Consider firms which engage in Cournot competition over a common product, but can undertake innovation to improve the quality of their product. In this scenario it can often happen that innovation is discouraged by too much or too little competition, and occurs only when the industry is of intermediate size.

We consider repeated two-person zero-sum games where the number of repetitions theta is unknown. The information about the uncertain duration is identical to both players and can change during the play of the game. This is described by an uncertain duration process Theta. To each repeated game Gamma and uncertain duration process Theta is associated the Theta repeated game Gamma_Theta with value V_Theta. We establish a recursive formula for the value V_Theta. We study asymptotic properties of the value v_Theta=V_Theta/E(theta) as the expected duration E(theta) goes to infinity. We extend and unify several asymptotic results on the existence of lim v_n and lim v_lambda and their equality to lim v_Theta. This analysis applies in particular to stochastic games and repeated games of incomplete information.

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We consider repeated games where at any period each player knows only his set of actions and the stream of payoffs that he has received in the past. He knows neither his own payoff function, nor the characteristics of the other players (how many there are, their strategies and payoffs). In this context, we present an adaptive procedure for play - called "modified-regret- matching" - which is interpretable as a stimulus-response or reinforcement procedure, and which has the property that any limit point of the empirical distribution of play is a correlated equilibrium of the stage game.

The present research contrasts two seemingly complementary decision strategies: acceptance and elimination. In acceptance, a choice set is created by including suitable alternatives from an initial set of alternatives, whereas in elimination it is created by removing inappropriate alternatives from that same initial set. The research used realistic career decision-making scenarios and presented to respondents sets of alternatives that varied in their pre-experimental strength values. Whereas complementarity of acceptance and elimination is implied by three standard (normative) assumptions of decision theory, we find a systematic discrepancy between the outcomes of these procedures: choice sets were larger in elimination than in acceptance. This acceptance/elimination discrepancy is directly tied to sub-complementarity. The central tenet of the theoretical framework developed here is that acceptance and elimination procedures imply different types of status quo for the alternatives, thereby invoking a different selection criterion for each procedure. A central prediction of the dual-criterion framework is the "middling" alternatives should be most susceptible to the type of procedure used. The present studies focus on this prediction which is substantiated by the results showing that "middling" alternatives yield the greatest discrepancy between acceptance and elimination. The implications of this model and findings for various research domains are discussed.

Our framework for understanding advice-taking in decision making rests on two theoretical concepts that motivate the studies and serve to explain the findings. The first is egocentric discounting of others' opinion and the second is reputation formation for advisors. We review the evidence for these concepts, trace their theoretical origins, and point out some of their implications. In three studies we measured decision makers' "weighting policy" for the advice, and in a fourth study, their "willingness to pay" for it. Briefly, we found that advice is discounted relative to own opinion, and reputation for advisors is rapidly formed and asymmetrically revised. The asymmetry implies that it may be easier for advisors to lose a good reputation than to gain it. The cognitive and social origins of these phenomena are considered.

The Intergroup Prisoner's Dilemma (IPD) game was suggested by Bornstein (1992) for modeling intergroup conflicts over continuous public goods. We analyze data of an experiment in which the IPD game was played for 150 rounds, under three matching conditions. The objective is to study differences in the investment patterns of players in the different groups. A repeated measures analysis (Goren & Bornstein, 1999) involved data aggregation and strong distributional assumptions. Here we introduce a non-parametric approach based on permutation tests, applied to the raw data. Two new measures, the cumulative investment and the normalized cumulative investment, provide additional insight into the differences between groups. The proposed tests, based on the area under the investment curves, identify overall and pairwise differences between groups. A simultaneous confidence band for the mean difference curve is used to detect games which account for pairwise differences.

The management of risk is important in financial institutions. In particular, investment houses dealing with volatile financial markets such as foreign exchange or government bonds may find it difficult ot maintain "proper" levels of risk taking. On one hand, firms encourage traders to take risks in trading government bonds, but on the other, they promote risk aversion since they value reputation as careful and solid investors rather than having a reputation of risk takers. Government bond traders work in a very volatile and fast moving market. They are compensated by a base salary plus a bonus which relates to the profit and loss (P&L) they create for the firm on the securities they trade. Recent models of risk taking (Kahneman and Tversky, 1979; March and Shapira, 1992; Shapira, 1995) suggest that risk taking is affected by the targets or reference points that people use to evaluate risky prospects. Such targets can be set by "objective" grounds, that is, based on some rational economic considerations of profitability. However, often the targets are set in a "comparative" sense, that is, by comparison to the performance of other similar firms. The above models suggest some alternative ways in which targets may affect risk taking. These predictions are tested using data on actual purchase and sell decision made by government bond traders. Implications for risk management are discussed.

With four persons there is an example of a probability space where 1) the space is generated by hierarchies of knowledge concerning a single proposition, 2) the subjective beliefs of the four persons are continuous regular conditional probability distributions of a common prior probability distribution (continuous with respect to the weak topology), and 3) for every subset that the four persons know in common there is no common prior probability distribution. Furthermore, for every measurable set, every person, and at every point in the space, the subjective belief in this measurable set is one of the quantities 0, 1/2 or 1. This example presents problems for understanding games of incomplete information through common priors.

This paper proves the existence of epsilon-equilibria in non-zero-sum positive recursive stochastic games with finitely many states, using a kind of discount factor.

Stochastic stability is applied to the problem of exchange. We analyze the stochastic stability of two dynamic trading processes in a simple housing market. In both models traders meet in pairs at random and exchange their houses when trade is mutually beneficial, but occasionally they make mistakes. The models differ in the probability of mistakes. When all mistakes are equally likely, the set of stochastically stable allocations contains the set of efficient allocations. When more serious mistakes are less likely, the stochastically stable states are those allocations, always efficient, with the lowest envy-level.

In multi-armed bandit situations, gamblers must choose repeatedly between options that differ in reward probability, without prior information on the options' relative profitability. Foraging bumblebees encounter similar situations when choosing repeatedly among flower species that differ in food rewards. Unlike proficient gamblers, bumblebees do not choose the highest-rewarding option exclusively. We simulated two-armed bandit situations in laboratory experiments to characterize this choice behavior.

Hart and Mas-Colell (2000) show that if all players play "regret matching" strategies, i.e. they play with probabilities proportional to the regrets, then the empirical distributions of play converge to the set of correlated equilibria, and the regrets of each player converge to zero. Here we show that if only one player, say player i , plays according to these probabilities, while the other players are "not too sophisticated", then the result that player i's regrets converge to zero continues to hold. The condition of "not too sophisticated" essentially says that the effect of one change of action of player i on the future actions of the other players decreases to zero as the horizon goes to infinity. Furthermore, we generalize all these results to a whole class of "regret based" strategies. In particular, these include the "smooth fictitious play" of Fudenberg and Levine (1998).

The one-state machine that always defects is the only evolutionarily stable strategy in the machine game that is derived from the prisoner's dilemma, when preferences are lexicographic in complexity. This machine is the only stochastically stable strategy of the machine game when players are restricted to choosing machines with a uniformly bounded complexity.

Bees learn the location, odor, color and shape of flowers, and use these cues hierarchically to make dietary choices. If two such cues always appear together, they provide the bees with identical information about their food source. In such a situation, bees may base dietary choices on one cue and ignore the other, or they may continue to consider both cues. We studied this question by allowing bumblebees to forage on two patches of artificial flowers that differed in location, color and presence of reward in a two-phase laboratory experiment. We switched either the display color, the location, or both color and location associated with the rewarding patch between experimental phases. We tested for the effects of switches by comparing the bees' choices across treatments, and by evaluating each bee's performance before and after the change. In our analysis we characterized the different patterns of visits to empty flowers by a plot of the cumulative frequency of such visits over time. This plot enabled us to identify two regimes: ( I ) a learning regime, when new associations between reward and display cues are formed, followed by (2) a steady-state where bees make periodic visits to the empty patch. We used likelihood analysis to estimate the length of short-term memory that can account for the bees' steady-state foraging choices. The bees' performance decreased immediately following a switch in location of the rewarding patch. Switches in both reward color and location elicited a similar decrease to switches in location only. No temporary decrease in foraging performance occurred when only color of the rewarding patch was changed, and in no-change controls. The bees' flower choices at steady-state were most likely generated by a short-term memory of the last 4-6 flower visits.

Time is one of the more salient constraints on managerial behavior. This constraint may be very taxing in high velocity environments where managers have to attend to many tasks simultaneously. Earlier work by Radner [1976] proposed models based on notions of the thermostat or putting out fires  to guide managerial time and effort allocation among tasks. We link these ideas to the issue of the level of complexity of the tasks to be attended to while alluding to the sequential versus parallel modes of processing. We develop a stochastic model to analyze the behavior of a manager who has to attend to a few short term processes while attempting to devote as much time as possible to pursue a long term project. A major aspect of this problem is how does the manager deal with interruptions. Different rules of attention allocation are proposed and their implications to managerial behavior are discussed.

We revisit the well-known result that asserts that an increase in the degree of one's risk aversion improves the position of one's opponents. To this end, we apply Yaari's dual theory of choice under risk both to Nash's bargaining problem and to Rubinstein's game of alternating offers. Under this theory, unlike under expected utility, risk aversion influences the bargaining outcome only when this outcome is random, namely, when the players are risk-lovers. In this case, an increase in one's degree of risk aversion increases one's share of the pie.

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which both are subsolutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a subsolution of the reactive (pre) bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by nonemptiness, anonymity, reasonablenss, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.

{Let X_i

The Ultimatum Bargaining paradigm is often thought of as a demonstration of extreme disagreement between experimental evidence and game theoretical predictions and the basic assumption of rationality from which they are derived. Using the data of four experiments on Ultimatum Bargaining which I am involved in, I argue that, quite differently from this general impression, rationality in the sense of self-interested motives, is very much present in the observed behavior of both proposers and responders in the Ultimatum Bargaining game. Part of the argument calls for a broader interpretation of the notion of rationality than just immediate money maximization and the backward induction argument.