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Smart Transformations: The Evolution of Choice Principles
Abstract
Evolutionary game theory classically investigates which behavioral patterns
are evolutionarily successful in a single game. More recently, a number of
contributions have studied the evolution of preferences instead: which
subjective conceptualizations of a game's payoffs give rise to evolutionarily
successful behavior in a single game. Here, we want to extend this existing
approach even further by asking: which general patterns of subjective
conceptualizations of payoff functions are evolutionarily successful across a
class of games. In other words, we will look at evolutionary competition of
payoff transformations in "meta-games", obtained from averaging over payoffs of
single games. Focusing for a start on the class of 2x2 symmetric games, we show
that regret minimization can outperform payoff maximization if agents resort to
a security strategy in case of radical uncertainty.
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What preferences will prevail in a society of rational individuals when preference evolution is driven by their success in terms of resulting payoffs? We show that when individuals’ preferences are their private information, a convex combinations of selfishness and morality stand out as evolutionarily stable. We call individuals with such preferences homo moralis. At one end of the spectrum is homo oeconomicus, who acts so as to maximize his or her material payoff. At the opposite end is homo kantiensis, who does what would be “the right thing to do,” in terms of material payoffs, if all others would do likewise. We show that the stable degree of morality - the weight placed on the moral goal - equals the index of assortativity in the matching process. The motivation of homo moralis is arguably compatible with how people often reason, and the induced behavior agrees with pro-social behaviors observed in many laboratory experiments.
We present a logical setting that incorporates a belief-revision mecha-nism within Dynamic-Epistemic logic. As the "static" basis for belief revision, we use epistemic plausibility models, together with a modal language based on two epistemic operators: a "knowledge" modality K (the standard S5, fully introspective, notion), and a "safe belief" modality 2 ("weak", non-negatively-introspective, notion, capturing a version of Lehrer's "indefeasible knowledge"). To deal with "dy-namic" belief revision, we introduce action plausibility models, repre-senting various types of "doxastic events". Action models "act" on state models via a modified update product operation: the "Action-Priority" Update. This is the natural dynamic generalization of AGM revision, giving priority to the incoming information (i.e. to "ac-tions") over prior beliefs. We completely axiomatize this logic, and show how our update mechanism can "simulate", in a uniform man-ner, many different belief-revision policies.
This paper, prepared for the forthcoming The Social Economics Handbook (Jess Benhabib, Alberto Bisin and Matthew Jackson, editors, El-sevier Press), surveys recent work on the evolutionary origins of preferences. We are especially interested in the circumstances under which evolution would push preferences away from the self-interested perfectly-rational ex-pected utility maximization of classical economic theory in order to incor-porate environmental or social considerations.
Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In The Philosophy of Logical Atomism, Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell's own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world's most significant philosophers is a remarkable attempt to establish a novel way of thinking. © 2010 The Bertrand Russell Peace Foundation Ltd. All rights reserved.
We consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game. Thus, over time, the strategy mix should evolve to some type of optimal or stable state. Maynard Smith and Price (1973) have introduced the concept of ESS (evolutionarily stable strategy) to describe a stable state of the game. We attempt to model the dynamics of the game both in the continuous case, with a system of non-linear first-order differential equations, and in the discrete case, with a system of non-linear difference equations. Using this model, we look at the notions of stability and asymptotic behavior. Our notion of stable equilibrium for the continuous dynamic includes, but is somewhat more general than, the notion of ESS.
The assumption that decision makers choose actions to maximize their preferences is a central tenet in economics, often justified formally or informally by appealing to evolutionary arguments. In contrast, we show that in almost every game and for almost every family of distortions of a player's actual payoffs, some degree of this distortion is beneficial to the player, and will not be driven out by any evolutionary process involving payoff-monotonic selection dynamics. Consequently, under any such selection dynamics the population will not converge to payoff-maximizing behavior. We also show that payoff-maximizing behavior need not prevail when preferences are imperfectly observed.
We study the evolution of preferences via payoff monotonic dynamics in strategic environments with and without complete information. It is known that, with complete information and subgroup matching, empirically plausible interdependent preference relations may entail the local instability of individualistic preferences (which target directly the maximization of material payoffs/fitness). In contrast, under incomplete information (unobservability of preference types), we show that independent preferences are globally stable in a large set of environments and locally stable in essentially any standard environment, provided that the number of subgroups that form in the society is large. Since these results are obtained within the context of a very general model, they may be thought of as providing an evolutionary rationale for the prevalence of individualistic preferences. Journal of Economic Literature Classification Numbers: C72, D42.
A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.
I want in this article to trace the history of an idea. It is beginning to become clear that a range of problems in evolution theory can most appropriately be attacked by a modification of the theory of games, a branch of mathematics first formulated by Von Neumann and Morgenstern in 1944 for the analysis of human conflicts. The problems are diverse and include not only the behaviour of animals in contest situations but also some problems in the evolution of genetic mechanisms and in the evolution of ecosystems. It is not, however, sufficient to take over the theory as it has been developed in sociology and apply it to evolution. In sociology, and in economics, it is supposed that each contestant works out by reasoning the best strategy to adopt, assuming that his opponents are equally guided by reason. This leads to the concept of a ‘minimax’ strategy, in which a contestant behaves in such a way as to minimise his losses on the assumption that his opponent behaves so as to maximise them. Clearly, this would not be a valid approach to animal conflicts. A new concept has to be introduced, the concept of an ‘evolutionary stable strategy’.
Acts are functions from states of nature into finite-support distributions over a set of ‘deterministic outcomes’. We characterize preference relations over acts which have a numerical representation by the functional where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature. In addition to the usual assumptions on the preference relation as transitivity, completeness, continuity and monotonicity, we assume uncertainty aversion and certainty-independence. The last condition is a new one and is a weakening of the classical independence axiom: It requires that an act f is preferred to an act g if and only if the mixture of f and any constant act h is preferred to the same mixture of g and h. If non-degeneracy of the preference relation is also assumed, the convex set of priors C is uniquely determined. Finally, a concept of independence in case of a non-unique prior is introduced.
We characterize, in the Anscombe-Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that, for all acts f and g, [GRAPHICS] The function u represents the decision maker's risk attitudes, while the index c captures his ambiguity attitudes. These preferences include the multiple priors preferences of Gilboa and Schmeidler and the multiplier preferences of Hansen and Sargent. This provides a rigorous decision-theoretic foundation for the latter model, which has been widely used in macroeconomics and finance.
The theory of subjective expected utility (SEU) has been recentlyextend#I to allow ambiguity to matter for choice. We propose a notion of absolute ambiguity aversion by build#wJ on a notion of comparative ambiguity aversion. We characterize it for a preference mo d#w which encompasses some of the most popular mod#wk in the literature. We nextbuild on these id#se to provid# ad efinition of unambiguous actand event, and showthe characterization of the latter. As an illustration, weconsid#w the classical Ellsberg 3-color urn problemand find that the notionsd#t eloped in the paper provid# intuitive answers. Journal of E onomic Literature Classification Number: D81 JEL classification numbers: D81 Key word#1 Ambiguity Aversion, Card#n,w Risk Aversion, Choquet Expected Utility, Maxmin Expected Utility, Biseparable Preferences AmbiguityMq5 Precise: A Comparative Foundation # PaoloGhirard#Iw Massimo Marinacci Introduction In this paper we proposeand characterize a formald#rmalwRk of ambigui...
For some well-known games, such as the Traveler's Dilemma or the Centipede Game, traditional game-theoretic solution concepts--and most notably Nash equilibrium--predict outcomes that are not consistent with empirical observations. In this paper, we introduce a new solution concept, iterated regret minimization, which exhibits the same qualitative behavior as that observed in experiments in many games of interest, including Traveler's Dilemma, the Centipede Game, Nash bargaining, and Bertrand competition. As the name suggests, iterated regret minimization involves the iterated deletion of strategies that do not minimize regret.
Evolution of Preferences. The Review of Economic Studies
- E Dekel
- J C Ely
- O Ylankaya
E. Dekel, J.C. Ely, and O. Ylankaya. Evolution of Preferences. The Review of Economic Studies, 74:3:685-704, 2007.