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.

In 1994, Statistical Science published astonishing statistical evidence proving the existence of a hidden code in the book of Genesis, relating to future events. New research deprives this evidence of its import by proving that the same code can be found in the Hebrew translation of War and Peace.

Witztum, Rips and Rosenberg describe the outcomes of two experiments which purport to statistically prove the existence of a hidden code in the Book of Genesis. We show that these two experiments, viewed as two random samples from the same pop- ulation, yielded numerical outcomes which are more similar to each other than expected. We also show that the distributions obtained in some control experiments performed by Witztum et al. are flatter than expected. Our hypothesis is that Witztum et al. tailored their experimental procedures to meet naive expectations regarding how outcomes of ex- perimental replication and experimental controls should look. We give some statistical and empirical evidence supporting this hypothesis.

We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An ex- ogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player. We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels. In addition we will explicitly construct the punishment strategy of the unrestricted player with certain uniform properties.

We investigate the non-symmetric values of finite games on a given, possibly finite, univrse of players. It turns out that in the case of values symmetric with respect to some coalitional structure with infinite elements (types), the axioms are powerful enough to force such a value to be a mixture of the random arrival values (or path value in the sense of [Owen(1973)], with identically distributed random arrival times of players inside the same type. The general non-symmetric values are shown to be the random order values (as in[Weber(1988)] for a finite univrse). The non-symmetric semivalues and those symmetric with respect to a coalitional structure with large types are also completely characterized.

There is a value (of norm one) on the closed space of games that is generated by all games of bounded variation f o mu where mu is a vector of non-atomic probability measures and f is continuous at 0=mu(varnothing) and at mu(I).

We model the decision problems faced by the members of societies whose new members are determined by vote. We adopt a number of simplifying assumptions: the founders and the candidates are fixed; the society operates for k periods and holds elections at the beginning of each period; one vote is sufficient for admission, and voters can support as many candidates as they wish; voters assess the value of the streams of agents with whom they share the society, while they belong to it. In spite of these simplifications, we show that interesting strategic behavior implied by the dynamic structure of the problem: the vote for friends may be postponed, and it may be advantageous to vote for enemies. We discuss the exsitence of different types of equilibria in pure strategic and point out interesting equilibria in mixed strategies.

In this paper I draw a distiction between fulfilling an intention and satisfying it. This distinction enables me to argue that, contrary to what is often assumed, intention is not a purely internal relation. I take this point, which goes against Wittgenstein, to be supportive - in an indirect but principled way - of Davidson's causal theory of reasons, or intentions. At the same time, however, the fulfillment/satisfaction distinction seems to allow for the possibility that an intention will be partially determined retroactively, by later events. If I am right that after-facts may indeed constitute, at least in part, the intention with which an action was performed, then this poses a problem for the causal theory of intentions, as well as for ordinary models of rational action.

In this paper we will show that the usually accepted principle of decision theory that the "the more information the better" seemingly breaks down in stategic contexts. We will show through several examples that almost every situation is conceivable: Information can be beneficial for all the players, or only for the one who receives it,or, less intuitively, just for the one who does not receive it, or it could be bad for both. The only class of games that escapes these seemingly surprising phenomena is the class of zero-sum games, but only under the assumption of common beliefs for the players. We will show that even aminor departure from the assumptions of zero-sum and common beliefs can produce the phenomenon of information-rejection. We will show that these phenomena may appear even in coordination games, where one would expect that public information should facilitate coordination. It should be emphasized that there is here neither a pathology nor a paradox: aside from the particular examples that may merit attention, the message is that in an interactive decision framework with incomplete information, the relevant issue is that of interactive knowledge rather than simply knowledge per se.

Every 3-person repeated game with absorbing states has an equilibrium payoff.

A repeated game with absorbing states is played over the infinite future. A fixed one-shot game is played over and over again. However, for each action combination there is a probability that once it has occurred all future payoffs for the players are constant (that depends on the action combination that caused the "termination"), whatever the players play in the future. Given such a game, we define a modified game, by changing the payoff function. The new daily payoff for each player is the minimum between his expected payoff given the mixed-actions the players play in this stage, and his min-max value of the original game. Clearly the min-max value of the modified game, when the players are restricted to pure strategies (i.e. they cannot lotter between mixed-actions) cannot exceed the min-max value of the original game. We prove that the two values are equal.