In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable.

This paper defends judicial review on the grounds that judicial review is necessary for protecting a right to a hearing.  Judicial review is praised by its advocates on the basis of instrumentalist reasons, i.e., because of its desirable contingent consequences such as protecting rights, romoting democracy, maintaining stability, etc. We argue that instrumentalist easons for judicial review are bound to fail and that an adequate defense of udicial review requires justifying judicial review on non-instrumentalist grounds. A non-instrumentalist justification grounds judicial review in essential attributes of he judicial process. In searching for a non-instrumental justification we establish that judicial review is designed to protect the right to a hearing. The right to a hearing consists of hree components: the opportunity to voice a grievance, the opportunity to be rovided with a justification for a decision that impinges (or may have impinged) on one s rights and, last, the duty to reconsider the initial decision giving rise to the grievance. The right to a hearing is valued independently of the merit of the decisions generated by the judicial process. We also argue that the recent proposals to reinforce popular or democratic participation in shaping the Constitution are wrong because they are detrimental to the right to a hearing.

A review of Steven E. Landsburg's book More Sex is Safer Sex, the Unconventional Wisdom of Economics. The surprise 2005 best seller Freakonomics by Steven Levitt and Stephen Dubner launched a small genre of books by economists applying economic reasoning to everyday life and finding counterintuitive results. Mathematician and economist Steven Landsburg, whose online Slate column ``Everyday Economics predates the Levitt and Dubner volume, has now collected and expanded some of those columns to form the basis of his new book.In his book, Landsburg uses the ``weapons of evidence and logic, especially the logic of economics to draw surprising conclusions which run against common sense. ``If your common sense tells you otherwise, says Landsburg, ``remember that common sense also tells you the Earth is flat. In this review, scheduled to appear in the June/July 2008 issue of the Notices of the American Mathematical Society, we describe and discuss some of the issues and claims raised in Landsburg's book. For further discussion see the May 29 post in http://gilkalai.wordpress.com/ .

The Gibbard-Satterthwaite theorem states that every non-trivial voting method between at least 3 alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with non-negligible probability for every neutral voting method between 3 alternatives that is far from being a dictatorship.

The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distribution. This class contains the Normal, log Normal, Gamma, Weibull and many other distributions. The selection rules are the better than average  (² = 1) and the ²-better than average  rule, defined as follows. After the first item is selected, another item is admitted into the group if and only if its score is greater than ² times the average score of those already selected. Denote by Yk the average of the k first selected items, and by Tk the time it takes to amass them. Some of the key results obtained are: Under mild conditions, for the better than average rule, Yk less a suitable chosen function of log k converges almost surely to a finite random variable. When 1 ˆ’ F(x) = exp(-[x$\pm$ +h(x)]) , $\pm$>0 and h(x)/x$\pm$†’0 as x†’ˆ\v z, then Tk is of approximate order k2 . When ² > 1, the asymptotic results for Yk are of a completely different order of magnitude. Interestingly, for a class of distributions, Tk, suitably normalized, asymptotically approaches 1, almost surely for relatively small ² > 1, in probability for moderate sized ² and in distribution when ² is large.

Sexual selection theory states that male reproductive success is commonly limited by opportunities for fertilization, while female reproductive success is more often resource-limited. This creates higher selective pressure on males to attract mating partners as compared with females. Similar reasoning, when applied to plant reproduction, predicts higher investment in pollinator-attracting traits, such as nectar production, in male flowers than in female flowers. Contrary to this prediction, nectar production by female-phase flowers in the protandrous hermaphrodite shrub Salvia hierosolymita (Boiss.) (Lamiaceae) was significantly higher than in male-phase flowers in two populations over three years. Female-biased nectar production may reflect selection for pollinator attraction by female-phase flowers, possibly due to pollen limitation. In support of this interpretation, (a) the number of pollen grains on female-phase stigmas was substantially higher than on male-phase stigmas, suggesting that the female phase received more insect visits ; (b) the number of germinating pollen grains in female-phase styles only slightly exceeded the number of ovules per flower, therefore pollen availability may restrict female fitness. Proportions of female-phase flowers decreased from the base of the inflorescences towards their top. This creates a vertical gradient of nectar production, which may help reduce geitonogamous pollination by effecting pollinator behavior.

The high cost of searching for employers borne by prospective employees increases friction in the labor market and inhibits formation of efficient employer-employee relationships. It is conventionally agreed that mechanisms that reduce the search costs (e.g., internet portals for job search) lower unemployment and improve overall welfare. We demonstrate that a reduction of the search costs may have the converse effect. We consider a labor market in which workers can either establish a long-term relationship with an employer by being productive, or shirk and move from one employer to the next. In addition, the workers can signal to a potential employer their intention to be productive. We show that lower search costs lead to fewer employees willing to exert effort and, in a separating equilibrium, to more individuals opting to stay completely out of the job market and remain unemployed. Furthermore, we show that lower search costs not only deteriorate the market composition, but also impair efficiency by leading to more expensive signaling in a separating equilibrium.

In the role of judges in bankruptcy problems, people may prescribe various just divisions of the available goods to claimants who have rights for them. Two widespread division rules are equality and proportionality. A less known rule is the Talmudic "Shnaim Ohazin" principle, whose basic rationale is applying an equal division only to that part of the goods which is genuinely under dispute. This paper demonstrates that the ratio of subjects that prefer the "Shnaim Ohazin" principle over equality and proportionality can be increased by a simple framing manipulation. These results suggest that framing effects might be a prevalent factor in the realm of distributive justice.

John F. Nash, Jr., submitted his Ph.D. dissertation entitled Non-Cooperative Games to Princeton University in 1950. Read it 58 years later, and you will find the germs of various later developments in game theory. Some of these are presented below, followed by a discussion concerning dynamic aspects of equilibrium.

Question: Which ecological factors favor the transition from plants with hermaphrodite flowers to monoecious plants with separate male and female flowers on the same individual?Mathematical methods: ESS computation in sex allocation models Key assumptions: Within a flower, costs of attraction, pollen production, style/ovary and fruit with seeds are assumed fixed. Often costs of fruit with seeds outweigh other costs. Female flowers produce more seeds than hermaphrodite flowers, due to less pollen-stigma interference.Conclusions: When sex allocation is female-biased at the flower level, plants respond by producing either male flowers or flowers without fruit. Hermaphroditism evolves to andromonoecy (male and hermaphrodite flowers on the same plant) and then to monoecy. In species with large fruits, sex allocation is female-biased at the flower level and the production of male flowers is favored. This facilitates the production of female flowers. The alternative route via gynomonoecy (female and hermaphrodite flowers on the same plant) is improbable since it requires unrealistically high levels of seed production in female flowers. Monoecious species are likely to have: (i) small, inexpensive flowers, (ii) large, costly fruits and seeds, and (iii) high fertilization rates.

Large red bowl-shaped flowers characterize the Mediterranean poppy guild  plants, andwere suggested to reflect convergence for beetle pollination. However, the earliest-bloomingspecies in this guild, Anemone coronaria (L.), starts flowering about a month before beetleemergence. Early flowering can be adaptive if the plant receives sufficient pollination by othermeans during this period. We investigated A. coronaria s pollination prospects throughout itsflowering season by monitoring its flowering phenology, the composition of the surroundinginsect community, and insect visitors. Clear protogyny precluded self pollination, and anthesisoccurred gradually over several days. Released pollen was quickly collected by insects,suggesting no major role for wind pollination. Beetles, flies and bees were trapped at the studysite throughout the flowering period. Honeybees were the main anemone visitors during the firstseven weeks of flowering, and were joined by Glaphyrid beetles in the remaining three weeks.Early- and late-blooming flowers had similar female reproductive success. We propose thateffective pollination by honeybees may allow anemones to bloom in early spring and therebyreduce competition for pollinators with later-blooming species. Our results support previousevidence for pollination of red flowers by bees, and for the importance of generalization inpollination interactions in heterogeneous environments.

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff

People's actions often deviate from rationality, i.e., self-interested behavior. We propose a paradigm called rule-rationality, according to which people do not maximize utility in each of their acts, but rather follow rules or modes of behavior that usually-but not always-maximize utility. Specifically, rather than choosing an act that maximizes utility among all possible acts in a given situation, people adopt rules that maximize average utility among all applicable rules, when the same rule is applied to many apparently similar situations. The distinction is analogous to that between Bentham's "act-utilitarianism" and the "rule-utilitarianism" of Mill, Harsanyi, and others. The genesis of such behavior is examined, and examples are given. The paradigm may provide a synthesis between rationalistic neo-classical economic theory and behavioral economics.

Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical meaning. They provide a formal framework that subsumes both classical boolean logic concerned with sets and subsets and quantum logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel notion that is free of linear algebra.

In the interest of improving their decision-making, individuals revise their opinions on the basis of samples of opinions obtained from others. However, such a revision process may lead decision-makers to experience greater confidence in their less accurate judgments. We theorize that people tend to underestimate the informative value of independently drawn opinions, if these appear to conflict with one another, yet place some confidence even in the "spurious consensus" which may arise when opinions are sampled interdependently. The experimental task involved people s revision of their opinions (caloric estimates of foods) on the basis of advice. The method of sampling the advisory opinions (independent or interdependent) was the main factor. The results reveal a dissociation between confidence and accuracy. A theoretical underlying mechanism is suggested whereby people attend to consensus (consistency) cues at the expense of information on interdependence. Implications for belief-updating and for individual and group decisions are discussed.

We consider stochastic dynamics whose expected (average) vector field is not necessarily continuous. We generalize the ordinary differential equation method for analyzing stochastic processes to this case, by introducing leading functions that 'lead  the stochastic process across the discontinuities, which yields approximation results for the asymptotic behavior of the stochastic dynamic. We then apply the approximation results to the classical best-response dynamics used in game theory.

R. J. Aumann and J. H. Dr¨ze (2008) define a rational expectation of a player i in a game G as the expected payo of some type of i in some belief system for G in which common knowledge of rationalityand common priors obtain. Our goal is to characterize the set of rational expectations in terms of the game's payoff matrix. We provide such a characterization for a specific class of strategic games, calledsemi-elementary, which includes Myerson's "elementary" games.