limits of state and federal regulatory powers. Our game-theoretical analysis shows that although debates have centered on the role of the individual mandate in solving a micro-level separating game among low-risk individuals who do not purchase insurance and high-risk individuals who cannot afford it, a more compelling account focuses on the Act's role in solving a macro-level separating game played among the states. By comparing the ACA to several important historical policy splits among statespublic accommodations laws, abortion funding, the death penalty, civil remedies for violent crimes against women, and same-sex marriage-we demonstrate

In this paper I quantize the stag hunt game in the framework proposed by Marinatto and Weber which, is introduced to quantize the Battle of the Sexes game and gives a general quntization scheme of various game theories. Then I discuss the Nash equibilium solution in the cases of which starting strategies are taken in both non entangled state and entangled state and uncover the structure of Nash Equilibrium solutions and compare the case of the Battle of the Sexes game. Since the game has 4 parameters in the payoff matrix has rather rich structure than the Battle of the Sexes game with 3-parameters in the payoff matrix, the relations of the magnitude of these payoff values in Nash Equilibriums are much involuved. This structure is uncovered completly and it is found that the best strategy which give the maximal sum of the payoffs of both players strongly depends on the initial quntum state. As the bonus of the formulation the stag hunt game with four parameters we can discuss various...