An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative ("mutant") strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper, we address the question of what happens when the size of the game increases: does an ESS exist for "almost every large" game? Letting the entries in the n x n game matrix be randomly chosen according to an underlying distribution F, we study the number of ESS with support of size 2. In particular, we show that, as n goes to infinity, the probability of having such an ESS: (i) converges to 1 for distributions F with "exponential and faster decreasing tails" (e.g., uniform, normal, exponential); and (ii) it converges to 1 - 1/sqrt(e) for distributions F with "slower than exponential decreasing tails" (e.g., lognormal, Pareto, Cauchy). Our results also imply that the expected number of vertices of the convex hull of n random points in the plane converges to infinity for the distributions in (i), and to 4 for the distributions in (ii).

Regularities in the environment are used to decide what course of action to take and how to prepare for future events. Here we focus on the utilization of regularities for prediction and argue that the commonly considered measure of regularity - the strength of the contingency between antecedent and outcome events - does not fully capture the goodness of a regularity for predictions. We propose, instead, a new measure - the level of expected prediction accuracy (ExpPA) - which takes into account the fact that, at times, maximal prediction accuracy can be achieved by always predicting the same, most prevalent outcome, and in others, by predicting one outcome for one antecedent and another for the other. Two experiments, testing the ExpPA measure in explaining participants' behavior, found that participants are sensitive to the twin facets of ExpPA and that prediction behavior is best explained by this new measure.

Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals' preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, a mediator coordinates the players' strategies in a way that discourages deviation. Our main result is a complete characterization of social choice correspondences which are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important social choice correspondences which are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium.

Harsh sanctions are conventionally assumed to primarily benefit vulnerable targets. Contrary to this perception, this article shows that augmented sanctions often serve the less vulnerable targets. While decreasing crime, harsher sanctions also induce the police to shift enforcement efforts from more to less vulnerable victims. When this shift is substantial, augmented sanctions exacerbate–rather than reduce–the risk to vulnerable victims. Based on this insight, this article suggests several normative implications concerning the efficacy of enhanced sanctions, the importance of victims' funds,and the connection between police operations and apprehension rates.

The Gibbard-Satterthwaite Theorem asserts the impossibility of designing a non-dictatorial voting rule in which truth-telling always constitutes a Nash equilibrium. We show that in voting games of complete information where a mediator is on hand, this troubling impossibility result can be alleviated. Indeed, we characterize families of voting rules where, given a mediator, truthful preference revelation is always in strong equilibrium. In particular, we observe that the family of feasible elimination procedures has the foregoing property.

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0,X1, ¦,Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for P(Xn+1|X0,X1, ...Xn) can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.

This note revisits the problem of selection bias, using a simple binomial example. It focuses on selection that is introduced by observing the data and making decisions prior to formal statistical analysis. Decision rules and interpretation of confidence measure and results must then be taken relative to the point of view of the decision maker, i.e., before selection or after it. Such a distinction is important since inference can be considerably altered when the decision maker's point of view changes. This note demonstrates the issue, using both the frequentist and the Bayesian paradigms.

One of the most intriguing questions in insurance is the preference of consumers for low or zero deductible insurance policies. This stands in sharp contrast to a theorem proved by Mossin, 1968, that under quite common assumptions when the price of insurance is higher than its actuarial value, then full coverage is not optimal.We show in a series of experiments that amateur subjects tend to underestimate the value of a policy with a deductible and that the degree of underestimation increases with the size of the deductible. We hypothesize that this tendency is caused by the anchoring heuristic. In particular, in pricing a policy with a deductible subjects first consider the price of a full coverage policy. Then they anchor on the size of the deductible and subtract it from the price of the full coverage policy. However, they do not adjust the price enough upward to take into account the fact that there is only a small chance that the deductible will be applied toward their payments. We also show that professionals in the field of insurance are less prone to such a bias. This implies that a policy with a deductible priced according to the true expected payments may seem overpriced  to the insured and therefore may not be purchased. Since the values of full coverage policies are not underestimated the insured may find them as relatively better deals .

In a series of experiments, Bar-Hillel and Budescu (1995) failed to find a desirability bias in probability estimation. The World Cup soccer tournament (of 2002 and 2006) provided an opportunity to revisit the phenomenon, in a context where wishful thinking and desirability bias are notoriously rampant (e.g., Babad, 1991). Participants estimated the probabilities of various teams to win their upcoming games. They were promised money if one particular team, randomly designated by the experimenter, would win its upcoming game. Participants judged their target team more likely to win than other participants, whose promised monetary reward was contingent on the victory of its rival team. Prima facie this seems to be a desirability bias. However, in a follow-up study we made one team salient, without promising monetary rewards, by simply stating that it is "of special interest". Again participants judged their target team more likely to win than other participants, whose "team of special interest" was the rival team. Moreover, the magnitude of the two effects was very similar. On grounds of parsimony, we conclude that what seemed like a desirability bias may just be a salience/marking effect, and – though optimism is a robust and ubiquitous human phenomenon – wishful thinking still remains elusive.In 2008, a shorter version of this paper was published under the title Wishful thinking in predicting world cup results as chapter 2 of Rationality and Social Responsibility (J. Krueger, ed.), 175-186.  In the link todp448, it follows the version published in Psychonomic Bulletin and Review.

Foreign firms to break into a new market commonly undercut domestic prices and, hence, subsidise the consumer's costs of switching in order to get a positive market share. However, this may constitute the act of dumping as drawn in Article VI of the General Agreement on Tariffs and Trade (GATT). Consequently, domestic firms trying to protect themselves against potential competitors often demand an anti-dumping (AD) investigation. In a two-period model of market entry with horizontally differentiated products and exogenous switching costs, it is demonstrated that the mere existence of switching costs and AD-rules may result in an anti-competition effect: the administratively set minimum-price rule protects the domestic firm and yields larger prices. Therefore, there are some consumers who will not buy either product in both periods although they would have done so in absence of AD. Consequently, competition policy should reassess the AD-regulation.

The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. This paper proposes an in-depth analysis of superpositions. It claims that superpositions must be considered when one cannot distinguish between possible paths, i.e., histories, leading to the current state of the system. In such a case the resulting state is some compound of the states that result from each of the possible paths. It claims that states can be compounded, i.e., superposed in such a way only if they are not orthogonal. Since different classical states are orthogonal, the claim implies no non-trivial superpositions can be observed in classical systems. It studies the parameters that define such compounds and finds two: a proportion defining the mix of the different states entering the compound and a phase difference describing the interference between the different paths. Both quantities are geometrical in nature: relating one-dimensional subspaces in complex Hilbert spaces. It proposes a formal definition of superpositions in geometrical terms. It studies the properties of superpositions.

Consider an exchange economy with asymmetric information. What is the set of outcomes that are consistent with common knowledge of rationality and market clearing?We propose the concept of CKRMC as an answer to this question. The set of price functions that are CKRMC is the maximal set F with the property that every fˆˆF defiłdots}nes prices that clear the markets for demands that can be rationalized by some profile of subjective beliefs on F. Thus, the difference between CKRMC and Rational Expectations Equilibrium (REE) is that CKRMC allows for a situation where the agents do not know the true price function and furthermore may have different beliefs about it. We characterize CKRMC, study its properties, and apply it to a general class of economies with two commodities. CKRMC manifests intuitive properties that stand in contrast to the full revelation property of REE. In particular, we obtain that for a broad class of economies: (1) There is a whole range of prices that are CKRMC in every state. (2) The set of CKRMC outcomes is monotonic with the amount of information in the economy.

The vertical inflorescences of the Mediterranean annual Salvia viridis carry many small, colorful flowers, and are frequently terminated by a conspicuous tuft of colorful leaves ("flags") that attracts insect pollinators. Insects may use the flags as indicators of the food reward in the inflorescences, as long-distance cues for locating and choosing flowering patches, or both. Clipping of flags from patches of inflorescences in the field significantly reduced the number of pollinators that arrived at the patches, but not the total number of inflorescences and flowers visited by them. The number of flowers visited per inflorescence significantly increased with inflorescence size, however. Inflorescence and flower visits rates signific antly increased with patch size when flags were present, but not after flag removal. 6% of the plants in the study population did not develop any flag during blooming, yet suffered no reduction in seed set as compared to flag-bearing neighboring individuals. These results suggest that flags signal long-distance information to pollinators (perhaps indicating patch location or size), while flower-related cues may indicate inflorescence quality.Plants that do not develop flags probably benefit from the flag signals displayed by their neighbors, without bearing the costs of flag production. Thus, flagproducing plants can be viewed as altruists that enhance their neighbors' fitness. Greenhouse-grown S. viridis plants allocated '' 0.5% of their biomass to flag production, and plants grown under water stress did not reduce their biomassallocation to flags as compared to irrigated controls. These findings suggest that the expenses of flag production are modest, perhaps reducing the cost of altruism. We discuss additional potential evolutionary mechanisms that may select for the maintenance of flag production.

{In the context of survival analysis, we define a covariate X as protective (detrimental) for the failure time T if the conditional distribution of [T | X = x] is stochastically increasing (decreasing) as a function of x. In the presence of another covariate Y, there exist situations where [T | X = x

This work studies the value of two-person zero-sum repeated games in which at least one of the players is restricted to (mixtures of) bounded recall strategies. A (pure) k-recall strategy is a strategy that relies only on the last k periods of history. This work improves previous results [Lehrer, Neyman and Okada] on repeated games with bounded recall. We provide an explicit formula for the asymptotic value of the repeated game as a function of the stage game, the duration of the repeated game, and the recall of the agents.

The paper analyzes an economy with asymmetric information in which agents trade in contingent assets. The new feature in the model is that each agent may have any prior belief on the states of nature and thus the posterior belief of an agent maybe any probability distribution that is consistent with his private information. We study two solution concepts: Equilibrium, which assumes rationality and market clearing, and common knowledge equilibrium (CKE) which makes the stronger assumption that rationality, market clearing, and the parameters which de'łdots}ne the economy are common knowledge. The two main results characterize the set of equilibrium prices and the set of CKE prices in terms of parameters which specify for each state s and event E the amount of money in the hands of agents who know the event E at the state s. The characterizations that are obtained apply to a broad classof preferences which include all preferences that can be represented by the expectation of a state dependent monotone utility function. One implication of these results is a characterization of the information that is revealed in a CKE.

We study the problem of reaching Nash equilibria in multi-person games that are repeatedly played, under the assumption of uncoupledness: every player knows only his own payoff function. We consider strategies that can be implemented by 'łdots}finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash equilibrium is reached in every game where such an equilibrium exists.

Nectar yields (standing crops) in flowers within an individual plant are often highly variable. This variability may be a by-product of the foraging activity of insect pollinators. Alternatively, plants may be selected to produce highly variable rewards to reduce consecutive visitation by risk-averse pollinators, thus diminishing within-plant pollen transfer. This study evaluated the roles of pollinator control vs. plant control over nectar variability in the bee-pollinated shrub Rosmarinus officinalis L. We sampled nectar production, yield and pollinator visits in three shrubs of one population over 17 days during one blooming season. Nectar production rates were highly variable (CV=1.48), and increased after rainy days. Nectar yields were even more variable (CV=2.16), and decreased with increasing temperatures. Pollinator visit rates decreased with variability in nectar yields, increased with flower number per shrub, and were unaffected by variability in nectar production rates. Repeated sampling of marked flowers revealed no correlation between their nectar yields and production rates. These findings support the role of reward variance in reducing pollinator visits, but suggest that plants are not in complete control of this variability. Rather, plant-generated variability can be modified by intensive foraging activity of pollinators. Such pollinator control over nectar variability is likely to reduce the selective advantage of plant-generated reward variation. Plant-controlled variability may provide evolutionary advantage when pollinator activity is insufficient to generate reward variation.

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions.