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.

We propose a simple adaptive procedure for playing a game. In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies (these measures are updated every period). It is shown that our adaptive procedure guaranties that with probability one, the sample 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).

All classical "prophet inequalities" for independent random variables hold also in the case where only a noise corrupted version of those variables is observable. That is, if the pairs (X1, Z1),...,(Xn,Zn) are independent with arbitrary, known joint distributions, and only the sequence Z1,...,Zn is observable, then all prophet inequalities which hold if the X's were directly observable still hold, even though the expected X-values (i.e. the payoffs) for both the and statistician, will be different. Our model includes, for example, the case when Zi=Xi+Yi, where the Y's are any sequence of independent random variables.

Almost all equilibria in dominant strategies of finite strategic games are coalition-proof.

This paper presents a generalization of the results of van den Nouweland, Peleg and Tijs on the axiomatization of the Walras correspondence to generalized (pure exchange) economies where the commodity space is the positive cone in an ordered locally convex topological vector space. Our main result characterizes the Walras correspondence completely over an "acceptable" class of economies in terms of consistency, converse consistency, and weak versions of Pareto optimality and non-emptiness. Important examples of economies that are "acceptable" are given in detail.

We have obtained experimental results on the ultimatum bargaining game that support an evolutionary explanation for subjects' behavior in the game. In these experiments we have created enviornments in which subjects interact with each other in addition to interacting with virtual players, i.e. computer programs with pre-specified stategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behavior closer to the subgame-perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behavior of real subjects depending on the type of "mutants" (virtual players) that were present in their enviornment.

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The literary source of the main ideas in Aumann's article "Backward Induction and Common Knowledge of Rationality" is exposed and analyzed. The primordial archetypal images that underlie both this literary source and Aumann's work are delineated and are used to explain the great emotive impact that this work had on the community of game theorists.

This article concerns the interactive model propositional calculus, using the multi-agent epistemic logic S5. With regard to the space % of maximally consistent sets of formulas, the knowledge of an agent is defined by its knowledge of a set of formulas. Common knowledge can be defined in at least two ways, as the common knowledge of a set of formulas or according to the meet partition generated by the knowledge partitions of the agents. With at least two agents, this meet partition is a much finer partition of % than that generated by the common knowledge of sets of formulas, yet for some points of % the two partition members coincide. Whether the two partition members coincide has radical implications for the structure of the meet partition members.