This paper analyzes symmetric, single item auctions in the private values framework, with buyers whose preferences satisfy the axioms of Yaari's (1987) dual theory of choice under risk. It is shown that when their valuations are independently and identically distributed, buyers are indifferent among all the auctions contained in a big family of mechanisms that includes the standard auctions. It is also shown that in the linear equilibria of the sealed bid double auction, as the degree of players' risk aversion grows arbitrarily large, the ex post inefficiency of the mechanism tends to vanish. JEL Classification Numbers: D44; D81

Teachers of history note that pupils are often surprised to learn that a certain event in Europe happened at the same time as another in America, since to them the latter appears to have happened more recently. The validity of this anecdotal observation is supported by an experiment. This bias is explained by noting that America is The New World, while Europe is The Old World. Independent verification is offerred for this explanation. It is shown that the accessibility principle (i.e. that better known events appear more recent than less well known ones) neither accounts for the bias nor even operates with our stimuli.'An earlier version of this paper, titled The Europe-America Bias:' Where a historical event occurred affects when people think it occurred, was published later,'in 2005, in Advances in Psychology Research (S. P. Shohov, ed.), vol. 33, 39-63.' It is fuller, and in the link todp208 it'follows the version published in Psychological Science in 2002.

This paper analyzes a two-stage sealed-bid auction that is frequently employed in privatization, takeover, and merger and acquisition contests. This auction format yields the same expected revenue as the open ascending (English) auction, yet is less susceptible to preemptive bidding and collusion.

We propose a new and simple adaptive procedure for playing a game: " regretmatching." In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game. To compute these regret measures, a player needs to know his payoff function and the history of play. We also offer a variation where every player knows only his own realized payoff history ( but not his payoff function).

Naive bumble bees (Bombus terrestris) that did not learn to handle artificial flowers were examined for sampling frequency and duration before giving up. The munber of sample-bouts and the time of each sample-bout were measured, as well as the time in between two subsequent sample-bouts (pauses). This flower-sampling behavior of un successful individual bumble bees was related to the age of the bees, cohort and colony size. Younger bees sampled the flowers more frequently but stayed a shorter time each sample-bout than older bees. The duration of each separate pause was longer for older bees as well. The total sampling-time before giving up tended to be higher for the older bees. For all bees the subsequent sample-bouts showed a decrease in duration, while the duration of each subsequent pause increased. This was possibly caused by a negative re-enforcement by the unsuccessful samples. The higher unsuccessful sample-frequency of the younger bees could beconsidered a part ofa first orientation and learning process of flower handling. Therefore this sampling could influence the future behavior of young bees and might result in a higher capability of handling comlex flowers. Finally it should be emphasized that these results are our first prove of age-related learning and it is suggested that research along this line could result in more evidence of age-related foraging behavior.

Within this series of papers we plan to exhibit to any noncooperative game in strategic or normal form a 'canonical' representation in extensive form that preserves all symmetries of the game. The operation defined this way will respect the restriction of games to subgames and yield a minimal total rank of the tree involved. Moreover, by the above requirements the 'canonical extensive game form' will be uniquely defined. Part I is dealing with isomorphisms of game forms and games. An auto- morphism of the game is called motion. A symmetry of a game is a permuta- tion which can be augmented to a motion. Some results on the existence of symmetry groups are presented. The context to the notion of symmetry for coalitional games is exhibited.

The consistent value is an extension of the Shapley value to the class of games with non-transferable utility In this paper, the consistent value will be characterized for market games with a continuum of players of 2 types. We will show that for such games the consistent value need not belong to the core, and conditions under which there is equivalence between the two concepts will be given.

We consider the structure of the set of correlated equilibria for games with a large number n of players. Since the number of equilibrium constraints grows slower than the number of strategy arrays, it might be conjectured that the set of correlated equilibra is large. In this paper we show (1) that the average relative measure of the solution set is smaller than 2^-n, but also (2) that the solution set contains a number c^n of equilibria having disjoint supports with a probability going to I as n grows large. The proof of the latter result hinges on a combinatorial result on the number of nonnegative linear combinations of vectors representing a given point, which may be of independent interest.

Large flowers often contain larger nectar rewards, and receive more pollinator visits, than small flowers. We studied behavioural mechanisms for the formation of flower preferencce in bumblebees in a two-phase laboratory experiment. Flower-naive Bombus terrestris (L.) foraged on artificial flowers that bore either a big (3.8 cm diameter) or a small (2.7 cm diameter) display of a uniform colour. Only flowers of one display size contained nectar rewards. We changed the display colour and the locations of big and small flowers in the second experimental phase. We recorded the bees' choices in both trials. 41% of the bees made their first visit to a small flower. The bees learned to associate display size with food reward, and chose rewarding flowers with > 85% accuracy by the end of each learning trial. Some learning occured within the bees' first three flower visits. Learning of the size-reward association was equally good for big and small displays in the first trial, but better for small displays in the second trial. Formation of size-reward associations followed a similar course in both trials. This suggests that the bees did not apply their experience from the first learning trial to the new situation of the second trial. Rather, they treated each phase of the experiment as an independent learning trial. We suggest that pollinators from flower-size preferences through associative learning, and that they may not transfer the concept of "flower size" from one situation to another. Implications for the possible evolution of floral displays are discussed.

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The paper studies extensive-form correlated equilibria in stochastic games. An extensive-form correlated equilibrium is an equilibrium in an extended game, where a correlation device chooses at every stage, as a function of past signals (but independently of the actions of the players) a private signal for each player. We define the notion of individually rational payoffs for these games, and characterize the set of extensive-form correlated equilibrium payoffs using feasible and individually rational payoffs. Our result implies that extensive-form correlated equilibria and communication equilibria are payoff-equivalent in our model.

It is shown that in any diffusive one-factor model of the term structure, the prices of bonds and of term structure puts decrease as the short-term interest rate increases. However, these prices need not be monotone in the short-term rate, if that rate can experience jumps. An important comparative statics implication of the monotonicity resuly for diffusive models is that to a higher short-term interest rate corresponds a yield curve that lies uniformly above the curve that corresponds to a lower short-term rate. Furthermore, if the diffusion that describes the short-term rate is also homogeneous, then two yield curves that are measured at dfferent dates cannot intersect when drawn from the same time origin. If empirically they do intersect, then the short-term rate cannot be described by a one-factor homogeneous diffusion. It is also shown that if the second partial derivative w.r.t. to the short-term interest rate of the drift of the one-factor diffusion describing that rate is less than or equal to 2 - special cases being the linear drift models-then the prices of deterministic-coupon bonds and term structure puts are convex in that rate. The last result is derived using probabilistic representations of solutions to parabolic partial differential equations. The same methodology is used to derive restrictions on prices of European, American, and Asian options when the underlying price follows a stochastic volatility diffusion. Bounds, asymptotic results, and representations are derived for different linear differential transformations of derivative price functions like option`s delta, rho, and theta. An example from these results is the fact that the rho of a European call written on a stochastic volatility underlying asset is equal to the price of a digital call with the same exercise price, the same time to expiration, and the same underlying asset as the call, multiplied by the time to expiration and by the exercise price. The methodology is described in sufficient detail to allow for its ready application in a variety of situations.

We propose a model of gradual bargaining in the spirit of the Nash axiomatic theory. In this model the underlying set of payoff opportunities expands continuously with time. Unlike Nash`s solution, that predicts a single agreement for each bargaining problem, our solution yields a continuous path of agreements - one for each point in time. It emerges from a simple and intuitive differential equation. We discuss the relationship between the gradual solution and the Nash solution, and characterize it axiomatically by using essentially one property, which is Invariance with Respect to Increasing Transformations. We intetrpret this property as an incentive compatibility requirement. By using the richer framework of gradual bargaining, our aproach avoids some of the shortcomings of Nash`s axiomatization. In particular we do not need the controversial axiom of the ILA and the sets of payoff opportunities need not be convex. In the spirit of the Nash Program we propose several non-cooperative bargaining models that sustain our solution. Finally, we apply our model to discuss the allocation of physical (or monetary) assets when individuals` risk aversion changes over time.

It has been repeatedly suggested that bees use short-term information for making food-choice decisions. According to this hypothesis, the elimination of such information should reduce bees' performance in learning tasks. Naive bumblebees, foraging on differentially-rewarding artificial flowers, were exposed to either 1.5 s or 15 s of darkness between foraging visits. These treatments were intended to diminish the amount of short-term information for the bees' next foraging choice. The bees' flower choices were compared to the choices of untreated controls. Control-treatment bees chose rewarding flowers significantly more often then short-darkness (1.5 s) bees. Shifts between flowers of different colors were more frequent during long inter-visit intervals than during short inter-visit intervals in the control treatment, but not in the darkness treatments. The results suggest that short-term experience, when available, improves the choice performance of bees. However, possible effects of darkness itself on decision-making were not controlled for, and require further study.

This paper presents a new unifying approach to the study of nonsymmetric (or quasi-) valuesof nonatomic and mixed games. A family of path values is defined, using an appropriate generalization of Mertens diagonal formula. A path value possesses the following intuitive description: consider a function (path) gamma attaching to each player a distribution function on [0; 1]. We think of players as arriving randomly and independently to a meeting when the arrival time of a player is distributed according to gamma. Each player s payoff is defined as his marginal contribution to thecoalition of players that have arrived earlier.Under certain conditions on a path, different subspaces of mixed games (pNA; pM; bv'FL) areshown to be in the domain of the path value. The family of path values turns out to be verywide - we show that on pNA;pM and their subspaces the path values are essentially the basicconstruction blocks (extreme points) of quasi-values.

A common assumption of practical reasoning is that, in order to act rationally, agents are to act on the basis of the totality of evidence available to them. Common practice and introspection, however, suggest that people often do not want to know. The paper explores various aspects of the phenomenon of not wanting to know in an attempt to find out whether it is inherently unreasonable. The exploration leads, first, to weakeningthe principle of total evidence through replacing it with a rebuttable presumption in favor of additional knowledge. The sustainability of this presumption is then examined in light of the large variety of circumstances in which it seems to be reasonably rebutted. The alternative which in the end is recommended is to give up both the general principle and the presumption, and adopt instead something like a case by case cost-benefit approach, where the value of additional knowledge is matched up against its cost. In the process, the key notions of available knowledge, the value of knowledge , and the cost of knowledge are elucidated; also, separate attention is given to the question whether not wanting to know may sometimes be argued to be either morally required or morally reprehensible.

We investigate values of differentiable non-atomic and mixed games, in the situation where there are several types of players, and replacements are allowed only wiyhin each type. We show that if the types are considerably large, then the values are the path values and their mixtures (i.e., the path is random). In particular, the symmetric values on pM are characterized, as mixtures of values defined in [Hart (1973)].

Economic agents (e.g., firms, corporations) are often treated as unitary players. The internal organization of these agents and, in particular, the possibility of conflicting interests within agents, is overlooked. The present study uses an experimental approach to examine whether market performance is sensitive to the violation of the unitary player assumption. Toward this goal, we modeled a duopolistic market as a team game involving two teams with three members in each team. Each player simultaneously demanded a price and the team whose total demand was lower won the competition and was paid its price. The losing team was paid nothing. In case of a tie, each team was paid half its price. This composite duopoly was studied under two conditions; one in which the team's profit was divided equally amongst its members (and, hence, each team could be considered a unitary player) and another in which each individual member was paid her own price. Based on the reinforcement learning principle as modeled by Roth and Erev (1995), we predicted that convergence to the competitive price would be much faster in the former treatment than in the latter. The experimental results strongly confirmed this prediction.

People are often reluctant to make decisions by calculating the costs and benefits of alternative courses of action in particular cases. Knowing, in addition that they may err, people and institutions often resort to second-order strategies for reducing the burdens of, and risk of error in, first-order decisions. They make a second order decision when they choose one from among such possible strategies. They adopt rules of presumptions; they create standards; they delegate authority to others; they take small steps; they pick rather than choose. Some of these strategies impose high costs before decision but low costs at the time of ultimate decision; others impose low costs both before and at the time of ultimate decision; still others impose low costs before decision while exporting to others the high costs at the time of decision. We assess these second-order strategies and provide grounds for choosing among them in both legal and nonlegal contexts, by exploring the extent to which they minimize the overall costs of decision and costs of error. We also attempt to cast light on political, legal, and ethical issues raised by second-order decisions.

Whover exists belongs to a species, which did not become extinct, has a (geno-)type, which should be well adjusted, and lives in a habitat which has been sustainable for a long time. To capture the first aspect we allow for interspecies competition and analyze the conditions for species survival. The second aspect refers to success in intraspecies competition of (geno-)types as in evolutionary biology and game theory. Survival in inter- and intraspecies competition together with sustainability define ecological stability, a concept which we illustrate by an example of solitary and social grazers who compete for food supply and who are endangered by the same predators. Although our approach is inspired by empirical evidence, no systematic attempt is made to apply it to some specific ecology.