Horst Zank
“Gain-Loss Utility for Prospect Theory,” joint work with Chi Chong Leong
An extension to original prospect theory is provided in which the gain-loss utility is formally identified. To this aim, we demand some standard properties, including monotonicity with respect to first order stochastic dominance, and combine them with a new property called gain-loss consistency. For simple prospects that give a gain and a loss (and else the reference point), these properties characterize an extension of original prospect theory with probability weighting that depends on whether probabilities are attached to gains or to losses. For general prospects with multiple gains and multiple losses, the probability weighting functions apply to the overall probability of gaining and of losing. Further, the gain-loss utility function determines the value of a prospect by transforming the expected utility of the gain part and the expected utility of the loss part of that prospect before those components are aggregated to obtain that prospect’s value. This way, the gain-loss utility can be decomposed into a basic utility for outcomes and a transformation thereof that captures loss aversion.
Stéphane Zuber
"Infinite population utilitarian criteria" joint with Geir B. Asheim and Kohei Kamaga
We examine utilitarian criteria for evaluating profiles of wellbeing among infinitely many individuals. Motivated by the non-existence of a natural 1-to-1 correspondence between people when alternatives have different population structures, with a different number of people in each generation, we impose equal treatment in the form of Strong Anonymity. We show how a novel criterion, Strongly Anonymous Utilitarianism, can be characterized by combining Strong Anonymity with other regularity axioms (Monotonicity, Finite Completeness, and continuity axioms) as well as axioms of equity, sensitivity, separability, and population ethics. We relate it to other strongly anonymous utilitarian criteria and demonstrate its applicability by showing how it leads to an efficient and sustainable stream in the Ramsey model.
Ani Guerdjikova
"Cases and States" co-authored with Jürgen Eichberger
In this paper, we provide a novel framework for decision making under uncertainty based on information available in the form of a data set of cases. A case contains information about an action taken, an outcome obtained, and other circumstances that were recorded with the action and the outcome. The set of actions, the set of outcomes and the set of possibly relevant recorded characteristics are derived from the cases in the data set. The information from the data set induces a belief function over outcomes for each action. From a decision maker’s preferences over belief functions one can derive a representation evaluating outcomes according to the α-maxmin criterion. New data affects behavioural parameters, such as awareness, ambiguity and ambiguity attitude, and may suggest a classifications of data into states.
Philippe Bich
« Discounting under weak anonymity » joint with Dong Xuan Bach
It is well known that there does not exist aggregation rules of infinite utility streams which respect Pareto and anonymity axioms (Basu Mitra ECMA 2003). In this paper, we define a familly of new weak anonymity axioms and characterize the aggregation rules which respect Pareto and weak anonymity axioms (together with other standard axioms). This allows to recover some standard rules (like maxmin aggregation rule of Chambers and Echenique, ECMA 2018), but also provide new alternative rules. The method of proof seems new in this literature, and mixes the use of Schauder fixed-point theorem together with the theory of eigenvalues of infinite dimensional operators.
Lukasz Wozny
"Global version of Tarski-Kantorovich theorem for correspondences and iterative monotone comparative statics" joint with L. Balbus, W. Olszewski and K. Reffett
For a strong set order increasing (resp., strongly monotone) upper order hemicontinuous correspondence F : A ⇒ A, where A is a complete lattice (resp., a σ-complete lattice), we provide sufficient conditions for tight fixedpoint bounds for sufficiently large iterations F k (a 0 ), starting from any point a 0 ∈ A. Our results prove a local version of the Veinott-Zhou generalization of Tarski’s theorem, as well as provide a new global version of the Tarski-Kantorovich principle for correspondences.
John Quah
"Comparative statics with adjustment costs and the le Chatelier principle" with Eddie Dekel and Ludvig Sinander.
We develop a theory of monotone comparative statics in the presence of adjustment costs. We show that comparative statics conclusions may be drawn under the usual ordinal complementarity assumptions on the objective function, assuming almost nothing about costs: the only requirement is that non-adjustment be costless. We use this insight to provide a general treatment of the le Chatelier principle based on adjustment costs. We extend these results to a fully dynamic, forward-looking model of adjustment over time: given only minimal structure on costs, optimal adjustment follows a monotone path. We apply our results to models of investment and of sticky prices.
Lorenzo Bastianello
"Gain-Loss Hedging and Cumulative Prospect Theory"
Two acts are comonotonic if they yield high payoffs in the same states of nature. The main purpose of this paper is to derive a new characterization of Cumulative Prospect Theory (CPT) through simple properties involving comonotonicity. The main novelty is a concept dubbed gain-loss hedging: mixing positive and negative acts creates hedging possibilities even when acts are comonotonic. This allows us to clarify in which sense CPT differs from Choquet expected utility. Our analysis is performed under the simpler case of (piece-wise) constant marginal utility which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes.
Joseph Abdou
"Topology and Politics : A Qualitative Theory of Conflict Resolution and Political Compromise" with Hans Keiding
We consider a basic model of political structure, given through the description of its agents or forces and the viable configurations that can emerge as political decision body. When the set of all agents is not viable, a compromise must be searched for. We model a political structure as a simplicial complex where a viable configuration is a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of other agents acting as representatives. A delegated compromise is a more elaborated version of a compromise obtained by iteration of the process of delegation. Existence of such compromises depends on the discrete topology of the simplicial complex. In the paper, we study represented and delegated compromises in their dependence on the combinatorial structure of the viable configurations, and in particular we show that existence of a delegated compromise is equivalent to strong contractibility of the simplicial complex.
Jean-Marc Bonnisseau
"Regular economies with ambiguity aversion"
We consider a family of exchange economies with complete markets where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number, local differentiable selections of the equilibrium prices. Thus, even if ambiguity aversion is represented by non-differentiable multiprior preferences, economies retain generically the properties of the differentiable approach.
Michel Grabisch
“On the convex hull of k-additive 0-1 capacities and its application to model identification in decision making” with Christophe Labreuche
The Choquet integral w.r.t. a capacity is a versatile tool commonly used in decisionmaking. Its practical identification requires, however, to solve an optimization problem with exponentially many variables and constraints. The introduction of k-additive capacities, through the use of the Möbius transform, permits to reduce the number of variables to a polynomial size, but leaves the number of constraints exponential. When k = 2, the use of vertices of the set of 2-additive capacities permits to solve the problem as the number of vertices is polynomial. When k > 2, this solution is no more applicable as the set of vertices of k-additive capacities is not known. We propose in this paper to use instead the set of vertices which are 0-1 valued. We show that the loss of generality is small, and that the number of such vertices is polynomial. Also, we study the geometric properties of the convex hull of 0-1 valued k-additive capacities.
İsmail Mehmet
"Conditional strategy equilibrium" co-authored with L. Bastianello
In this note, we prove the existence of an equilibrium concept, dubbed conditional strategy equilibrium, for non-cooperative games in which a strategy of a player is a function from the other players' actions to her own actions. We study the properties of efficiency and coalition-proofness of the conditional strategy equilibrium in n-person games.
Lorenzo Stanca
“Recursive Preferences and Ambiguity Attitudes” with Giulio Principi
We illustrate the strong effects of recursivity, a standard assumption in dynamic environments, on attitudes toward uncertainty. We distinguish between two main abstractions of a dynamic choice problem: sequential and intertemporal consumption choice problems. In sequential choice problems, recursivity implies constant absolute ambiguity aversion (CAAA) when preferences are biseparable. In intertemporal consumption choice problems, recursivity always implies CAAA under the standard extension of first order stochastic dominance to dynamic settings. When uncertainty aversion is modeled as a form of convexity of preferences, recursivity implies as a byproduct that one cannot go beyond recursive variational preferences.
Andrei Savochkin
"Subjective risk, probability distortions, and pessimism" (joint work with Anna Gumen and Efe Ok).
We follow the subjective risk approach in which preferences over risky alternatives are viewed as arising from more basic preferences over info-acts — objects that can be split into information presented to the subject and an uncertain payoff prospect. We adopt the definition of pessimism via Schmeidler's Uncertainty Aversion axiom and study what that definition entails for a number of well-known models of choice under risk. As we show, defining pessimism via uncertainty aversion gives consistent answers for models in which the notion of pessimistic probability distortions is well understood and leads to new insights for other models.
Peter Norman Sørensen
“Comparison of Experiments in Monotone Problems” with Alfredo di Tillio (Bocconi), Marco Ottaviani (Bocconi)
Blackwell (1951) characterized when an experiment is more informative than another, in the sense that no rational decision maker would prefer observing the second experiment rather than the first. This paper provides a novel characterization for a binary-signal experiment A to be more informative than another arbitrary experiment B for all decision makers with preferences in Quah and Strulovici’s (2009) interval dominance ordered class, encompassing monotone decision problems (Karlin and Rubin, 1956) and single-crossing preferences (Milgrom and Shannon, 1994). We show that if experiment A satisfies the monotone likelihood ratio property, then A is more informative than B if and only if all posterior beliefs induced by B are dominated by (dominate) the belief induced by the highest (lowest) signal from A in the likelihood ratio order. If instead experiment A fails to satisfy the monotone likelihood ratio property, Blackwell’s (1951) characterization applies: A is more informative than B if and only if B is a garbling of A.
Evan Piermont
"Vague Preferences and Contracts"
In this paper, I examine decision making in an environment where payoff relevant contingencies are vague, that is, neither absolutely true nor absolutely false. In this model, the decision maker values acts that are predicated on linguistic statements, rather than an exogenous state-space. I axiomatize a class of preferences under which the state-space representing the decision maker’s beliefs about the degree of truth of contingencies is identified from her choices.
I then apply this model to a simple contracting environment wherein contracts must be explicitly constructed using said linguistic statements. I show that while different restrictions on the contract writing technology can impart different outcomes, under mild conditions, the dictate that contracts are explicitly constructable is not distortionary. This serves as a theoretical justification for the use of state-space models even when representing real-world (hence linguistic) contracting environments.
Miguel Angel Ballester
"Choice-based foundations of ordered logit"
We provide revealed preference foundations to ordered logit for continuous decision problems.
Bertrand Wigniolle
“Time Inconsistent Preferences with Time Dependent Relative Risk Aversion: a Model with some Macroeconomic Applications”
This paper proposes a model of intertemporal preferences where the relative risk aversion depends on the time horizon of the agent. The agent is supposed to evaluate risk in the short run with a relative risk aversion coefficient which differs from its long run value. As preferences are no more time consistent, decisions are the solution of a game between the successive selves. The model is applied to the problem of the optimal choice of saving with a risky interest rate and to the equity premium puzzle. A time-dependent risk aversion may help to solve the puzzle.
Marello Basili
“Strategy-proof aggregation of approximate and imprecise judgments”
We study strategy-proof aggregation rules for exact and approximate judgments of agents when the judgement space is a bounded distributive lattice. We show that bounded distributivity of the judgment space guarantees that the same structure is inherited by its intervals. Relying on such facts we prove the existence of a large class of inclusive and unanimity-respecting strategy-proof aggregation rules for both exact and approximate judgments. Amongst them, the simple majority aggregation rule is characterized as the only one that satisfies both anonymity and bi-idempotence (i.e. ensures a definite choice between the two judgments nominated by a maximally polarized opinion profile). Finally, we consider several applications of our results including approximate probability estimates as modeled by intervals of probability values, numerical measurements with explicit error bounds, approximate classifications, and conditional judgments that are amenable to composition by means of a set of logical connectives.
Adam Dominiak
"Common Belief in Choquet Rationality with an “Attitude”" co-authored with Burkhard Schipper
We consider finite games in strategic form with Choquet expected utility. We characterize a preference-based notion of belief, define Choquet rationalizability, and characterize it by Choquet rationality and common beliefs in Choquet rationality in the universal capacity type space in a purely measurable setting. We also show that Choquet rationalizability is equivalent to iterative elimination of strictly dominated actions (not in the original game but) in an extended game. This allows for computation of Choquet rationalizable actions for economic applications without the need to first compute Choquet integrals. Choquet expected utility enables us to investigate common belief in ambiguity love/aversion. We show that Choquet rationality and common belief in Choquet rationality and ambiguity love/aversion leads to smaller/larger sets of action profiles, respectively.