Giovanni Paolo Crespi

Propensity to invest in stocks is highly heterogeneous, with many households avoiding stock market participation altogether. This heterogeneity is difficult to reconcile with standard economic theory. We study the role of memories in shaping investment decisions and in influencing how individuals incorporate stock-related information. Across two experiments, participants invest in a stock and are compensated based on its actual price realization. In the first experiment, we verify that activating memories prior to investing systematically shifts investment behavior. Participants asked to recall stock market–related memories before the investment task make more polarized choices: recalling positive memories increases investment relative to recalling non-positive ones, while activating non-positive memories lowers investment compared with not activating them. The second experiment reveals our central finding: the effect of information critically depends on the type of memory activated. All participants recall a memory before investing, after which some receive positive and truthful information about the stock. Information meaningfully increases investment only among participants who recalled non-personal memories; in contrast, recalling personal memories completely eliminates the response to information. We show that this sharp interaction cannot be explained by changes in beliefs, overconfidence, or mistrust in experts. Instead, it can be rationalized within a selective memory framework.

Catastrophic events, which are becoming increasingly frequent due to climate change, have significant negative impacts on housing. Yet, decision-makers remain puzzled by the low uptake rates for insurance coverage against these events. In this paper, we investigate whether this phenomenon is driven by individuals having miscalibrated beliefs about the likelihood of such events occurring. Additionally, we examine the impact of an information treatment designed to correct these perceived probabilities. Our experimental results show that participants in the treatment respond as expected, adjusting their beliefs accordingly. Moreover, these belief shifts influence participants’ demand for information on the topic and their interest in purchasing insurance. However, a follow-up survey conducted two months after the main experiment reveals that the effects of the treatment are short-lived, dissipating entirely within this period. Moreover, the information treatment shifts estimates about past mortality due to circulatory diseases, which are not closely related to the content of the information treatment, although more modestly. These two insights suggest ways of improving survey design in the field of information provision experiments. Our overall findings provide important insights for policymakers, highlighting the transient nature of the treatment-induced effects.

In this paper, we provide a systematization of the equilibrium concepts for vector-valued games. In general abstract setting, we give the definitions of Nash equilibrium, weak Nash equilibrium, and proper Nash equilibrium, we investigate the relationships among them, and we provide existence results for proper Nash equilibria and weak Nash equilibria. The link between the introduced equilibrium concepts and Nash equilibria of a game with scalar payoffs obtained by means of linear scalarization is investigated. For a vector matrix game, we show that the notions of proper Nash equilibrium and Nash equilibrium are equivalent, we prove existence of both Nash equilibria and weak Nash equilibria, we give characterizations of proper and weak best correspondence sets respectively, by defining characterizing functions from the matrices and the preference cones, and finally we list all best correspondence sets. The given definitions are illustrated by means of examples.

A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization equilibrium, is guaranteed by standard regularity conditions. The paper investigates the sensitivity to the level of uncertainty of this equilibrium focusing on robust games with no private information. Specifically, we prove that a robust-optimization equilibrium is an epsilon-Nash equilibrium of the nominal counterpart game, where epsilon measures the extra profit that a player would obtain by reducing his level of uncertainty. Moreover, given an epsilon-Nash equilibrium of a nominal game, we prove that it is always possible to introduce uncertainty such that the epsilon-Nash equilibrium is a robust-optimization equilibrium. These theoretical insights increase our understanding on how uncertainty impacts on the solutions of a robust game. Solutions that can be extremely sensitive to the level of uncertainty as the worst-case approach introduces non-linearity in the payoff functions. An example shows that a robust Cournot duopoly model can admit multiple and asymmetric robust-optimization equilibria despite only a symmetric Nash equilibrium exists for the nominal counterpart game.

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponding complete lattice of sets. Functions mapping into the preordered set are extended to complete lattice-valued ones, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared with existing ones in vector and set optimization. Its relevance is shown by means of many examples from multicriteria decision making, statistics, and mathematical economics and finance.

Set-valued extensions of vector-valued functions are used to investigate the relations between weak efficiency and variational inequalities (both Stampacchia and Minty type) which allows to apply the complete lattice framework from set optimization. Since the seminal work of Giannessi, it has been a challenge to generalize scalar results to the vector case. In this effort, some notions of generalized derivatives for vector-valued functions have been introduced, either in the form of set-valued functions or introducing appropriate notions of infinite elements in vector spaces. Switching the focus to set optimization in conlinear spaces, we propose a Dini-type derivative, that keeps the same set-valued form of the optimization problem.

We study a vector-valued game with uncertainty in the pay-off functions. We reduce the notion of Nash equilibrium to a robust set optimization problem and we define accordingly the notions of robust Nash equilibria and weak robust Nash equilibria. Existence results for the latter are proved and a comparison between the former and the analogous notion in Yu and Liu (J Optim Theory Appl 159:272–280, 2013) is shown with an example. The proposed definition of weak robust Nash equilibrium is weaker than that already introduced in Yu and Liu (2013). On the contrary, the robust Nash equilibrium we introduce is not comparable with the notion of robust equilibrium in Yu and Liu (2013), that is defined componentwise. Nevertheless, by means of an example, we show that our notion has some advantages, avoiding some pitfalls that occurs with the other.

Risk measures are defined as functionals of the portfolio loss distribution, thus implicitly assuming the knowledge of such a distribution. However, in practical applications, the need for estimation arises and with it the need to study the effects of mis-specification errors, as well as estimation errors on the final conclusion. In this paper we focus on the qualitative robustness of a sequence of estimators for set-valued risk measures. These properties are studied in detail for two well-known examples of set-valued risk measures: the value-at-risk and the maximum average value-at-risk. Our results illustrate, in particular, that estimation of set-valued value-at-risk can be given in terms of random sets. Moreover, we observe that historical set-valued value-at-risk, while failing to be sub-additive, leads to a more robust procedure than alternatives such as the maximum likelihood average value at-risk.

The question we address is how robust solutions react to changes in the uncertainty set. We prove the location of robust solutions with respect to the magnitude of a possible decrease in uncertainty, namely when the uncertainty set shrinks, and convergence of the sequence of robust solutions. In decision making, uncertainty may arise from incomplete information about people's (stakeholders, voters, opinion leaders, etc.) perception about a specific issue. Whether the decision maker (DM) has to look for the approval of a board or pass an act, they might need to define the strategy that displeases the minority. In such a problem, the feasible region is likely to unchanged, while uncertainty affects the objective function. Hence the paper studies only this framework.

The aim of this paper is to characterize some of the pointwise and global well-posedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.