Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff

People's actions often deviate from rationality, i.e., self-interested behavior. We propose a paradigm called rule-rationality, according to which people do not maximize utility in each of their acts, but rather follow rules or modes of behavior that usually-but not always-maximize utility. Specifically, rather than choosing an act that maximizes utility among all possible acts in a given situation, people adopt rules that maximize average utility among all applicable rules, when the same rule is applied to many apparently similar situations. The distinction is analogous to that between Bentham's "act-utilitarianism" and the "rule-utilitarianism" of Mill, Harsanyi, and others. The genesis of such behavior is examined, and examples are given. The paradigm may provide a synthesis between rationalistic neo-classical economic theory and behavioral economics.

Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical meaning. They provide a formal framework that subsumes both classical boolean logic concerned with sets and subsets and quantum logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel notion that is free of linear algebra.

In the interest of improving their decision-making, individuals revise their opinions on the basis of samples of opinions obtained from others. However, such a revision process may lead decision-makers to experience greater confidence in their less accurate judgments. We theorize that people tend to underestimate the informative value of independently drawn opinions, if these appear to conflict with one another, yet place some confidence even in the "spurious consensus" which may arise when opinions are sampled interdependently. The experimental task involved people s revision of their opinions (caloric estimates of foods) on the basis of advice. The method of sampling the advisory opinions (independent or interdependent) was the main factor. The results reveal a dissociation between confidence and accuracy. A theoretical underlying mechanism is suggested whereby people attend to consensus (consistency) cues at the expense of information on interdependence. Implications for belief-updating and for individual and group decisions are discussed.

We consider stochastic dynamics whose expected (average) vector field is not necessarily continuous. We generalize the ordinary differential equation method for analyzing stochastic processes to this case, by introducing leading functions that 'lead  the stochastic process across the discontinuities, which yields approximation results for the asymptotic behavior of the stochastic dynamic. We then apply the approximation results to the classical best-response dynamics used in game theory.

R. J. Aumann and J. H. Dr¨ze (2008) define a rational expectation of a player i in a game G as the expected payo of some type of i in some belief system for G in which common knowledge of rationalityand common priors obtain. Our goal is to characterize the set of rational expectations in terms of the game's payoff matrix. We provide such a characterization for a specific class of strategic games, calledsemi-elementary, which includes Myerson's "elementary" games.

Under the conventional tort law paradigm, a tortfeasor behaves unreasonably when two conditions are met: the tortfeasor could have averted the harm by investing in cost-effective precautions and failed to do so, and other, more cost-effective precautions were not available to the victim. Torts scholarship has long argued that making such a tortfeasor responsible for the ensuing harm induces optimal care. This Article shows that by applying the conventional analysis, courts create incentives for opportunistic investments in prevention. In order to shift liability to others, parties might deliberately invest in precautions even where such investments are inefficient. The Article presents two possible solutions to the problem. By instituting a combination of (1) broader restitution rules and (2) an extended risk-utility standard, legislators and judges can reform tort law to discourage opportunistic precautions and maximize social welfare.

What motivates individual self-sacrificial behavior in intergroup conflicts? Is it the altruistic desire to help the ingroup or the aggressive drive to hurt the outgroup? This paper introduces a new game paradigm, the Intergroup Prisoner s Dilemma "Maximizing Difference (IPD-MD) game, designed specifically to distinguish between these two motives. The game involves two groups. Each group member is given a monetary endowment and can decide how much of it to contribute. Contribution can be made to either of two pools, one which benefits the ingroup at a personal cost, and another which, in addition, harms the outgroup. An experiment demonstrated that contributions in the IPD-MD game are made almost exclusively to the cooperative within-group pool. Moreover, pre-play intragroup communication increases intragroup cooperation but not intergroup competition. These results are compared with those observed in the Intergroup Prisoner's Dilemma (IPD) game, where group members' contributions are restricted to the competitive between-group pool.

In this paper I classify situations of interdependent decision-making, or games based on the type of decision-makers, or players involved. The classification builds on a distinction between three basic types of decision-making agents: individuals, cooperative or unitary groups – groups whose members can reach a binding (and costless) agreement on a joint strategy – and non-cooperative groups – groups whose members act independently without being able to make a binding agreement. Pitting individuals, unitary groups, and non-cooperative groups against one another, and adding Nature as a potential opponent , generates a 3 (type of agent) X 4 (type of opponent) matrix of social situations. This framework is used to review the experimental decision-making literature and point out the gaps that still exist in it.

When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the and then operation that combines old and new information. The and then connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claimed. Classical physical systems are exactly characterized by the commutativity, the associativity, or the monotonicity of the and then connective. Entailment is defined in this logic and can be proved to be a partial order. In orthomodular lattices, the operation proposed by Finch in [3] satisfies all the properties studied in this paper. All properties satisfied by Finch's operation in modular lattices are valid in Quantum Logic. It is not known whether all properties of Quantum Logic are satisfied by Finch's operation in modular lattices.

We prove that games with absorbing states with compact action sets have a value.

Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a "duality" axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dominance, and for gambles with normal distributions, is half of variance/mean. Examples are calculated, additional properties derived, and the index is compared with others in the literature.

The voting rules proposed by Dodgson and Young are both designed to find the candidate closest to being a Condorcet winner, according to two different notions of proximity; the score of a given candidate is known to be hard to compute under both rules. In this paper, we put forward an LP-based randomized rounding algorithm which yields an O(log m) approximation ratio for the Dodgson score, where m is the number of candidates. Surprisingly, we show that the seemingly simpler Young score is NP-hard to approximate by any factor.

We define the riskiness of a gamble g as that unique number R(g) such that no-bankruptcy is guaranteed if and only if one never accepts gambles whose riskiness exceeds the current wealth.

In this paper, I present a Bayesian decision theory and define choice-based subjective probabilities that faithfully represent Bayesian decision makers prior and posterior beliefs regarding the likelihood of the possible effects contingent on his actions. I argue that no equivalent results can be obtained in Savage s (1954) subjective expected utility theory and give an example illustrating the potential harm caused by ascribing to a decision maker subjective probabilities that do not represent his beliefs.

We consider a sequential rule, where an item is chosen into the group, such as a university faculty member, only if his score is better than the average score of those already belonging to the group. We study four variables: The average score of the members of the group after k items have been selected, the time it takes (in terms of number of observed items) to assemble a group of k items, the average score of the group after n items have been observed, and the number of items kept after the first n items have been observed. We develop the relationships between these variables, and obtain their asymptotic behavior as k (respectively, n) tends to infinity. The assumption throughout is that the items are independent, identically distributed, with a continuous distribution. Though knowledge of this distribution is not needed to implement the selection rule, the asymptotic behavior does depend on the distribution. We study in some detail the Exponential, Pareto and Beta distributions. Generalizations of the "better than average" rule to the ² better than average rules are also considered. These are rules where an item is admitted to the group only if its score is better than ² times the present average of the group, where ² > 0.

A decision maker (an agent) is engaged in a repeated interaction with Nature. The objective of the agent is to guarantee to himself the long-run average payoff as large as the best-reply payoff to Nature’s empirical distribution of play, no matter what Nature does. An agent with perfect recall can achieve this objective by a simple better-reply strategy. In this paper we demonstrate that the relationship between perfect recall and bounded recall is not straightforward: An agent with bounded recall may fail to achieve this objective, no matter how long recall he has and no matter what better-reply strategy he employs.

We study an economic setting in which a principal motivates a team of strategic agents to exert costly effort toward the success of a joint project. The action taken by each agent is hidden and affects the (binary) outcome of the agent's individual task stochastically. A Boolean function, called technology, maps the individual tasks' outcomes into the outcome of the whole project. The principal induces a Nash equilibrium on the agents' actions through payments that are conditioned on the project's outcome (rather than the agents' actual actions) and the main challenge is that of determining the Nash equilibrium that maximizes the principal's net utility, referred to as the optimal contract. Babaioff, Feldman and Nisan [1] suggest and study a basic combinatorial agency model for this setting. Here, we concentrate mainly on two extreme cases: the AND and OR technologies. Our analysis of the OR technology resolves an open question and disproves a conjecture raised in [1]. In particular, we show that while the AND case admits a polynomial-time algorithm, computing the optimal contract in the OR case is NP-hard. On the positive side, we devise an FPTAS for the OR case, which also sheds some light on optimal contract approximation of general technologies.

What makes a choice difficult, beyond being complex or difficult to calculate? Characterizing difficult choices as posing a special challenge to the agent, and as typically involving consequences of significant moment as well as clashes of values, the article proceeds to compare the way difficult choices are handled by rational choice theory and by the theory that preceded it, Kurt Lewin's "conflict theory." The argument is put forward that within rational choice theory no choice is in principle difficult: if the object is to maximize some value, the difficulty can be at most calculative. Several prototypes of choices that challenge this argument are surveyed and discussed (picking, multidimensionality, "big decisions" and dilemmas); special attention is given to difficult choices faced by doctors and layers. The last section discusses a number of devices people employ in their attempt to cope with difficult choices: escape, "reduction" to non-difficult choices, and second-order strategies.

When two agents of unequal strength compete, the stronger one is expected to always win the competition. This expectation is based on the assumption that evaluation of performance is flawless. If, however, the agents are evaluated on the basis of only a small sample of their performance, the weaker agent still stands a chance of winning occasionally. A theoretical analysis indicates that for this to happen, the weaker agent must introduce variability into the effort he or she invests in the behavior, such that on some occasions the weaker agent's level of performance is as high as that of the stronger agent, whereas on others it is . This, in turn, would drive the stronger agent to introduce variability into his or her behavior. We model this situation in a game, present its game-theoretic solution, and report an experiment, involving 144 individuals, in which we tested whether players are actually sensitive to their relative strengths and know how to allocate their resources given those relative strengths. Our results indicate that they do.