Papers

Unpublished papers

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"Inferring Cognitive Heterogeneity from Aggregate Choices", with Valentino Dardanoni, Marco Mariotti, and Chris Tyson, University of St. Andrews Discussion Paper No. 1701
Abstract. We study the problem of recovering the distribution of cognitive characteristics in a population of boundedly rational agents from the aggregate choices they make from a fixed menu of alternatives. Two models of limited attention are examined from this point of view, and it is shown that both "consideration probability" and "consideration capacity" distributions are substantially identified by aggregate choice shares. These models are applied to data on over-the-counter painkiller sales, yielding concurrent estimates that on average two or three out of the eight available products are considered in this market.
"Dual Random Utility Maximisation", with Marco Mariotti, University of St. Andrews Discussion Paper No. 1605, revised March 2017
Abstract. Dual Random Utility Maximisation (dRUM) is Random Utility Maximisation when utility depends on only two states. This class has many relevant behavioural interpretations and practical applications. We show that dRUMs are (generically) the only stochastic choice rules that satisfy Regularity and two new properties: Constant Expansion (if the choice probability of an alternative is the same across two menus, then it is the same in the merged menu), and Negative Expansion (if the choice probability of an alternative is less than one and differs across two menus, then it vanishes in the merged menu). We extend the theory to allow for menu-dependent probabilities and violations of Regularity, as happens in the attraction, similarity and compromise effects.
"Stochastic Complementarity", with Marco Mariotti, and Levent Ülkü, University of St. Andrews Discussion Paper No. 1505, revised March 2017
Abstract. The Hicksian definition of complementarity and substitutability may not apply in contexts in which agents are not utility maximisers or where prices, whether implicit or explicit, are not available. We look for tools to identify complementarity and substitutability satisfying the following criteria: they are behavioural (based only on observable choice data); model-free (valid whether the agent is rational or not); and they do not rely on price variation. We uncover a conflict between properties that any complementarity notion should intuitively possess. We discuss three different possible resolutions of the conflict.


Papers published in economics journals

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"Competing for Attention: Is the Showiest also the Best?", with Marco Mariotti, forthcoming in the Economic Journal
Abstract. There are many situations in which alternatives ranked by quality wish to be chosen and compete for the imperfect attention of a chooser by selecting their own salience. The chooser may be “tricked” into choosing more salient but inferior alternatives. We investigate when competitive forces ensure instead that (strictly) higher salience is diagnostic of (strictly) higher quality, and the most frequently chosen alternative is the best one. We prove that the structure of externalities in the technology of salience is key. Broadly speaking, positive externalities in salience favour correlation between quality and salience.
"Procedures for Eliciting Time Preferences ", with David Freeman, Marco Mariotti and Luigi Mittone, Journal of Economic Behavior and Organization, 126 (Part A): 235-242, 2016
Abstract. We study three procedures to elicit attitudes towards delayed payments: the Becker-DeGroot-Marschak procedure; the second price auction; and the multiple price list. The payment mechanisms associated with these methods are widely considered as incentive compatible, thus if preferences satisfy Procedure Invariance, which is also widely (and often implicitly) assumed, they should yield identical time preference distributions. We find instead that the monetary discount rates elicited using the Becker-DeGroot-Marschak procedure are significantly lower than those elicited with a multiple price list. We show that the behavior we observe is consistent with an existing psychological explanation of preference reversals.
"Partial Knowledge Restrictions on the Two-Stage Threshold Model of Choice", with Marco Mariotti and Chris Tyson, Journal of Mathematical Economics, 64 (4): 41-47, 2016
Abstract. In the context of the two-stage threshold model of decision making, with the agent’s choices determined by the interaction of three “struc- tural variables,” we study the restrictions on behavior that arise when one or more variables are exogenously known. Our results supply nec- essary and sufficient conditions for consistency with the model for all possible states of partial knowledge, and for both single- and multi- valued choice functions.
"State Dependent Choice ", with Marco Mariotti , Social Choice and Welfare, vol. 45, issue 2, pages 239-268, 2015.
Abstract. We propose a theory of choices that are influenced by the psychological state of the agent. The central hypothesis is that the psychological state controls the urgency of the attributes sought by the decision maker in the available alternatives. While state dependent choice is less restricted than rational choice, our model does have empirical content, expressed by simple "revealed preference" type of constraints on observable choice data. We demonstrate the applicability of simple versions of the framework to economic contexts. We show in particular that it can explain widely researched anomalies in the labour supply of taxi drivers.
"Stochastic Choice and Consideration Sets", with Marco Mariotti, Econometrica, 82 (3): 1153-1176, 2014 (supplemental appendix)
Abstract. We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximizes a preference relation within the set of considered alternatives. We show that this random choice rule is the only one for which the impact of removing an alternative on the choice probability of any other alternative is asymmetric and menu independent. Both the preference relation and the attention parameters are identified uniquely by stochastic choice data.
"Welfare economics and bounded rationality: the case for model-based approaches", with Marco Mariotti, Journal of Economic Methodology (Special issue on "Methodological perspectives on recent theories of bounded rationality") 21 (4): 343-360, 2014.
Abstract. In this paper, we examine the problems facing a policy maker who observes inconsistent choices made by agents who are boundedly rational. We contrast a model-less and a model-based approach to welfare economics. We make the case for the model-based approach and examine its advantages as well as some problematic issues associated with it.
"Two-stage Threshold Representations", with Marco Mariotti and Christopher J. Tyson, Theoretical Economics, 8: 875–882, 2013.
Abstract. We study two-stage choice procedures in which the decision maker first preselects the alternatives whose values according to a criterion pass a menu-dependent threshold and then maximizes a second criterion to narrow the selection further. This framework overlaps with several existing models that have various interpre- tations and impose various additional restrictions on behavior. We show that the general class of procedures is characterized by acyclicity of the revealed "first- stage separation relation".
"Categorize Then Choose: Boundedly Rational Choice and Welfare", with Marco Mariotti, Journal of the European Economic Association, 10(5): 1141-1165, 2012.
Abstract. We propose a boundedly rational model of choice where agents categorize alternatives before choosing. The model explains some behavioral anomalies, and it is fully characterized by a property of choice data: a categorizer can never exhibit certain patterns of “revealed preference reversals”. This model offers clues on the problem of making welfare judgements in the presence of boundedly rational agents.
"Choice by lexicographic semiorders", with Marco Mariotti, Theoretical Economics, 7: 1-23, 2012.
Abstract. In Tversky's (1969) model of a lexicographic semiorder, a preference is generated via the sequential application of numerical criteria by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a fixed threshold. We generalize this idea to a fully fledged model of boundedly rational choice. We explore the connection with sequential rationalizability of choice (Apesteguia and Ballester 2010, Manzini and Mariotti 2007) and we provide axiomatic characterizations of both models in terms of observable choice data.
"A million answers to twenty questions: choosing by checklist", with Michael Mandler and Marco Mariotti, Journal of Economic Theory, 147(1): 71-92, 2012.
Abstract. Several decision models in marketing science and psychology assume that a consumer chooses by proceeding sequentially through a checklist of desirable properties. These models are contrasted to the utility maximization model of rationality in economics. We show on the contrary that the two approaches are nearly equivalent. Since the number of preference discriminations that an agent can make increases exponentially in the number of properties used, checklists provide a rapid procedural basis for utility maximization.
"Choosing monetary sequences: theory and experimental evidence", with Marco Mariotti, and Luigi Mittone, Theory and Decision, 65 (3): 327-354, 2010.
Abstract. We formulate and investigate experimentally a model of how individuals choose between time sequences of monetary outcomes. The model assumes that a decision maker uses, sequentially, two criteria to screen options. Each criterion only permits a decision between some pairs of options, while the other options are incomparable according to that criterion. When the first criterion is not decisive, the decision maker resorts to the second criterion to select an alternative. We find that: (1) traditional economic models based on discounting alone cannot explain a significant (almost 30%) proportion of the data no matter how much variability in the discount functions is allowed; (2) our model, despite considering only a specific (exponential) form of discounting, can explain the data much better solely thanks to the use of the secondary criterion; (3) our model explains certain specific patterns in the choices of the "irrational" people. We reject the hypothesis that anomalous behavior is due simply to random "mistakes" around the basic predictions of discounting theories: deviations are not random and there are clear systematic patterns of association between "irrational" choices.
"Consumer choice and revealed bounded rationality", with Marco Mariotti, Economic Theory, 41(3): 379-392, 2009.
Abstract. We study two boundedly rational procedures in consumer behavior. We show that these procedures can be detected by conditions on observable demand data of the same type as standard revealed preference axioms. This provides the basis for a non-parametric analysis of boundedly rational consumer behavior mirroring the classical one for utility maximization.
"On Smiles, Winks, and Handshakes as Coordination Devices", (with Abdolkarim Sadrieh, and Nicolaas J. Vriend), Economic Journal, 119 (537): 826-854, 2009.
Abstract. In an experimental study we examine a variant of the 'minimum effort game', a coordination game with Pareto ranked equilibria and risk considerations pointing to the least efficient equilibrium. We focus on the question whether simple cues such as smiles, winks and handshakes could be recognised and employed by the players as a tell-tale sign of each other's trustworthiness, thus enabling them to coordinate on the more risky but more rewarding Pareto efficient equilibrium. Our experimental results show that such cues may indeed play a role as coordination devices as their information value is significant and substantial.
"Alliances and negotiations: an incomplete information example", with Marco Mariotti, Review of Economic Design (special issue on “Institutional Design and Conflict”), 13 (3): 195-203, 2009.
Abstract. We study a bargaining game between an individual and an 'alliance' in the sense of Manzini and Mariotti (J Econ Theory 121:128-41, 2005), in which the opponent of the alliance is incompletely informed about the relative strengths of its members. The best equilibrium outcome for the alliance under a unanimity rule is not attainable with a non-unanimity rule. However, unlike in the complete information model, less than optimal outcomes and delays may occur with positive probability even under unanimity, depending on the prior beliefs and the preferences of the agents.
"On the Representation of Incomplete Preferences over Risky Alternatives", with Marco Mariotti, Theory and Decision, 65 (4), pp. 303-323, 2008.
Abstract. We study preferences over lotteries which do not necessarily satisfy completeness. We provide a characterization which generalizes Expected Utility theory. We show in particular that various sure-thing axioms are needed to guaranteee the representability in terms of utility intervals rather than numbers, and to provide a linear interval order representation which is very much in the spirit of Expected Utility theory.
"Sequentially Rationalizable Choice", with Marco Mariotti, American Economic Review, 97: 1824-1839, 2007.
Abstract. A sequentially rationalizable choice function is a choice function that can be retrieved by applying sequentially to each choice problem the same xed set of asymmetric binary relations (rationales) to remove inferior alternatives. These con- cepts translate into economic language some human choice heuristics studied in psychology and explain cyclical patterns of choice observed in experiments. We study some properties of sequential rationalizability and provide a full character- ization of choice functions rationalizable by two and three rationales.
"A Vague Theory of Choice Over Time", with Marco Mariotti, Advances in Theoretical Economics, Berkeley Electronic Press, Vol. 6 : Iss. 1, Article 6, 2006.
Abstract. We propose a novel approach to modelling time preferences, based on a cognitive shortcoming of human decision makers: the perception of future events becomes increasingly 'blurred' as the events are pushed further in time. Our model explains behavioural `anomalies' such as preference reversal and cyclical choice.
"Stakeholder Bargaining Games", with Clara Ponsati, International Journal of Game Theory, 34 (1), pp. 67-77, 2006.
Abstract. We study bilateral bargaining problems with an interested third party, the stakeholder, that enjoys benefits upon a bilateral agreement. To address the strategic implications of stakeholders over negotiations, we consider a model where two bargainers interact in the presence of a third party that (a) can transfer a share of her benefits to the bargainers but cannot receive a share of the bilateral surplus, and (b) while she may not participate in all periods of the negotiation, she cannot remain entirely inhibited. Our main findings are:(1) the stakeholder’s (reverse) liquidity constraint implies the existence of a multiplicity of stationary subgame perfect equilibria that include outcomes with very asymmetric bilateral agreements, and (2) the partial participation of the stakeholder may be the source of severe inefficiency.
"Stakeholders in Bilateral Conflict", with Clara Ponsati, Mathematical Social Sciences, 50 (2), pp. 166-180, 2005.
Abstract. The resolution of a conflict often has an impact which extends beyond the remits of the parties directly involved in the confrontation (e.g. labour negotiations in sectors of public interest, where a strike would impact on the public at large). Once this is recognised, models addressing negotiations in such situations ought to account for the role and interests of the stakeholder - a third party whose stake is linked to the original negotiations. In this paper we address the strategic role of stakeholders in bilateral confrontations that take the form of a war of attrition; we assume that the bilateral confrontation runs concurrently with the parties interaction with the stakeholder, that chooses strategically her timing to intervene and take action to promote agreement. We show that under complete information the interplay of different interests in this tripartite timing game results in delayed outcomes. We also explore the role of incomplete information and show that asymmetries of information do not necessarily translate in increased inefficiency.
"Alliances and Negotiations", with Marco Mariotti, Journal of Economic Theory, 121 (1), pp. 128-141, 2005.
Abstract. A characteristic of many bargaining situations is that the negotiators represents the interests of a set of parties (trade unions, political parties, etc.) with composite interests, whose bargaining behaviour is regulated by some collective decision mechanism. In this paper we provide a natural model of such circumstances, and show how different preference aggregation procedures within the composite player affect the bargaining outcome. In particular we find that unanimity procedures lead to 'more aggressive' behaviour than majority procedures, and that procedures which introduce minimum safeguards for the members of an alliance may result in agreements that are worse than without those safeguards.
"A Theory of Vague Expected Utility", with Marco Mariotti, Topics in Theoretical Economics, vol. 4: No. 1, Article 10.
Abstract. We propose a new theory of choice between lotteries, which combines an 'economic' view of decision making - based on a rational,though incomplete, ordering - with a 'psychological' view - based onheuristics. This theory can explain observed violations of EU theory,namely all cyclical patterns of choice as well as violations of indepen-dence.
"Going alone together: Joint Outside Options in Bilateral Negotiations", with Marco Mariotti, Economic Journal, 2 (498), pp. 943-960 2004.
Abstract. Several contractual situations are such that the parties may 'step out' of negotiations and take up outside opportunities only if there is mutual consent to do so. Examples include employer-employee negotiations, divorce and inheritance procedures, and arbitration. To analyse such cases we develop the general concept of a 'joint outside option' and study its effect in the standard bargaining game. Examples from the international trade and theory of the firm are considered in some depth.
"Does divorce law matter?", with Giulio Fella and Marco Mariotti, Journal of the European Economic Association, 2 (4), pp. 607-633, 2004.
Abstract. In this paper we derive an explicit model of negotiations between spouses when unconstrained transfers are possible only in case of separation. We show that inefficient separation may occur in equilibrium even under consensual divorce law. This provides theoretical support for the view that changes in social norms rather than in legislation may be responsible for increasing divorce rates.
"A Bargaining Model of Voluntary Environmental Agreements", with Marco Mariotti, Journal of Public Economics, 87 (12), pp. 2755-2767, 2003.
Abstract. We present an explicit model of firm-regulator negotiations in a market with several firms. We describe how the regulatory surplus is distributed between firms and regulator, and analyse the impact of various parameters on the resulting level of environmental regulation. Our main result is that a 'toughest firm principle' holds: the outcome of negotiations is essentially determined by the firm with the most aggressive attitude towards environmental control.
"The effect of disagreement on non-cooperative bargaining", with Marco Mariotti, Journal of Economic Theory, 107 (2), pp. 490-499, 2002.
Abstract. A seemingly mild assumption of the standard alternating offers bargaining model under risk is that the breakdown event is not strictly worse than the worst agree- ment. When this assumption is relaxed the structure of the equilibrium set of agreements changes in an interesting way. We analyse the effect of disagreement on equilibrium, and relate our result to a class of outside option models.
"A Tragedy Of The Clubs: Excess Entry in Exclusive Coalitions", with Marco Mariottii, Journal of Public Economic Theory, 4 (1), pp. 115-136, 2002.
Abstract. We model club formation as a noncooperative game of coalition formation and surplus division. We show how social norms and individual rationality sustain a particular type of collective inefficiency, namely, excessive entry in the joint production and exploitation of an excludable good. We term this phenomenon the "tragedy of the clubs". The tragedy of the clubs is a pervasive equilibrium phenomenon.
"Perfect Equilibria in a Model of Bargaining with Arbitration", with Marco Mariotti, Games and Economic Behavior, 37 (1), pp. 170-195, 2001.
Abstract. We consider an alternating offer bargaining model in which the players may agree to call in an arbitrator in case of disagreement. The main message of our study is that the mere presence of an arbitrator-who can only become active with the consent of both parties-in the background of negotiations may entirely drive their outcome. We compare our results with those obtained in models with outside options.
"Strategic Bargaining with Destructive Power", Economics Letters, 65 (3), pag. 315-322, 1999.
Abstract. This note studies a two-player alternating offers bargaining model in which one of the agents has the ability to damage permanently the 'pie' bargained over. Beside the 'Rubinsteinian' bilateral monopoly outcome, I show that it is possible to select a 'harming' equilibrium in which the sequence of damages to the pie is endogenously determined.
"Game Theoretic Models of Wage Bargaining", Journal of Economic Surveys, 12 (1), pag 1-49, 1998.
Abstract. This paper aims at being a tool to help apply game theoretic bargaining models to wage negotiations. In this perspective, we review a number of articles which explicitly deal with wage determination as well as purely game theoretical models which we believe can be fruitfully extended to account for specific features of labour markets. We discuss some common shortcomings in the wage negotiation literature, and suggest possible lines of research worth pursuing to deal with such weaknesses.
"Strategic Wage Bargaining with Destructive Power: the Role of Commitment", Economics Letters, 54 (1), pag.15-22, 1997.
Abstract. We build a simple allernating-offers bargaining model in which one of the players call commit to damage the "pie" that they are bargaining over. In the unique equilibrium partition his share does not vary monotonically with the discount factor.


Papers published elsewhere

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"Choice over time", with Marco Mariotti, chapter 10 in P. Anand, P. Pattanaik and C. Puppe (eds.) Oxford Handbook of Rational and Social Choice, Oxford University Press, 2009.
Abstract. This chapter reviews both the theoretical modeling and the experimental evidence, relating to choice over time. Most of the space is devoted to choices between outcome‐date pairs, which has been better studied, especially experimentally, but it also discusses choices between time sequences of outcomes. It distinguishes between “soft anomalies”, which can be accommodated by a simple modification of the standard exponential discounting model (e.g. hyperbolic discounting) and “hard anomalies” which pose a more fundamental challenge.
"Arbitration and Mediation: an Economic Perspective", with Marco Mariotti, European Business Organization Law Review, vol. 3, p. 623-642, 2002.
Abstract.This paper deals with the effects that intermediation has on strategic behaviour in negotiations. To this end, we use the tools of game theory to analyse how different institutional settings can provide specific strategic incentives and thereby condition the outcome of negotiations. We concentrate on some very recent contributions, which have addressed gaps in this literature and stress the economic intuition behind some predicted behaviours.


Dying a slow, unjust death...

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"Two-stage bargaining solutions", with Marco Mariotti, Queen Mary Working paper n. 572/2006, September 2006 and SSRN Working paper, July 2006, Revised December 2012
Abstract. We introduce and characterize a new class of bargaining solutions: those which can be obtained by sequentially applying two binary relations to eliminate alternatives. As a by-product we obtain as a particular case a partial characterization result by Zhou (Econometrica, 1997) of an extension of the Nash axioms and solution to domains including non-convex problems, as well as a complete characterizations of solutions that satisfy Pareto optimality, Covariance with positive affine transformations, and Independence of irrelevant alternatives.
"Revealed Preferences and Boundedly Rational Choice Procedures: an Experiment", with Marco Mariotti, (available in earlier incarnation as IZA Discussion Paper No. 2341) Revised February 2010
Abstract. If people are irrational, how are they irrational? And how can we describe their behavior and perform welfare analysis? We study the question experimentally. We test several boundedly rational decision models which are testable by means of simple revealed preference type of axioms. In an experiment, we first show `menu effects' to drive irrationality more than cycles of choice. Then, by using the revealed preference methodology, we show that a version of the Categorise Then Choose model we propose performs best (in terms of the Selten score of predictive success) in a group of models. (most recent version here). The technical and data appendix is here
" Shortlisting", with Marco Mariotti, Working paper EconWPA ewp-pe/0503006, March 2005, Revised March 2006
Abstract. We study the properties of decisions made by committees who select alternatives by constructing shortlists. We find that even when committees are themselves rational, such procedures may not give rise to rational choices. A necessary condition for this to occur is disagreement between committees. However, we delimit substantially the extent of `irrationality' that these procedures allow.
"Intergenerational Justice in the Hobbesian State of Nature", with Marco Mariotti e Roberto Veneziani, 2010
Abstract. We analyse the issue of justice in the allocation of resources across generations. Our starting point is that if all generations have a claim to natural resources, then each generation should be entitled to exercise veto power on the unpalatable choices of the other generations. We analyse this situation as one of bargaining μa la Rubinstein, Safra and Thomson (1992), which incorporates a notion of justice as mutual advantage, rather than justice as impartiality, as in the Kantian-Rawlsian tradition. Our framework captures some key aspects of the interaction between isolated agents in a Hobbesian state of nature, in which agents are not placed behind a veil of ignorance, but none of them is su±ciently strong to impose their will against all others (state of war of all against all). We analyse some new social welfare relations emerging from this Hobbesian framework.
"Wage Determination and the Sources of Bargaining Power", May 2002, (with Dennis Snower) Revised January 2005
Abstract. This paper explores the sources of bargaining power in wage negotiations. In the standard analyses of wage bargaining, the negotiating partners are specified a priori, and thus it is impossible to address the question of how they achieve and retain their negotiating positions, on which their bargaining power is based. In our analysis, by contrast, the firm can choose between two sets of wage negotiations: those it can conduct with its incumbent employees and those with new job seekers. These negotiations are imperfectly substitutable, and the degree of substitutability is determined by the firm's labor turnover costs (e.g. costs of hiring, training, and firing). In this context, labor turnover costs not only influence the negotiators' alternatives to bargaining (i.e. their fall-back positions and outside options); they affect the nature of the bargaining process itself. This approach leads to a new theory of wage determination.
"How vague can one be? Rational preferences without completeness or transitivity", with Marco Mariotti, December 2003, Working paper EconWPA ewp-game/0312006, Revised April 2004
Abstract. What can it mean for preferences to be rational when transitivity or completenss are not assumed? In this paper we provide a framework and a set of conditions to deal with this question. We provide representation results in terms of a pair of functions, a utility function and a vagueness function.
"Time preferences: do they matter in bargaining?", Working Paper n. 445, Department of Economics, Queen Mary, University of London.
Abstract. Experimental studies of bargaining generally impose time preferences' on subjects, in the sense that in case of disagreement, the experimenter reduces the size of the surplus bargained over by imposing exogenously some monetary cost. Contrary to this practice, in this study time preferences are first elicited in a preliminary phase, and then bargaining begins. I show that although subjects are sensitive to the timing of a monetary reward, this plays no role in determining bargaining behaviour. Furthermore, when the bargaining game is played in conventional experimental setting with monetary costs of delay, these do have an impact on subjects' conduct in negotiations.