ABSTRACT
MONDAY THE 17TH OF DECEMBER
Session I : Fixed Points & Strategies
Massimo Marinacci (Bocconi University, with Luigi Montrucchio): Unique Tarski Fixed Points
Abstract: We establish sufficient conditions that ensure the uniqueness of Tarski-type Fixed points of monotone operators. Several applications are presented.
Eric Danan (University of Cergy, with Thibault Gajdos & Jean-Marc Tallon): Tailored Recommendations
Abstract : Many internet platforms use so-called «collaborative filtering» techniques to provide a user with «tailored»
recommendations depending on both her own and other users’ past behavior. We analyze the problem of making such recommendations from a social choice perspective, by formalizing it as a «constrained» aggregation problem. Within this framework, we characterize the unique recommendation rule satisfying two simple axioms, establish further properties of this rule, and compare it with typical collaborative filtering rules.
Itzhak Gilboa (HEC - Tel Aviv University, with Rossella Argenziano): Statistical Games and Similarity-Nash Equilibria
Abstract : We define Statistical Games. We suggest statistical-strategic reasoning for equilibrium selection in such games.We define the empirical similarity and Similarity-Nash equilibria Show that these capture the example. We finally show that (only) second-order induction can identify the intuitive equilibria.
Session 2 : The Structure of Preferences
Simone Cerreia-Voglio (Bocconi University, with Efe Ok): The Rational Core of Preference Relations
Abstract: We consider revealed preference relations over risky (or uncertain) prospects, and allow them to be nontransitive and/or fail the classical Independence Axiom. We identify the ìrational partîof any such preference relation as its largest (transitive) subrelation that satisÖes the Independence Axiom and that exhibits some coherence with the original relation. It is shown that this subrelation, which we call the rational core of the given revealed preference, exists in general, and under fairly mild conditions, it is continuous. We obtain various representation theorems for the rational core, and decompose it into other core concepts for preferences. These theoretical results are applied to compute the rational cores of a number of well-known preference models (such as Fishburnís SSB model, justiÖable preferences, and variational and multiplier modes of rationalizable preferences). We also use the rational core operator to deÖne and characterize a new risk aversion concept for nontransitive nonexpected utility models (which may not even be complete). Finally, we show that, under some mild monotonicity conditions, the Preference Reversal Phenomenon does not arise from the rational core of oneís preferences.
Efe Ok (New York University, with Hiroki Nishimura): Preference Structures
Abstract: We suggest the use of two binary relations to describe the preferences of an agent. The first of these, %, aims to capture the rankings of the agent that are (subjectively) “obvious/easy.” As such, it is transitive, but not necessarily complete. The second one, R, arises from what we observe the agent choose in the context of pairwise choice problems. As such, it is assumed to be complete, but not necessarily transitive. Finally, we posit that % and R are consistent in the sense that (i) R is an extension of %, and (ii) R is transitive with respect to %. This yields what we call a preference structure. It is shown that this model allows for phenomena like rational choice, indecisiveness, imperfect ability of discrimination, regret, and advise taking, among others. We show how one may represent preference structures by using (sets of) utility functions, but the bulk of the paper is about choice behavior that arises from preference structures which we model by using the notion of top cycles. It is shown that this leads to a rich theory of choice with a large explanatory power, and still with a surprising amount of predictive power. Under general conditions, we prove that choice correspondences that are induced by preference structures are nonempty-valued, and then identify the largest preference structure that rationalizes a choice correspondence that is known to be rationalizable by some such structure. Thus, this choice theory, while much more general, possess existence and uniqueness properties that parallel those of the classical theory of rational choice.
Michael Richter (Royal Holloway, with Ariel Rubinstein): Convex Preferences
Abstract: We suggest a concept of convexity of preferences without relying on an algebraic structure. The decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is convex: if for each criterion there is an element that is both inferior to b by the criterion and superior to a by the preference relation, then b is preferred to a. The definition expands the standard Euclidean definition with the criteria being all algebraic linear orderings. Under general conditions, any strict convex preference relation is represented by a maxmin of utility representations of the criteria.
Session 3: Risk, Ambiguity & Strategies
Peter Klibanoff (Northwestern University, with Eran Hanany & Sujoy Mukerji): Incomplete Information Games with Ambiguity Averse Players
Abstract: We study incomplete information games with ambiguity averse players. Our focus is on equilibrium concepts satisfying sequential optimality ñ each playerís strategy is optimal at each information set given opponentsí strategies. We show sequential optimality, which does not make any explicit assumption on updating, is equivalent to sequential optimality with respect to beliefs updated using a particular generalization of Bayesian updating. Ambiguity aversion expands the set of equilibria compatible with players sharing common ambiguous beliefs. We connect ambiguity aversion with belief robustness. Examples illustrate new strategic behavior, including strategic use of ambiguity, under ambiguity aversion.
Jingyi Xue (Singapore Management University): Preferences with Changing Ambiguity Aversion
Abstract: In this paper provides, we study two extensions of Gilboa and Schmeidler (1989)’s maxmin expected utility decision rule to accommodate a decision maker’s changing ambiguity attitude. The two rules are respectively a weighted maxmin rule and a variant constraint rule. The former evaluates an act by a weighted average of its worst and best possible expected utilities over a set of priors, with the weight on the worst case depending on the act. The latter evaluates an act by its worst expected utility over a neighborhood of a set of approximating priors, with the size of the neighborhood depending on the act. Canonical representations of the two rules are provided for classes of preferences that exhibit respectively ambiguity aversion of Schmeidler (1989) and ambiguity aversion of Ghirardato and Marinacci (2002). When restricted to the class of preferences exhibits both versions of ambiguity aversion, our results provide two alternative representations in addition to the ambiguity averse representation provided by Cerreia-Vioglio, Maccheroni, Marinacci and Montrucchio (2011). In the second part of this paper, we study the wealth effect under ambiguity. We propose axioms on absolute and relative ambiguity aversion and derive the three representations for the ambiguity averse preferences displaying decreasing (increasing) absolute ambiguity aversion. In particular, decreasing absolute ambiguity aversion implies that as baseline utility increases, a weighted maxmin decision maker puts less weight on the worst case, and a variant constraint decision maker considers a smaller neighborhood of approximating priors.
Aloisio Araujo (IMPA-FGV, with Juan Pablo Gama & Timothy Kehoe): Risk-Loving & Taxes
We study the impact of tax and transfer polices in overlapping genera- tions models where agents have warm-glow bequest motives. We focus on models in which some dynasties of agents are risk averters and others are dynasties of risk lovers. Making simplifying assumptions, we construct a sequence of four models in which we are able to calculate invariant dis- tributions for wealth holdings. In the first model, the risky asset have the same expected return as the safe asset; in the second model and third model, only one type of agents can invest in the risky asset; and in the fourth, agents can only invest in one type of asset at a time. We interpret the decision to invest in the risky asset as the career choice to become an entrepreneur. These simplifying assumptions prevent risk averters from holding diversified portfolios of the risky asset and the safe asset, which allows us to calculate an invariant wealth distribution. A typical result across models is that increasing taxes and transfers reduces inequality but reduces growth. We identify parameter values for the model where agents are restricted to invest in only one type of assets in which high enough taxes and transfers insure risk averters and induce poor risk averters to invest in the risky asset. Those risk averters who are lucky and accumu- late a large enough level of wealth choose to switch to investing in the safe asset. In this case, increasing taxes and increases growth and the welfare of risk averters although it decreases the welfare of risk lovers.
Rabah Amir (University of Iowa): Dynamic Pricing of Green Goods under Discounted Network Effects
Abstract: This paper deals with dynamic pricing by a dominant firm selling a green good with network effects in an industry where a brown substitute is available from a competitive fringe. We explicitly model the accumulation process for the network, with consumers discounting more heavily the choices of more distant past cohorts of consumers. With linear demand, we get a unique closed-form solution for the infinite-horizon problem faced by the green good producer. For weak network effects, the steady-state network is finite, whereas strong network effects lead to universal adoption. We compare the private solution to first-best pricing by a benevolent social planner taking into account both network and environmental externalities. We find that the social planner favors universal adoption more frequently (i.e. for a wider domain of network effects) than the dominant firm. Even when both the firm and the planner endorse universal adoption, the network expansion is slower for the former, justifying policy intervention. As the first-best problem is a linear-quadratic dynamic optimization problem involving singular (or bang-bang) control, its solution calls for some methodological novelty.
TUESDAY THE 18TH OF DECEMBER
Session I : Random Choice
Igor Kopylov (University of California at Irvine): Minimal Rationalizations
Abstract: I find a minimal number m of linear orders on a finite set Z that rationalize all choices in all menus A (subsets of Z). The number m is computed explicitly in terms of choice data. If m = 2, then two rationalizations R and R’ are unique when sufficiently distinct from each other. Moreover, R and R’ can be identified in polynomial time with respect to |Z| and in terms of choices in triples - menus A such that |A| <=3. In general, the uniqueness is not guaranteed. However, minimal rationalizations can be still found in polynomial time with respect to m|Z| and in terms of choices in menus A such that |A| <=m+1. Minimal rationalizations can be combined with other primitives. In particular, they can be applied to stochastic choice data to capture a robust diversification heuristics.
Tomasz Strzalecki (Harvard University, with Mira Frick & Ryota Iijima): Dynamic Random Utility
Abstract: We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process (Ut) of utilities. We show first that even when (Ut) is arbitrary, dynamic random utility imposes new testable restrictions on how behavior across periods is related, over and above period-by-period analogs of the static random utility axioms: An important feature of dynamic random utility is that behavior may appear history dependent, because past choices reveal information about agents’ past utilities and (Ut) may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that when agents’ choices today influence their menu tomorrow (e.g., in consumption savings or stopping problems), imposing natural Bayesian rationality axioms restricts the form of randomness that (Ut) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allows us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model.
David Dillenberger (University of Pennsylvania, with Simone Cerreia-Vioglio, Pietro Ortolova & Gil Riella): Deliberately Stochastic
Abstract: We study stochastic choice as the outcome of deliberate randomization. We derive a general representation of a stochastic choice function where stochasticity allows the agent to achieve from any set the maximal element according to her underlying preferences over lotteries. We show that in this model stochasticity in choice captures complementarity between elements in the set, and thus necessarily implies violations of Regularity/Monotonicity, one of the most common properties of stochastic choice. This feature separates our approach from other models, e.g., Random Utility.
Session 2 (13h30-15h30) : Equilibrium
Nicholas Yannelis (Iowa University): Equilibrium Theory under Ambiguity: Existence, Implementation & Incentive Compatibility
Abstract: The introduction of Ambiguity in Equilibrium Theory with Asymmetric Information provides new insights and new results that cannot be obtained using the standard Bayesian preferences (Expected Utility). We will show how known counterexamples in equilibrium theory and Game Theory are not valid anymore if one introduces ambiguity. New results can be obtained that are false under Bayesian preferences.
Asen Kochov (University of Rochester): Unforeseen Contingencies & Sequential Trade
Abstract: TBA.
Bernard Cornet (PSE - University of Kansas, with Alain Chateauneuf): The Non-additive Risk- neutral Probability with Market Frictions and Put-Call Parity
Abstract: The fundamental theory of asset pricing has been developed under the two main assumptions that markets are frictionless and have no arbitrage opportunities. In this case the market enforces that replicable assets are valued by a linear function of their payoffs, or as the discounted expectation with respect to the so-called risk neutral probability. Important evidence of the presence of frictions in financial markets has led to study market pricing rules in such a framework. Recently, Cerreia-Vioglio, Maccheroni and Marinacci [2] have extended the Fundamental Theorem of Finance by showing that, with markets frictions, requiring the Put-Call Parity to hold, together with the mild assumption of Translation Invariance, is equivalent to the market pricing rule being represented as a discounted (Choquet) expectation with respect to a nonadditive risk neutral probability. This paper continues the study of Cerreia-Vioglio, Maccheroni and Marinacci by characterizing important properties of the (unique) nonadditive risk neutral probability vf associated with a Choquet pricing rule f, when it is not assumed to be subadditive. First, we show that the observed violation of the Call-Put Parity, a condition considered by Chateauneuf, Kast, and Lapied similar to, but different from, the Put-Call Parity in Cerreia-Vioglio, Maccheroni and Marinacci, is consistent with the existence of bid-ask spreads. Second, the balancedness of vf – or equivalently the non-vacuity of its core – is characterized by a notion of arbitrage-free, stronger than the one in Cerreia-Vioglio, Maccheroni and Marinacci, that eliminates all the arbitrage opportunities that can be obtained by splitting payoffs in parts; moreover the (nonempty) core of vf consists of additive probabilities below vf , called risk neutral probabilities, whose (standard) expectation is below the Choquet pricing rule f. Third, by strengthening again the previous notion of arbitrage-free, we show the existence of a a strictly positive risk neutral probability below vf, which allows to recover the standard formulation of the Fundamental Theorem of Finance for frictionless markets.
Session 3 (16h-18h) : Temporal Preferences
Marcus Pivato (University of Cergy): Intertemporal Choice with Continuity Constraints
Abstract: We consider a model of intertemporal choice where time is a continuum, the set of instantaneous outcomes (e.g. consumption bundles) is a topological space, and where intertemporal plans (e.g. consumption streams) must be continuous functions of time. We assume the agent can form preferences over plans defined on open time intervals. We axiomatically characterize the intertemporal preferences that admit a representation via discounted utility integrals. In this representation, the utility function is continuous and unique up to positive affine transformations, and the discount structure is represented by a unique Riemann-Stieltjes integral plus a unique linear functional measuring the long-run asymptotic utility.
Stefania Minardi (HEC, with Andrei Savochkin): Time for Memorable Consumption
Abstract: A consumption event is memorable if its memory affects an agent’s well-being at times after the material consumption. We develop an axiomatic model of memorable consumption in a dynamic setting. The representation takes the form of exponential discounting, and features additional terms that accumulate utility from the recollection of past consumption. We analyze alternative processes by which the memorable effect accrues over time and show that our model supports well-known phenomena in psychology, such as the peak-end rule, duration neglect, and adaptation trends. We study a prominent special case in which memory evolves according to a Markovian law and develop comparative statics with respect to strength and longevity of memory. As an application, we introduce memorable consumption into the standard linear-quadratic consumption-savings problem and examine its implications for life-cycle patterns..
Thai Ha-Huy (University of Evry Paris-Saclay, with Jean-Pierre Drugeon): A Not so Myopic Axiomatization of Multiple Discountings
Abstract: This article builds an axiomatization of inter-temporal trade-offs that makes an explicit account of the distant future and therefore encompasses motives related to sustainability, transmission to offsprings and altruism. The focus is on separable representations and the approach is completed following a decision-theory index based approach that is applied to utility streams. This enlightens the limits of the commonly used tail intensity requesites for the evaluation of utility streams: in this article, these are supersed and replaced by an axiomatic approach to optimal myopia degrees that in its turn precedes the determination of optimal discount. The overall approach is anchored in the new and explicit proof of a temporal decomposition of the preference orders between the distant future and the close future itself directly related to the determination of the optimal myopia degrees. The reference to robust orders and pessimism-like axioms finally allows for determining tractable representations for the indexes.
