A strategic foundation for the cooperator's advantage

Orbell and Dawes develop a non-game theoretic heuristic that yields a cooperator's advantage by allowing players to project their own cooperate-defect choices onto potential partners (1991, p. 515). With appropriate parameter values their heuristic yields a cooperative environment, but the cooperation depends, simply, on optimism about others' behavior (1991, p. 526). In earlier work, Dawes (1989) established a statistical foundation for such optimism. In this paper, I adapt some of the concerns of Dawes (1989) and develop a game theoretic model based on a modification of the Harsanyi structure of games with incomplete information (1967–1968). I show that the commonly made conjecture that strategic play is incompatible with cooperation and the cooperator's advantage is false.     

On the foundations of mean-variance analyses

Let (, ) and (, ) be mean-standard deviation pairs of two probability distributions on the real line. Mean-variance analyses presume that the preferred distribution depends solely on these pairs, with primary preference given to larger mean and smaller variance. This presumption, in conjunction with the assumption that one distribution is better than a second distribution if the mass of the first is completely to the right of the mass of the second, implies that (, ) is preferred to (, ) if and only if either > or ( = and < ), provided that the set of distributions is sufficiently rich. The latter provision fails if the outcomes of all distributions lie in a finite interval, but then it is still possible to arrive at more liberal dominance conclusions between (, ) and (, ).This research was supported by the Office of Naval Research.     

Utility theory and the Bayesian paradigm

In this paper, a problem for utility theory - that it would have an agent who was compelled to play Russian Roulette with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values of possible total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of risk. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between utilities and values.     

Rational choice and economic behavior

This paper discusses several concepts that can be used to provide a foundation for a unified, theory of rational, economic behavior. First, decision-making is defined to be a process that takes place with reference to both subjective and objective time, that distinguishes between plans and actions, between information and states and that explicitly incorporates the collection and processing of information. This conception of decision making is then related to several important aspects of behavioral economics, the dependence of values on experience, the use of behavioral rules, the occurrence of multiple goals and environmental feedback.Our conclusions are (1) the non-transitivity of observed or revealed preferences is a characteristic of learning and hence is to be expected of rational decision-makers; (2) the learning of values through experience suggests the sensibleness of short time horizons and the making of choices according to flexible utility; (3) certain rules of thumb used to allow for risk are closely related to principles of Safety-First and can also be based directly on the hypothesis that the feeling of risk (the probability of disaster) is identified with extreme departures from recently executed decisions. (4) The maximization of a hierarchy of goals, or of a lexicographical utility function, is closely related to the search for feasibility and the practice of satisficing. (5) When the dim perception of environmental feedback and the effect of learning on values are acknowledged the intertemporal optimality of planned decision trajectories is seen to be a characteristic of subjective not objective time. This explains why decision making is so often best characterized by rolling plans. In short, we find that economic man - like any other - is an existential being whose plans are based on hopes and fears and whose every act involves a leap of faith.This paper is based on a talk presented at the Conference, New Beginnings in Economics, Akron, Ohio, March 15, 1969. Work on this paper was supported by a grant from the National Science Foundation.     

The general relevance of the impossibility teorem in smooth social choice

A complete classification theorem for voting processes on a smooth choice spaceW of dimensionw is presented. Any voting process is classified by two integersv ^* () andw(), in terms of the existence or otherwise of the optima set, IO(), and the cycle set IC().In dimension belowv ^* () the cycle set is always empty, and in dimension abovew() the optima set is nearly always empty while the cycle set is open dense and path con nected. In the latter case agenda manipulation results in any outcome.For admissible (compact, convex) choice spaces, the two sets are related by the general equilibrium result that IO() union IC() is non-empty. This in turn implies existence of optima in low dimensions. The equilibrium theorem is used to examine voting games with an infinite electorate, and the nature ofstructure induced equilibria, induced by jurisdictional restrictions.This material is based on work supported by a Nuffield Foundation grant.     

On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games

Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition strong rationalizability), then the true (or actual) strategy profile is path equivalent to a Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C , the set of profiles that survive the iterative deletion of inferior profiles.     

A sound interpretation of minimality properties of common belief in minimal semantics

A soundness proof for an axiomatization of common belief in minimal neighbourhood semantics is provided, thereby leaving aside all assumptions of monotonicity in agents reasoning. Minimality properties of common belief are thus emphasized, in contrast to the more usual fixed point properties. The proof relies on the existence of transfinite fixed points of sequences of neighbourhood systems even when they are not closed under supersets. Obvious shortcoming of the note is the lack of a completeness proof.     

Constructs and empirical basis in theories of economic behavior

Theories of economic behavior often use as-if-languages: for example, analytical sentences or definitions are used as if they were synthetic and factual-normative theoretical constructs are used as if they were empirical concepts. Such as-if-languages impede the acquisition of knowledge and are apt to encourage the wrong assessment of actual research strategies. The author's criticism is first leveled at revealed-preference theory. In this theory observed behavior is often understood in an empirical sense although it is a pure theoretical construct. Another example can be found in von Mises' representations on marketing behavior: here theoretical valuations are used to achieve a spurious streamlining of reality. Result: Scientists should not ogle with reality if they have nothing to say about it.     

On Playing Fair: Professor Binmore on Game Theory and the Social Contract

This paper critically reviews Ken Binmores non- utilitarian and game theoretic solution to the Arrow problem. Binmores solution belongs to the same family as Rawls maximin criterion and requires the use of Nash bargaining theory, empathetic preferences, and results in evolutionary game theory. Harsanyi has earlier presented a solution that relies on utilitarianism, which requires some exogenous valuation criterion and is therefore incompatible with liberalism. Binmores rigorous demonstration of the maximin principle for the first time presents a real alternative to a utilitarian solution.     

Implications of behavioral consistency in dynamic choice under uncertainty

This paper considers two fundamental aspects of the analysis of dynamic choices under risk: the issue of the dynamic consistency of the strategies of a non EU maximizer, and the issue that an individual whose preferences are nonlinear in probabilities may choose a strategy which is in some appropriate sense dominated by other strategies. A proposed way of dealing with these problems, due to Karni and Safra and called behavioral consistency, is described. The implications of this notion of behavioral consistency are explored, and it is shown that while the Karni and Safra approach obtains dynamically consistent behavior under nonlinear preferences, it may imply the choice of dominated strategies even in very simple decision trees.     

Utilities for distributive justice

This paper falls within the field of Distributive Justice and (as the title indicates) addresses itself specifically to the meshing problem. Briefly stated, the meshing problem is the difficulty encountered when one tries to aggregate the two parameters of beneficence and equity in a way that results in determining which of two or more alternative utility distributions is most just. A solution to this problem, in the form of a formal welfare measure, is presented in the paper. This formula incorporates the notions of equity and beneficence (which are defined earlier by the author) and weighs them against each other to compute a numerical value which represents the degree of justice a given distribution possesses. This value can in turn be used comparatively to select which utility scheme, of those being considered, is best.Three fundamental adequacy requirements, which any acceptable welfare measuring method must satisfy, are presented and subsequently demonstrated to be formally deducible as theorems of the author's system. A practical application of the method is then considered as well as a comparison of it with Nicholas Rescher's method (found in his book, Distributive Justice). The conclusion reached is that Rescher's system is unacceptable, since it computes counter-intuitive results. Objections to the author's welfare measure are considered and answered. Finally, a suggestion for expanding the system to cover cases it was not originally designed to handle (i.e. situations where two alternative utility distributions vary with regard to the number of individuals they contain) is made. The conclusion reached at the close of the paper is that an acceptable solution to the meshing problem has been established.I would like to gratefully acknowledge the assistance of Michael Tooley whose positive suggestions and critical comments were invaluable in the writting of this paper.     

Fairness,Public Good,and Emotional Aspects of Punishment Behavior

We report an experiment on two treatments of an ultimatum minigame. In one treatment, responders reactions are hidden to proposers. We observe high rejection rates reflecting responders intrinsic resistance to unfairness. In the second treatment, proposers are informed, allowing for dynamic effects over eight rounds of play. The higher rejection rates can be attributed to responders provision of a public good: Punishment creates a group reputation for being tough and effectively educate proposers. Since rejection rates with informed proposers drop to the level of the treatment with non-informed proposers, the hypothesis of responders enjoyment of overt punishment is not supported.     

The behavioral function: An inquiry into the relation between behavior and utility

The idea that an individual's behavior is a function of its utility or Value represents a very common and fundamental assumption in the study of human conduct. In this paper it will be attempted to determine the nature of this function more precisely. Adopting a probabilistic conception of human action, it appears that an exponential function perfectly satisfies the empirical as well as formal conditions which it seems necessary to impose upon it initially. Empirical research into behavioral change lends additional support to the function thus constructed.     

Predictive superiority of the beta-characteristic function in cooperative non-sidepayment N-person games

This article reports an experimental study of decision-making outcomes in cooperative non-sidepayment games. The objective of this test was to determine which characteristic function, V (S) or V (S), provides the most accurate basis for payoff predictions from solution concepts. The experiment tested three solution concepts (core, stable set, imputation set) in the context of 5-person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both V (S) and V (S), making a total of six predictive theories under test. Consistent with earlier studies (Michener et al., 1984a; Michener et al., 1985), two basic findings emerged. First, the data show that for each of the solutions tested, the prediction from any solution concept computed from V(S) was more accurate than the prediction from the same solution concept computed from V (S). Second, the -core was the most accurate of the six theories tested. Overall, these results support the view that V (S) is superior to V (S) as a basis for payoff predictions in cooperative non-sidepayment games.     

A Note on the Computation of the Mean Random Consistency Index of the Analytic Hierarchy Process (Ahp)

In this paper, we use Saaty's Eigenvector Method and the Power Method as well as =1, 2, , 9, 1/2, 1/3, , 1/9} and -={1,2, ,9,1, 1/2, ,1/9} as the sets from which the pairwise comparison judgments are assigned at random to examine the variation in the values determined for the mean random consistency index. By extensive simulation analysis, we found that both methods produce the same values for the mean random consistency random index. Also, we found that the reason for producing two different sets of values is the use of vs. - and not the selection of the Power Method vs. Saaty's Eigenvector Method.     

Disparate goods and Rawls' difference principle: A social choice theoretic treatment

Rawls' Difference Principle asserts that a basic economic structure is just if it makes the worst off people as well off as is feasible. How well off someone is is to be measured by an index of primary social goods. It is this index that gives content to the principle, and Rawls gives no adequate directions for constructing it. In this essay a version of the difference principle is proposed that fits much of what Rawls says, but that makes use of no index. Instead of invoking an index of primary social goods, the principle formulated here invokes a partial ordering of prospects for opportunities.     

Flexibility,endogenous risk,and the protection premium

We introduce two types of protection premia. The unconstrained protection premium, ^u, is the individual's willingness to pay for certain protection efficiency given flexibility to adjust optimally the investment in protection. The constrained protection premium, ^c, measures willingness to pay for certain protection efficiency given no flexibility to adjust the investment in protection. ^u depends on tastes and wealth as well as protection technology whereas ^c depends only on technology. We show that ^c cannot exceed ^u and develop necessary conditions for ^c=^u. Optimal protection for an individual with decision flexibility may be larger or smaller than that desired under no flexibility.Journal Paper No. J-15504 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 3048.     

Simulation methodology

Operational researchers, management scientists, and industrial engineers have been asked by Russell Ackoff to become systems scientists, yet he stated that Systems Science is not a science. (TIMS Interfaces, 2 (4), 41). A. C. Fabergé (Science 184, 1330) notes that the original intent of operational researchers was that they be scientists, trained to observe. Hugh J. Miser (Operations Research 22, 903), views operations research as a science, noting that its progress indeed is of a cyclic nature.The present paper delineates explicitly the attributes of simulation methodology. Simulation is shown to be both an art and a science; its methodology, properly used, is founded both on confirmed (validated) observation and scrutinised (verified) art work.The paper delineates the existing procedures by which computer-directed models can be cyclically scrutinised and confirmed and therefore deemed credible. The complexities of the phenomena observed by social scientists are amenable to human understanding by properly applied simulation; the methodology of the scientist of systems (the systemic scientist).

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Résumé Russell Ackoff propose à ceux qui s'occupent de recherches opérationnelle, industrielle, et de gestion, d'agir en systems scientists, et pourtant il affirme que systems science n'est pas une science (TIMS Interfaces 2 (4), 41). A. C. Fabergé (Science 184, 1330) remarque, qu'à l'origine, le but de ceux qui s'occupaient de recherche opérationnelle était d'agir en hommes de science instruits à observer. Hugh J. Miser (Operational Research 22, 903) considère la recherche opérationnelle comme science, notant que ses progrès sont en effet de nature cyclique.La présente étude délimite explicitement les attributs de la méthode de la simulation. Il est démontré que la simulation est à la fois un art et une science; sa méthode, lorsqu'utilisée correctement, repose sur l'observation validée et le modèle vérifié.L'étude délimite les moyens actuels dont nous disposons pour vérifier et valider cycliquement les modèles bâtis à l'aide d'ordinateurs, établissant ainsi leur crédibilité. La nature complexe des phénomènes étudiés par les sciences sociales peut être comprise à l'aide de la simulation: la méthode dont se servent les hommes de science qui étudient les systèmes (les scientistes systémiques).

     

Five legitimate definitions of correlated equilibrium in games with incomplete information

Aumann's (1987) theorem shows that correlated equilibrium is an expression of Bayesian rationality. We extend this result to games with incomplete information.First, we rely on Harsanyi's (1967) model and represent the underlying multiperson decision problem as a fixed game with imperfect information. We survey four definitions of correlated equilibrium which have appeared in the literature. We show that these definitions are not equivalent to each other. We prove that one of them fits Aumann's framework; the agents normal form correlated equilibrium is an expression of Bayesian rationality in games with incomplete information.We also follow a universal Bayesian approach based on Mertens and Zamir's (1985) construction of the universal beliefs space. Hierarchies of beliefs over independent variables (states of nature) and dependent variables (actions) are then constructed simultaneously. We establish that the universal set of Bayesian solutions satisfies another extension of Aumann's theorem.We get the following corollary: once the types of the players are not fixed by the model, the various definitions of correlated equilibrium previously considered are equivalent.     

Correlated strategies as Institutions

Two institutions that are often implicit or overlooked in noncooperative games are the assumption of Nash behavior to solve a game, and the ability to correlate strategies. We consider two behavioral paradoxes; one in which maximin behavior rules out all Nash equilibria (Chicken), and another in which minimax supergame behavior leads to an inefficient outcome in comparison to the unique stage game equilibrium (asymmetric Deadlock). Nash outcomes are achieved in both paradoxes by allowing for correlated strategies, even when individual behavior remains minimax or maximin. However, the interpretation of correlation as a public institution differs for each case.