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Journal Articles of Carlos Alós-Ferrer

Forthcoming Articles

  • Performance Curiosity
    Carlos Alós-Ferrer, Jaume García-Segarra and Alexander Ritschel.
    Journal of Economic Psychology, forthcoming.



  • Inertia and Decision Making.
    Carlos Alós-Ferrer, Sabine Hügelschäfer and Jiahui Li.
    Frontiers in Psychology , Article 169, Volume 7, February 2016.
  • Preference Reversals: Time and Again
    Carlos Alós-Ferrer, Ðura-Georg Granic, Johannes Kern, Alexander K. Wagner.
    Journal of Risk and Uncertainty, February 2016, Vol. 52, Issue 1, pp 65-97.







  • Contagion and Efficiency
    Carlos Alós-Ferrer and Simon Weidenholzer.
    Journal of Economic Theory, Vol. 143, No. 1, November 2008, pp. 251-274.
  • Trees and Extensive Forms
    Carlos Alós-Ferrer and Klaus Ritzberger.
    Journal of Economic Theory, Vol. 143, No. 1, November 2008, pp. 216-250.

See also: Comment on Trees and Extensive Forms
Carlos Alós-Ferrer, Johannes Kern, and Klaus Ritzberger. 
Journal of Economic Theory




  • Trees and Decisions
    Carlos Alós-Ferrer and Klaus Ritzberger.
    Economic Theory, Vol. 25, No. 4, June 2005, pp. 763-798.
  • The Asset Market Game
    Carlos Alós-Ferrer and Ana B. Ania.
    Journal of Mathematical Economics,Vol. 41, No. 1-2, February 2005, pp. 67-90.

2004 and earlier

Contributions in Books

  • Imitation and Learning
    Carlos Alós-Ferrer and Karl Schlag.
    The Handbook of Rational and Social Choice, ed. by P. Anand, P. Pattanaik and C. Puppe, Oxford University Press, 2009.
  • An Evolutionary Model of Market Structure
    Carlos Alós-Ferrer, Fernando Vega-Redondo and Ana B. Ania.
    The Theory of Markets, ed. G. van der Laan, P.J.J. Herings, and A.J.J. Talman, North Holland, Amsterdam, 1999.

Other Publications

Working Papers and Mimeos

Abstracts of Journal Articles


Performance Curiosity
Carlos Alós-Ferrer, Jaume García-Segarra and Alexander Ritschel.
Journal of Economic Psychology, forthcoming.

Abstract: We show that performance curiosity –the desire to know one’s own (relative) performance– can trump inequality aversion. In two experiments (combined N=450), participants chose between an equal allocation and a performance-based one after generating surplus in a real-effort task. In the experimental treatment, choosing an equal allocation came at the cost of not knowing the own performance, which led to a substantial increase of performance-based choices in comparison with the control treatment. The effect seems especially pronounced for women, but the gender effect is due to a difference in expectations regarding performance. Interestingly, the manipulation equalized the proportion of equal allocation choices between males and females compensating for their difference in expectations.

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A Review Essay on Social Neuroscience: Can Research on the Social Brain and Economics Inform Each Other?
Carlos Alós-Ferrer.
Journal of Economic Literature, forthcoming.

A Dual-Process Diffusion Model
Carlos Alós-Ferrer.
Journal of Behavioral Decision Making, forthcoming.

Abstract: This paper presents a simple formal-analytical model delivering qualitative predictions for response times in binary-choice experiments. It combines a dual-process/multi-strategy approach with the standard diffusion model, modeling a utility decision process and a heuristic decision process as diffusion processes of evidence accumulation. For experiments with objective alternatives (including many tasks in judgment and decision making), the model predicts that errors will be quicker than correct responses in case of process conflict and slower in case of alignment, capturing a well-documented asymmetry regarding slow or fast errors. Further, the model also predicts that correct responses are slower in case of conflict than in case of alignment, capturing the well-known Stroop effect. The model is also extended to cover experiments with subjective alternative evaluations, i.e., preferential choice. In this case, results depend on whether trials are hard or easy, i.e., on whether the heuristic can be interpreted as relatively automatic or not.

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Cournot vs. Walras: A Reappraisal through Simulations
Carlos Alós-Ferrer and Johannes Buckenmaier.
Journal of Economic Dynamics and Control, Volume 82, September 2017, Pages 257-272.

Abstract: Best-reply behavior in Cournot oligopolies generally leads to Cournot-Nash equilibrium, but imitative behavior selects the Walrasian equilibrium as the unique stochastically stable state. Previous work (Alós-Ferrer, 2004) showed that in the presence of memory, imitative behavior leads to a non-trivial dynamics selecting all quantities between the Cournot and Walrasian outcomes. However, the scope of previous results was limited to specific assumptions on demand and cost functions, and did not provide information on the shape of the distribution of outcomes. We use computational simulations to address these limitations. We show that the selection result for non-trivial memory holds beyond the set of well-behaved Cournot games previously analyzed. Further, we find that, in Cournot games, the limit distribution of long-run outcomes is highly skewed towards the Walrasian quantity. Although longer memory increases the importance of the Cournot equilibrium, the competitive outcome remains the dominant prediction.

 Online Copy

Super-Additivity and Concavity are Equivalent for Pareto Optimal n-Agent Bargaining Solutions
Carlos Alós-Ferrer, Jaume Garcia-Segarra, and Miguel Ginés-Vilar.
Economics Letters, Volume 157, August 2017, Pages 50–52.

Abstract: We show that, for Pareto optimal n-player bargaining solutions, the conditions of super-additivity and concavity are equivalent. Further, either condition implies homogeneity.

 Online Copy

Does Backwards Induction Imply Subgame Perfection?
Carlos Alós-Ferrer and Klaus Ritzberger.
Games and Economic Behavior, Volume 103, May 2017, Pages 19-29.

Abstract: In finite games subgame perfect equilibria are precisely those that are obtained by a backwards induction procedure. In large extensive form games with perfect information this equivalence does not hold: Strategy combinations fulfilling the backwards induction criterion may not be subgame perfect in general. The full equivalence is restored only under additional (topological) assumptions. This equivalence is in the form of a one-shot deviation principle for large games, which requires lower semi-continuous preferences. As corollaries we obtain one-shot deviation principles for particular classes of games, when each player moves only finitely often or when preferences are representable by payoff functions that are continuous at infinity.

 Online Copy

Framing Effects and the Reinforcement Heuristic
Carlos Alós-Ferrer, Sabine Hügelschäfer and Jiahui Li.
Economics Letters, Volume 156, July 2017, pp 32–35.

Abstract: We examine the effect of win/loss framing on individuals’ use of a reinforcement heuristic in an incentivized probability-updating task. A loss frame strengthens the basic impulse to shift away from an unsuccessful option, but only if this option was chosen freely before.

 Online Copy

Characterizations of Perfect Recall
Carlos Alós-Ferrer and Klaus Ritzberger.
International Journal of Game Theory, May 2017, Volume 46, Issue 2, pp 311–326.

Abstract: This paper considers the condition of perfect recall for the class of arbitrarily large discrete extensive form games. The known definitions of perfect recall are shown to be equivalent even beyond finite games. Further, a qualitatively new characterization in terms of choices is obtained. In particular, an extensive form game satisfies perfect recall if and only if the set of choices, viewed as sets of ultimate outcomes, fulfill the "Trivial Intersection" property, that is, any two choices with nonempty intersection are ordered by set inclusion.

 Online Copy

On the Convergence of Logit-Response to (Strict) Nash Equilibria
Carlos Alós-Ferrer and Nick Netzer
Economic Theory Bulletin, April 2017, Volume 5, Issue 1, pp 1–8.

Abstract: We show that the logit-response dynamics converges to a subset of (strict) Nash equilibria for any weakly acyclic, N-player normal form game. The result holds independently of whether revision opportunities arise as in asynchronous learning or in other ways, as long as the dynamics is regular. Our analysis generalizes and organizes recent convergence results in the literature. Further, it provides a simple selection criterion, because convergence to strict Nash equilibria obtains even in the presence of non-strict, pure-strategy Nash equilibria.

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Market Selection by Boundedly-Rational Traders under Constant Returns to Scale
Carlos Alós-Ferrer and Georg Kirchsteiger.
Economics Letters, Volume 153, April 2017, pp. 51–53.

Abstract: We consider a dynamic, stochastic model of trading-institution selection with boundedly-rational traders where sellers produce with constant unit costs. Traders will in general fail to coordinate exclusively on market-clearing institutions. Rather, any institution biasing the price upwards is stochastically stable.

 Online Copy

Trader Matching and the Selection of Market Institutions
Carlos Alós-Ferrer and Johannes Buckenmaier.
Journal of Mathematical Economics, Volume 69, March 2017, pp. 118–127.

Abstract: We analyze a stochastic dynamic learning model with boundedly rational traders who can choose among trading institutions with different matching characteristics. The framework allows for institutions featuring multiple prices (per good), thus violating the “law of one price.” We find that centralized institutions are stochastically stable for a broad class of dynamics and behavioral rules, independently of which other institutions are available. However, some decentralized institutions featuring multiple prices can also survive in the long run, depending on specific characteristics of the underlying learning dynamics such as fast transitions or optimistic behavior.

 Online Copy

Characterizing Existence of Equilibrium for Large Extensive Form Games: A Necessity Result
Carlos Alós-Ferrer and Klaus Ritzberger.
Economic Theory, February 2017, Volume 63, Issue 2, pp 407–430.

Abstract: What is the minimal structure that is needed to perform equilibrium analysis in large extensive form games? To answer this question, this paper provides conditions that are simultaneously necessary and sufficient for the existence of a subgame perfect equilibrium in any well-behaved perfect information game defined on a large game tree. In particular, the set of plays needs to be endowed with a topology satisfying two conditions. (a) Nodes are closed as sets of plays; and (b) the immediate predecessor function is an open map.

 Online Copy


Faith in Intuition and Cognitive Reflection
Carlos Alós-Ferrer and Sabine Hügelschäfer.
Journal of Behavioral and Experimental Economics, Volume 64, October 2016, pp. 61-70.

Abstract:We compare two different measures of impulsive or intuitive behavior, the Cognitive Reflection Test (CRT) and a well-established psychological scale known as “Faith in Intuition” (FI), and investigate their relation to common biases in probability judgment. Using data from two laboratory experiments and a series of classroom experiments, the evidence we obtain is mixed. CRT scores and FI correlated in two data sets out of three. Both measures appear to be partially informative for some of the biases, but the effects are not systematic and depend on which exact probability-judgment question is used. Overall, CRT scores explain more variance in probability-judgment biases than FI scores. Further, gender effects interact with FI but not with CRT.

 Online Copy

Cognitive Reflection, Decision Biases, and Response Times
Carlos Alós-Ferrer, Michele Garagnani and Sabine Hügelschäfer.
Frontiers in Psychology, Volume 7, September 2016.

Abstract: We present novel evidence on response times and personality traits in standard questions from the decision-making literature where responses are relatively slow (medians around half a minute or above). To this end, we measured response times in a number of incentivized, framed items (decisions from description) including the Cognitive Reflection Test, two additional questions following the same logic, and a number of classic questions used to study decision biases in probability judgments (base-rate neglect, the conjunction fallacy, and the ratio bias). All questions create a conflict between an intuitive process and more deliberative thinking. For each item, we then created a non-conflict version by either making the intuitive impulse correct (resulting in an alignment question), shutting it down (creating a neutral question), or making it dominant (creating a heuristic question). For CRT questions, the differences in response times are as predicted by dual-process theories, with alignment and heuristic variants leading to faster responses and neutral questions to slower responses than the original, conflict questions. For decision biases (where responses are slower), evidence is mixed. To explore the possible influence of personality factors on both choices and response times, we used standard personality scales including the Rational-Experiential Inventory and the Big Five, and used them as controls in regression analysis.

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The Impact of Self-Control Depletion on Social Preferences in the Ultimatum Game
Anja Achtziger, Carlos Alós-Ferrer, and Alexander K. Wagner.
Journal of Economic Psychology, Volume 53, April 2016, pp. 1-16.

Abstract: We study the interaction of different motives and decision processes in determining behavior in the ultimatum game. We rely on an ego-depletion manipulation which consumes self-control resources, thereby enhancing the influence of default reactions, or in psychological terms, automatic processes. Experimental results provide evidence that proposers make higher offers under ego depletion. Based on findings from a closely related dictator game study, which shows that depleted dictators give less than non-depleted ones, we discard the possibility that other-regarding concerns are the default mode. Instead, we conclude that depleted proposers offer more because of a strategic ‘fear of rejection’ of low offers, consistent with self-centered monetary concerns. For responders, ego depletion increases the likelihood to accept offers, in line with unconditional monetary concerns being more automatic than affect-influenced reactions to reject unfair offers.

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Preference Reversals: Time and Again
Carlos Alós-Ferrer, Ðura-Georg Granić, Johannes Kern, Alexander K. Wagner.
Journal of Risk and Uncertainty, February 2016, Vol. 52, Issue 1, pp 65-97.

Abstract: We present a new, simple process-based model and experimental investigation of the preference reversal phenomenon. The model explains preference reversals and can be further validated through the measurement of decision times. Preference reversals are jointly caused by noisy lottery evaluations and an overpricing phenomenon associated with the compatibility hypothesis. The first cause explains the existence of reversals, while the second explains the predominance of a particular type thereof. A first laboratory experiment confirmed the model's predictions for both choice data and decision times. Choices associated with reversals take significantly longer than non-reversals, and non-reversal choices take longer whenever long-shot lotteries are selected. A second experiment showed that the overpricing phenomenon can be shut down, greatly reducing reversals, by using ranking-based, ordinally-framed evaluation tasks. This experiment also disentangled the two determinants of reversals, because imprecise evaluations still deliver testable predictions on decision times even in the absence of the overpricing phenomenon.

 Online Copy

Inertia and Decision Making
Carlos Alós-Ferrer, Sabine Hügelschäfer, Jiahui Li.
Frontiers in Psychology, Volume 7, Article 169, February 2016, pp. 1-9.

Abstract: Decision inertia is the tendency to repeat previous choices independently of the outcome, which can give rise to perseveration in suboptimal choices. We investigate this tendency in probability-updating tasks. Study 1 shows that, whenever decision inertia conflicts with normatively optimal behavior (Bayesian updating), error rates are larger and decisions are slower. This is consistent with a dual-process view of decision inertia as an automatic process conflicting with a more rational, controlled one. We find evidence of decision inertia in both required and autonomous decisions, but the effect of inertia is more clear in the latter. Study 2 considers more complex decision situations where further conflict arises due to reinforcement processes. We find the same effects of decision inertia when reinforcement is aligned with Bayesian updating, but if the two latter processes conflict, the effects are limited to autonomous choices. Additionally, both studies show that the tendency to rely on decision inertia is positively associated with preference for consistency.

 Online Copy

Equilibrium Existence for Large Perfect Information Games
Carlos Alós-Ferrer and Klaus Ritzberger.
Journal of Mathematical Economics, Volume 62, January 2016, pp. 5–18.

Abstract: This paper provides a novel existence theorem for subgame perfect equilibria of potentially large extensive form games with perfect information and continuous preferences, allowing for infinite horizon and infinite action spaces. The approach is based on the properties of the topology on the space of outcomes and differs from all previous approaches in the literature. Furthermore, the existence proof relies on a new algorithm that is independent of the horizon, hence can also be applied to infinite-horizon games.

 Online Copy


Self-Control Depletion and Decision Making
Carlos Alós-Ferrer, Sabine Hügelschäfer, Jiahui Li.
Journal of Neuroscience, Psychology, and Economics, Vol 8(4), Dec 2015, pp. 203-216..

Abstract: We examine the effects of ego depletion on an incentivized decision-making task where optimal decisions require Bayesian updating of beliefs. In this task, an impulsive reinforcement-based heuristic can either conflict or be aligned with Bayesian updating. According to the limited-resource model of self-control, depleted participants should have difficulties inhibiting the heuristic and commit more decision errors in case of conflict. We conducted three studies using different depletion manipulations plus controls with milder versions (as standard in the literature). Only one study found the predicted effect in case of conflict. One study found decreased error rates for depleted participants in case of alignment, which is consistent with an increased reliance on the heuristic in this case. We conclude that the effects of self-control depletion in complex decision-making tasks are less systematic and robust than assumed in the literature.

 Online Copy

Repeated Games in Continuous Time as Extensive Form Games
Carlos Alós-Ferrer and Johannes Kern.
Journal of Mathematical Economics, Volume 61, December 2015, Pages 34–57.

Abstract: Extensive form games modeling continuous-time decisions are plagued with problems of nonexistence and nonuniqueness of outcomes. As a “second-best,” the literature has imposed extraneous restrictions on the strategy sets, raising questions on the nature and interpretation of the resulting formal object, and on which restrictions are appropriate. We provide a “first-best” framework, formalizing continuous-time repeated games as extensive form games incorporating natural conditions from the onset. Every strategy profile induces a unique outcome, without any restrictions on the strategy sets. Further, the unrestricted strategy sets are equivalent to a specific class of strategies in a more naïvely specified continuous-time game.

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Higher Incentives Can Impair Performance: Neural Evidence on Reinforcement and Rationality
Anja Achtziger, Carlos Alós-Ferrer, Sabine Hügelschäfer and Marco Steinhauser.
Social Cognitive and Affective NeuroscienceVol. 10, No. 11, November 2015, pp. 1477-1483.

Abstract: Standard economic thinking postulates that increased monetary incentives should increase performance. Human decision makers, however, frequently focus on past performance, a form of reinforcement learning occasionally at odds with rational decision making. We used an incentivized belief-updating task from economics to investigate this conflict through measurements of neural correlates of reward processing. We found that higher incentives fail to improve performance when immediate feedback on decision outcomes is provided. Subsequent analysis of the feedback-related negativity (FRN), an early event-related potential following feedback, revealed the mechanism behind this paradoxical effect. As incentives increase, the win/lose feedback becomes more prominent, leading to an increased reliance on reinforcement and more errors. This mechanism is relevant for economic decision making and the debate on performance-based payment.

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Learning and Market Clearing: Theory and Experiments
Carlos Alós-Ferrer and Georg Kirchsteiger.
Economic Theory, Volume 60, No. 2, October 2015, pp 203-241.

Abstract: This paper investigates theoretically and experimentally whether traders learn to use market-clearing trading institutions or whether other (inefficient) market institutions can survive in the long run. Using a framework with boundedly rational traders, we find that market clearing institutions are always stable under a general class of learning dynamics. However, we show that there exist other, non-market clearing institutions that are also stable. Therefore, in the long run traders may fail to coordinate exclusively on market clearing institutions. Using a replica-economies approach, we find the results to be robust to large market size. The theoretical predictions were confirmed in a series of platform choice experiments. Traders coordinated on platforms predicted to be stable, including market-clearing as well as non-market clearing ones, while platforms predicted to be unstable were avoided in the long run.

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On the Characterization of Preference Continuity by Chains of Sets
Carlos Alós-Ferrer and Klaus Ritzberger.
Economic Theory Bulletin, October 2015, Volume 3, Issue 2, pp 115-128.

Abstract:This paper characterizes continuity, upper, and lower semicontinuity of preference relations, which may or may not be representable by utility functions, on arbitrary topological spaces. One characterization is by the existence of an appropriate chain of sets. This approach can be used to generate preference relations that fulfill predetermined conditions, to obtain examples or counterexamples. The second characterization of continuity is closely related to the concept of scale, but, in contrast to previous work, does not rely on the existence of a utility function.

 Online Copy

Political Space Representations with Approval Data
Carlos Alós-Ferrer and Ðura-Georg Granić.
Electoral Studies, Volume 39, September 2015, Pages 56–71.

Abstract: Data from political elections provide a snapshot of the political landscape of a country or region. This snapshot is filtered, and maybe also distorted, through the lens of the voting method in place. The standard Plurality Voting method, by virtue of asking every voter to report only the maximum of his or her preferences, might provide too little data for an accurate snapshot. We analyze data from two large-scale field experiments in Germany, where voters employed Approval Voting for both parties and candidates. The analysis reveals that the underlying political landscapes, as perceived by the voters, are inherently multidimensional and cannot be reduced to a single left-right dimension, or even to a two-dimensional space. We compare the obtained representations with those derived from party positions as revealed by the ‘Wahl-o-Mat’ voting advice application, and further compare the results with those of the W-Nominate procedure.

Online Copy              PDF Supplementary Online Materials

Money, Depletion, and Prosociality in the Dictator Game
Anja Achtziger, Carlos Alós-Ferrer and Alexanker K. Wagner
Journal of Neuroscience, Psychology, and Economics, Vol 8(1), Mar 2015, pp. 1-14.

We study the effects of ego depletion, a manipulation which consumes self-control resources, on social preferences in a dictator game. Depleted dictators give considerably less than non-depleted dictators and hence exhibit strong preferences for selfish allocation. In contrast to earlier studies, participants were explicitly paid for completing the ego- depletion task (with either a flat rate or strictly performance-based payment). We studied the dynamics of decisions by repeating the dictator game 12 times (anonymously). Depleted dictators start with much lower offers than non-depleted ones, but, strikingly, offers decrease in time for both groups, and more rapidly so for non-depleted dictators. We conclude that, while depleted dictators neglect fairness motives from the very first decision on, non-depleted dictators initially resist the tendency to act selfishly, but eventually become depleted or learn to act selfishly. Hence, prosocial behavior may be short-lived, and ego depletion uncovers the default tendencies for selfishness earlier.

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Choice-induced preference change and the free-choice paradigm: A clarification
Carlos Alós-Ferrer and Fei Shi
Judgment and Decision Making, Vol. 10, No. 1, January 2015, pp. 34-49.

Positive spreading of ratings or rankings in the classical free-choice paradigm is commonly taken to indicate choice- induced change in preferences and has motivated influential theories as cognitive dissonance theory and self-perception theory. Chen and Risen (2010) argued by means of a mathematical proof that positive spreading is merely a statistical consequence of a flawed design. However, positive spreading has also been observed in blind choice and other designs where the alleged flaw should be absent. We show that the result in Chen and Risen (2010) is mathematically incorrect, although it can be recovered in a particular case. Specifically, we present a formal model of decision making that satisfies all assumptions in that article but implies that spreading need not be positive in the absence of choice-induced preference change. Hence, although the free-choice paradigm is flawed, the present research shows that reasonable models of human behavior need not predict consistent positive spreading. As a consequence, taken as a whole, previous experimental results remain informative.

 PDF Online Copy

Robust Stochastic Stability
Carlos Alós-Ferrer and Nick Netzer.
Economic Theory, Vol. 58, No. 1, January 2015, pp. 31-57.

Abstract: A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary-action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.

 Online Copy (requires a subscription to Economic Theory)


Imitation and the Role of Information in Overcoming Coordination Failures
Carlos Alós-Ferrer and Simon Weidenholzer.
Games and Economic Behavior, Vol. 87, September 2014, pp. 397-411.

Abstract: We consider minimum-effort games played in an arbitrary network. For a
family of imitation behavioral rules, including Imitate the Best and the Proportional Imitation Rule, we show that inefficient conventions arise independently of the interaction structure, if information is limited to the interaction neighborhoods. In the presence of information spillovers, we provide a condition on the network structure that guarantees the emergence of efficient conventions. In contrast, if this condition is violated we will observe inefficient conventions, even in the presence of information spillovers.

Online Copy (requires a subscription to Games and Economic Behavior)

Fast or Rational? A Response-Times Study of Bayesian Updating
Anja Achtziger and Carlos Alós-Ferrer.
Management Science, Vol. 60, No. 4, April 2014, pp. 923-938.

Abstract: We present a simple model for decision making under uncertainty building on dual-process theories from psychology, and use it to illustrate a possible component of intuitive decision making of particular relevance for managerial settings. Decisions are the result of the interaction between two decision processes. The first one captures optimization based on Bayesian updating of beliefs. The second corresponds to a form of reinforcement learning capturing the tendency to rely on past performance. The model predicts that (i) in case of conflict between the two processes, correct responses are associated with longer response times, but (ii) if both processes are aligned, errors are slower. Further, (iii) response times in case of conflict are longer than in case of alignment. We confirm the predictions of the model in an experiment using a paradigm where an associative win-stay, lose-shift process conflicted with rational belief updating.

Online Copy (requires a subscription to Management Science)

From Dual Processes to Multiple Selves: Implications for Economic Behavior
Carlos Alós-Ferrer and Fritz Strack.
Journal of Economic Psychology, Vol. 41, April 2014, pp. 1-11.

Abstract: This article presents a short review of dual-process and dual-system theories from social and cognitive psychology and comments on their relevance for research on economic behavior. We view dual-process theories as a theoretical scaffolding which helps structure and interpret experimental results and can deliver important insights on human behavior in economic contexts. Dual-process ideas and concepts have already started to percolate into economics, contributing to the behavioral turn and the incorporation of bounded rationality into economic theory. The most recent development in this direction is represented by multiple selves models, which we view as a promising first step. We conclude the article with a brief discussion of the remaining articles in the special issue.

Online Copy (requires a subscription to the Journal of Economic Psychology)

Adaptive Preferences and Institutional Stability: Comment
Carlos Alós-Ferrer.
Journal of Institutional and Theoretical Economics
, Volume 170, Number 1, March 2014, pp. 27-36(10).

Abstract: Comment on “Adaptive Preferences and Institutional Stability” by Carl Christian von Weizsäcker

Online Copy (requires a subscription to the Journal of Institutional and Theoretical Economics)

The Neural Basis of Belief Updating and Rational Decision Making
Anja Achtziger, Carlos Alós-Ferrer, Sabine Hügelschäfer and Marco Steinhauser.
Social Cognitive and Affective Neuroscience, Vol. 9, No. 1, January 2014, pp. 55-62.

Abstract: Rational decision making under uncertainty requires forming beliefs which integrate prior and new information through Bayes’ rule. Human decision makers typically deviate from Bayesian updating by either overweighting the prior (conservatism) or overweighting new information (e.g., the representativeness heuristic). We investigated these deviations through measurements of electrocortical activity in the human brain during incentivized probability updating tasks and found evidence of extremely early commitment to boundedly rational heuristics. Participants who overweight new information display a lower sensibility to conflict detection, captured by an event-related potential (the N2) observed around 260 ms after the presentation of new information. Conservative decision makers (who overweight prior probabilities) make up their mind before new information is presented, as indicated by the lateralized readiness potential (LRP) in the brain. That is, they do not inhibit the processing of new information but rather immediately rely on the prior for making a decision.

Online Copy (requires a subscription to Social Cognitive and Affective Neuroscience)

Large Extensive Form Games
Carlos Alós-Ferrer, Klaus Ritzberger (Institute for Advanced Studies, Vienna). 
Economic Theory, Vol. 52, No. 1, January 2013, pp. 75-102.

Abstract: This paper provides a self-contained definition and a characterization of the class of extensive-form games that are adequate for applications, but still do not employ any finiteness assumptions. In spite of its simplicity, the resulting definition is more general than the classical ones. Moreover, we show that this class satisfies the basic desiderata: that strategies induce outcomes and do so uniquely. Within the class of playable extensive forms, the characterization is by the existence of an immediate predecessor function on the set of moves.

Online Copy (requires a subscription to Economic Theory)

Hidden Symmetries and Focal Points
Carlos Alós-Ferrer, Christoph Kuzmics (Bielefeld University). 
Journal of Economic Theory, Vol. 148, No. 1, January 2013, pp. 226-258.

Abstract: This paper provides a general formal framework to define and analyze the concepts of focal points and frames for normal form games. The information provided by a frame is captured by a symmetry structure which is consistent with the payoff structure of the game. The set of alternative symmetry structures has itself a clear structure (a lattice). Focal points are strategy profiles which respect the symmetry structure and are chosen according to some meta-norm, which is not particular to the framed game at hand. We also clarify the difference between different concepts of symmetry used in the literature.

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Choices and Preferences: Evidence from Implicit Choices and Response Times
Carlos Alós-Ferrer, Ðura-Georg Granić, Fei Shi, and Alexander K. Wagner.
Journal of Experimental Social Psychology, Vol. 48, No. 6, November 2012, pp. 1336-1342.

Abstract: We present a new experimental paradigm where choice-induced preference change is measured for alternatives which are never compared directly, but rather confronted with other alternatives in a way which keeps choices predictable without exogenously manipulating them. This implicit-choice design improves on the free-choice paradigm, avoiding the recently criticized selection bias. Rating and ranking spreads in two experiments show that preference-based choices feed back into and alter preferences even if choices are not directly among similarly evaluated alternatives. In agreement with recent brain-imaging evidence, response time measurements for direct choice pairs in our experiments indicate that reappraisal processes are already triggered during decision making, with larger post-choice spreads (sharper attitude change) being associated to quicker decisions.

Online Copy (requires a subscription to Journal of Experimental Social Psychology)

Faith in Intuition and Behavioral Biases
Carlos Alós-Ferrer, Sabine Hügelschäfer.
Journal of Economic Behavior and Organization, Vol. 84, No.1, September 2012, pp. 182-192.

Abstract: We use a 15-item self-report questionnaire known as “Faith in Intuition” to measure reliance on intuitive decision making, and ask whether the latter correlates with behavioral biases involving a failure of Bayesian updating. In a first experiment, we find that higher report scores are associated with an increased use of the representativeness heuristic (overweighting sample information). We find no evidence of increased conservatism (overweighting prior information). The results of a second experiment show that more intuitive decision makers rely more often on the “reinforcement heuristic” where successful decisions are repeated even if correctly updating prior beliefs indicates otherwise. However, this effect depends on the magnitude of incentives.

Online Copy (requires a subscription to Journal of Economic Behavior and Organization)

Job Market Signaling and Employer Learning
Carlos Alós-Ferrer, Julien Prat (Institute for Economic Analysis, Barcelona).
Journal of Economic Theory, Vol. 147, No. 5, September 2012, pp. 1787-1817.

Abstract: We consider a signaling model where the sender's continuation value after signaling depends on his type, for instance because the receiver is able to update his posterior. As a leading example, we introduce Bayesian learning in a variety of environments ranging from simple two-period to con- tinuous time models with stochastic production. Signaling equilibria present two major departures from those obtained in models without learning. First, new mixed-strategy equilibria involving multiple pooling are possible. Second, pooling equilibria can survive the Intuitive Criterion when learning is efficient enough.

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Two Field Experiments on Approval Voting in Germany
Carlos Alós-Ferrer, Ðura-Georg Granić.
Social Choice and Welfare, Vol. 39, No. 1, June 2012 , pp. 171-205.

Abstract: We report on two field experiments on approval voting conducted during actual state and federal elections in Germany. Voters provided approval ballots both for named district candidates and for state parties. The data reveal significant discrepancies in the outcomes under the official method and approval voting. Further, our analysis suggests that currently used voting methods do a poor job of representing the electorate's preferences. As a consequence, some recurring features of the political landscape in a given country might be, in part, an artifice of the employed voting method.

Online Copy (requires a subscription to Social Choice and Welfare)

Imitation with Asymmetric Memory
Carlos Alós-Ferrer, Fei Shi.
Economic Theory, Vol. 49, No. 1, January 2012, pp. 193-215.

Abstract: Models of learning in games based on imitation have provided fundamental insights as the relevance of risk-dominance equilibria or perfectly competitive outcomes. It has also been shown, however, that the introduction of nontrivial memory in those models fundamentally alters the results. This paper further considers the effect of asymmetric memory length in the population. We focus on two classical results and find that, while asymmetric memory crucially affects equilibrium selection in coordination games, it reinforces the stability of perfectly competitive outcomes in oligopoly games. The latter result is generalized to aggregative games and to finite-population ESS in symmetric games.

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General Equilibrium and the Emergence of (Non) Market Clearing Trading Institutions
Carlos Alós-Ferrer, Georg Kirchsteiger (Université Libre de Bruxelles).
Economic Theory, Vol. 44, No. 3, September 2010, pp. 339-360.

Abstract: We consider a pure exchange economy, where for each good several trading institutions are available, only one of which is market-clearing. The other feasible trading institutions lead to rationing. To learn on which trading institutions to coordinate, traders follow behavioral rules of thumb that are based on the past performances of the trading institutions. Given the choice of institutions, market outcomes are determined by an equilibrium concept that allows for rationing. We find that full coordination on the market-clearing institutions without any rationing is a stochastically stable outcome, independently of the characteristics of the alternative available institutions. We also find, though, that coordination on other, non-market-clearing institutions with rationing can be stochastically stable.

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Best-Response Dynamics in a Birth-Death Model of Evolution in Games
Carlos Alós-Ferrer, Ilja Neustadt (University of Zurich).
International Game Theory Review, Vol. 12, No. 2, June 2010, pp. 197-204.

Abstract: We consider a model of evolution with mutations as in Kandori et al (1993) [Kandori, M., Mailath, G.J., Rob, R., 1993. Learning, mutation, and long run equilibria in games. Econometrica 61, 29-56], where agents follow best-response decision rules as in Sandholm (1998) [Sandholm, W., 1998. Simple and clever decision rules for a model of evolution. Economics Letters 61, 165-170]. Contrary to those papers, our model gives rise to a birth-death process, which allows explicit computation of the long-run probabilities of equilibria for given values of the mutation rate and the population size. We use this fact to provide a direct proof of the stochastic stability of risk-dominant equilibria as the mutation rate tends to zero, and illustrate the outcomes of the dynamics for positive mutation rates.

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On the Evolution of Market Institutions: The Platform Design Paradox
Carlos Alós-Ferrer, Georg Kirchsteiger (Universite Libre de Bruxelles), Markus Walzl (Maastricht University).
Economic Journal, Vol. 120, No. 543, March 2010, pp. 215-243.

Abstract: This paper analyzes a situation where market designers create new trading platforms and traders learn to select among them. We ask whether “Walrasian” platforms, leading to market - clearing trading outcomes, will dominate the market in the long run. If several market designers are competing, we find that traders will learn to select non-market clearing platforms with prices systematically above the market-clearing level, provided at least one such platform is introduced by a market designer. This in turn leads all market designers to introduce such non-market clearing platforms. Hence platform competition induces non-competitive market outcomes.

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The Logit-Response Dynamics
Carlos Alós-Ferrer, Nick Netzer (University of Zurich).
Games and Economic Behavior, Vol. 68, No. 2, March 2010, pp. 413-427.

Abstract: We develop a characterization of stochastically stable states for the logit-response learning dynamics in games, with arbitrary specifcation of revision opportunities. The result allows us to show convergence to the set of Nash equilibria in the class of best-response potential games and the failure of the dynamics to select potential maximizers beyond the class of exact potential games. We also study to which extent equilibrium selection is robust to the specifcation of revision opportunities. Our techniques can be extended and applied to a wide class of learning dynamics in games.

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Contagion and Efficiency
Carlos Alós-Ferrer, Simon Weidenholzer (University of Vienna).
Journal of Economic Theory, Vol. 143, No. 1, November 2008, pp. 251-274.

Abstract: We consider a population of agents, either finite or countably infinite, located on an arbitrary network. Agents interact directly only with their immediate neighbors, but are able to observe the behavior of (some) other agents beyond their interaction neighborhood, and learn from that behavior by imitating successful actions. If interactions are not “too global” but information is fluid enough, we show that the efficient action is the only one which can spread contagiously to the whole population from an initially small, finite subgroup. This result holds even in the presence of an alternative, 1/2 -dominant action.

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Trees and Extensive Forms
Carlos Alós-Ferrer, Klaus Ritzberger (Institute for Advanced Studies, Vienna).
Journal of Economic Theory, Vol. 143, No. 1, November 2008, pp. 216-250.

Abstract: This paper addresses the question of what it takes to obtain a well-defined extensive form game. Without relying on simplifying finiteness or discreteness assumptions, we characterize the class of game trees for which (a) extensive forms can be defined and (b) all pure strategy combinations induce unique outcomes. The generality of the set-up covers “exotic” cases, like stochastic games or decision problems in continuous time (differential games). We find that the latter class fulfills the first, but not the second requirement.

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Comment on Trees and Extensive Forms
Carlos Alós-Ferrer, Johannes Kern, Klaus Ritzberger (Institute for Advanced Studies, Vienna).
Journal of Economic Theory, Vol. 146, No. 5, September 2011, pp. 2165-2168.

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Supplementary Material as PDF file

Learning, Bounded Memory, and Inertia
Carlos Alós-Ferrer.
Economics Letters, Vol. 101, No. 2, November 2008, pp. 134-136.

Abstract: This paper explores the role of memory and inertia in a learning model where bounded-memory players play a coordination game and imitate the actions which have led to the highest payoffs in remembered experience. In the presence of exogenous inertia, risk-dominant equilibria are selected independently of the length of memory. In the absence of exogenous inertia, and in contrast to the received literature, Pareto-dominant equilibria are selected when memory is long enough.

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Partial Bandwagon Effects and Local Interactions
Carlos Alós-Ferrer and Simon Weidenholzer (University of Vienna),
Games and Economic Behavior, Vol. 61, No. 2, November 2007, pp. 179-197.

Abstract: We consider partial bandwagon properties in the context of coordination games to capture the idea of weak network externalities. We then study a local interactions model where agents play a coordination game following a noisy best-reply process. We identify conditions such that Globally Pairwise Risk Dominant strategies are selected. Examples include arbitrary 3 X 3 coordination games and n X n supermodular games. A comparison with the global interactions benchmark shows that the nature of interactions might alter the long-run results themselves, and not only the speed of convergence. We also illustrate that the simultaneous coexistence of conventions is possible for games with at least 5 strategies.

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Nash Equilibria for Non-Binary Choice Rules
Carlos Alós-Ferrer and J.C.R. Alcantud (Department of Economics and Economic History, University of Salamanca)
International Journal of Game Theory, Vol. 35, No. 3, February 2007, pp. 455-464.

Abstract: We prove the existence of equilibria in games with players who employ abstract (non-binary) choice rules. This framework goes beyond the standard, transitive model and encompasses games where players have non-transitive preferences (e.g. Skew-Symmetric Bilinear preferences).

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A Simple Characterization of Approval Voting
Carlos Alós-Ferrer.
Social Choice and Welfare, Vol. 27, No. 3, December 2006, pp. 621-625.

Abstract: This note provides a characterization of Approval Voting as the only ballot aggregation function satisfying Faithfulness, Consistency, and Cancellation. The proof is simpler than those of the characterizations of Fishburn (1978), and also shows that the assumption of Neutrality used there was unnecessary.

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Imitation, Local Interactions, and Efficiency
Carlos Alós-Ferrer and Simon Weidenholzer.
Economics Letters, Vol. 93, No. 2, November 2006, pp. 163 - 168.

Abstract: We consider a model of evolution and local interactions in a circular city as in Ellison (1993) [Ellison, G., 1993. Learning, Local Interaction, and Coordination. Econometrica 61, 1047-1071], where agents follow imitation rules rather than myopic best-response. If interaction is limited to the two immediate neighbors, in the short run the process has a large number of absorbing states where both equilibria coexist, but risk-dominant equilibria are selected in the long run. Contrary to Ellison's model, though, payoff-efficient equilibria, and not risk-dominant ones, might be uniquely selected in the long run when players interact with neighbors further away.

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The Discretization of Continuum Strategy Spaces
Carlos Alós-Ferrer.
International Game Theory Review, Vol. 8, No. 3, September 2006, pp. 499-514.

Abstract: When the strategy set of a game is a continuum, its discretization may not conserve local properties even for arbitrarily fine strategy grids. Two technical lemmas are proven to solve the problem, one relying on differentiability properties and another for higher dimensions formulated for open-graph correspondences. Four applications are shown, regarding the discretization of Cournot and Bertrand settings, a consumer optimization problem, and an insurance market.

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The Evolutionary Stability of Perfectly Competitive Behavior
Carlos Alós-Ferrer and Ana B. Ania (Department of Economics, University of Vienna).
Economic Theory, Vol. 26, No. 3, October 2005, pp. 497-516

Abstract: In a (generalized) symmetric aggregative game, payoffs depend only on individual strategy and an aggregate of all strategies. Players behaving as if they were negligible would optimize taking the aggregate as given. We provide evolutionary and dynamic foundations for such behavior when the game satisfies supermodularity conditions. The results obtained are also useful to characterize evolutionarily stable strategies in a finite population.

The working paper version was circulated with the title The Evolutionary logic of feeling small

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Trees and Decisions
Carlos Alós-Ferrer and Klaus Ritzberger (Institute for Advanced Studies, Vienna).
Economic Theory, Vol. 25, No. 4, June 2005, pp. 763-798.

Abstract: The traditional model of sequential decision making, for instance in extensive form games, is a tree. Most texts define a tree as a connected graph without loops and a distinguished node, called the root. But a graph is not a domain for decision theory. Decision theory perceives of acts as functions from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural definition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be defined as specific collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.

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The Asset Market Game
Carlos Alós-Ferrer and Ana B. Ania (Department of Economics, University of Vienna).
Journal of Mathematical Economics, Vol. 21, No. 1-2, February 2005, pp. 67-90.

Abstract: This paper models asset markets as a game where assets pay according to an arbitrary payoff matrix, investors decide on fractions of wealth to allocate to each asset, and prices result from market clearing. The only pure-strategy Nash equilibrium is to split wealth proportionally to the assets' expected returns, which can be interpreted as investing according to the fundamentals. Further, the equilibrium strategy is evolu- tionarily stable in the sense of Schaffer (1988). We also study the stability properties of the equilibrium in an evolutionary dynamics where wealth flows with higher probability into those strategies that obtain higher realized payoffs.

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Some Remarks on Pseudotrees
Carlos Alós-Ferrer and Klaus Ritzberger (Institute for Advanced Studies, Vienna).
Order, Vol. 22, No. 1, February 2005, pp. 1-9.

Abstract: This paper provides new results on pseudotrees. First, it is shown that pseudotrees are precisely those posets for which consistent sets, directed sets, and nonempty chains coincide. Second, we show that chain-complete pseudotrees yield complete meet-semilattices. Third, we prove that pseudotrees are precisely those posets that admit a set representation by sets of appropriate chains. This latter result generalizes results needed for applications in game theory and economics.

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Cournot vs. Walras in Dynamic Oligopolies with Memory
Carlos Alós-Ferrer.
International Journal of Industrial Organization, Vol. 22, No. 2, February 2004, pp. 193-217.

Abstract: This paper explores the impact of memory in Cournot oligopolies where firms learn through imitation of success (as suggested in Alchian (1950) and modeled in Vega-Redondo (1997)). As long as memory includes at least one period, the long-run outcomes correspond to all the quantities in the interval between the Cournot quantity and the Walrasian one. There is a conceptual tension between the evolutionary stability associated to the Walrasian outcome (which relies on comparisons of simultaneous profits) and the stability of the Cournot-Nash equilibrium (derived from intertemporal comparisons of profits).

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Finite Population Dynamics and Mixed Equilibria
Carlos Alós-Ferrer.
International Game Theory Review, Vol. 5, No. 3, September 2003, pp. 263-290.

Abstract: This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered and combined with different assumptions about the speed of adjustment. It is found that specific refinements of mixed Nash equilibria serve to identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 X 2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

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A Comment on 'The Selection of Preferences through Imitation'
Carlos Alós-Ferrer and Manfred Nermuth (Univ. Vienna).
Economics Bulletin, Vol. 3, No 7, 2003, pp. 1-9.

Abstract: We observe that the imitation dynamics of Cubitt and Sugden (CS) is the same as the Replicator Dynamics for a certain class of games. Known results for such games then permit a more complete analysis of the CS imitation process, containing their results as special cases, and extending them considerably. We also offer a comment on the special role of ``pure" prospects, and an as if interpretation of the CS process in terms of payoff-guided imitation.

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Random Matching of Several Infinite Populations.
Carlos Alós-Ferrer.
Annals of Operations Research, Vol. 114, August 2002, pp. 33-38.

Abstract : Random matching models with infinite populations present formal difficulties due to the lack of a law of large numbers for a continuum of random variables. In a previous paper (Alós-Ferrer, 1999), random matching processes for a continuum of agents were studied, proving their existence. The present work extends the analysis to the case of several populations, which includes general equilibrium buyers–sellers models, and evolutionary models with underlying asymmetric games.

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Local Equilibria in Economic Games
Carlos Alós-Ferrer, Ana B. Ania (Univ.Vienna).
Economics Letters, Vol. 70, No. 2, February 2001, pp. 165-173.

Abstract :We study solution concepts for economic games that are resistant to local deviations. Strategy spaces are subsets of Rl and local deviations are small in the Euclidean metric. We define local Nash equilibrium and local evolutionarily stable strategy, and present applications to Walrasian outcomes in Cournot games and separating outcomes in screening models.

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An Evolutionary Model of Bertrand Oligopoly
Carlos Alós-Ferrer, Ana B. Ania (Univ.Vienna), and Klaus Reiner Schenk-Hoppé (Univ.Zürich).
Games and Economic Behavior, Vol. 33, No. 1, October 2000, pp. 1-19.

Abstract: This paper presents an evolutionary model of Bertrand competition in a market for a homogeneous good, where identical firms face a technology with decreasing returns to scale. Only quoted prices and realized profits are observed. The behavior of firms is based on imitation of success and experimentation, and is formally modeled through behavioral principles. We find that, even under simple behavior, the dynamic process selects a strict subset of the Nash equilibria of the underlying game. In the long run all firms make positive profits. Adding more sophistication, we obtain a finer prediction, named "central prices.'' This prediction essentially coincides with the Walrasian equilibrium, if costs are quadratic.

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Dynamical Systems with a Continuum of Randomly Matched Agents.
Carlos Alós-Ferrer.
Journal of Economic Theory, Vol. 86, No. 2, June 1999, pp. 245-267.

Abstract: Many models postulate a continuum of agents of finitely many different types who are repeatedly randomly matched in pairs to perform certain activities (e.g. play a game) which may in turn make their types change. The random matching process is usually left unspecified, and some Law of Large Numbers is informally invoked to justify a deterministic approximation of the resulting stochastic system. Nevertheless, it is well-known that such "laws of large numbers'' may not hold in this framework. This work shows that there exist random matching processes over a continuum of agents satisfying properties that are sufficient to simplify the analysis of the stochastic system. Moreover, the evolution of the population frequencies of types induced by this system can be described (almost surely) through a set of deterministic equations.

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Contributions in Books:

Approval Voting in Germany: Description of a Field Experiment
Carlos Alós-Ferrer and Ðura-Georg Granić.
"Handbook on Approval Voting", ed. J.F. Laslier and M.R. Sanver, Springer, 2010.

Online Copy

Imitation and Learning
Carlos Alós-Ferrer and Karl Schlag (European University Institute).
"The Handbook of Rational and Social Choice", ed. by P. Anand, P. Pattanaik and C. Puppe, Oxford University Press, 2009.

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An Evolutionary Model of Market Structure
Carlos Alós-Ferrer, Fernando Vega-Redondo (Univ.Alicante), and Ana B. Ania (Univ.Vienna).
"The Theory of Markets," North Holland, Amsterdam, 1999.

Abstract: We study a market for a homogeneous good in which firms adjust their production decisions on the basis of imitation, learning from own experience, and local experimentation. For any fixed set of firms (more than one), long run behavior settles on a symmetric marginal cost pricing equilibrium. When market entry and exit are allowed, we find a sharp effect of technology on long-run market structure. Specifically, we show that, under decreasing returns and some fixed cost, the market grows to "full capacity'' at Walrasian equilibrium; on the other hand, if returns are increasing, the unique long run outcome involves a profit-maximizing monopolist.

Other Publications:

Teoría de Juegos e historia Económica: una simbiosis necesaria
Información Comercial Española - Revista de Economía, No. 812, January 2004, pp. 27-33.

Online Copy and a link to the journal's database

Working Papers and Mimeos:

Social Preferences and Self-Control
Anja Achtziger, Carlos Alós-Ferrer, Alexander Wagner, Current Version April 2014.

Abstract: We study the interaction of different motives and decision processes in determining behavior in the ultimatum game. We rely on an experimental manipulation called ego depletion which consumes self-control resources, thereby enhancing the influence of default reactions or, in psychological terms, automatic processes. We find that proposers make lower offers under ego depletion, i.e. self-centered monetary concerns are the default mode and not other-regarding considerations (fairness towards others). Responders are more likely to reject low offers under ego depletion, i.e. the affect-influenced reaction to reject unfair offers (reaction to unfairness towards oneself) is more automatic than unconditional monetary concerns.

Working Paper at SSRN

Individual Randomness in Economic Models with a Continuum of Agents.
Carlos Alós-Ferrer

Revised version, 2002 (a previous version appeared as Working Paper 9807, Department of Economics, University of Vienna.)

Abstract : The lack of a law of large numbers for a continuum of random variables has cast doubt on several important economic models. This work presents a new framework for the analysis of stochastic mass phenomena in economics, without departing from the usual measure theory techniques. The approach is based on the idea of modelling first the aggregate level and derive the properties of the individual one afterwards. Through this procedure, the formal object which many economic models implicitly use is defined and classified.