|
on Utility Models and Prospect Theory |
|
Issue of 2024‒03‒18
twenty papers chosen by |
| By: | Alireza Fallah; Michael I. Jordan; Ali Makhdoumi; Azarakhsh Malekian |
| Abstract: | We consider a producer's problem of selling a product to a continuum of privacy-conscious consumers, where the producer can implement third-degree price discrimination, offering different prices to different market segments. In the absence of privacy constraints, Bergemann, Brooks, and Morris [2015] characterize the set of all possible consumer-producer utilities, showing that it is a triangle. We consider a privacy mechanism that provides a degree of protection by probabilistically masking each market segment, and we establish that the resultant set of all consumer-producer utilities forms a convex polygon, characterized explicitly as a linear mapping of a certain high-dimensional convex polytope into $\mathbb{R}^2$. This characterization enables us to investigate the impact of the privacy mechanism on both producer and consumer utilities. In particular, we establish that the privacy constraint always hurts the producer by reducing both the maximum and minimum utility achievable. From the consumer's perspective, although the privacy mechanism ensures an increase in the minimum utility compared to the non-private scenario, interestingly, it may reduce the maximum utility. Finally, we demonstrate that increasing the privacy level does not necessarily intensify these effects. For instance, the maximum utility for the producer or the minimum utility for the consumer may exhibit nonmonotonic behavior in response to an increase of the privacy level. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.08223&r=upt |
| By: | Jarrod Burgh; Emerson Melo |
| Abstract: | We present a model elucidating wishful thinking, which comprehensively incorporates both the costs and benefits associated with biased beliefs. Our findings reveal that wishful thinking behavior can be accurately characterized as equivalent to superquantile-utility maximization within the domain of threshold beliefs distortion cost functions. By leveraging this equivalence, we establish conditions that elucidate when an optimistic decision-maker exhibits a preference for choices characterized by positive skewness and increased risk. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.01892&r=upt |
| By: | Tao Lin; Yiling Chen |
| Abstract: | We study a repeated Bayesian persuasion problem (and more generally, any generalized principal-agent problem with complete information) where the principal does not have commitment power and the agent uses algorithms to learn to respond to the principal's signals. We reduce this problem to a one-shot generalized principal-agent problem with an approximately-best-responding agent. This reduction allows us to show that: if the agent uses contextual no-regret learning algorithms, then the principal can guarantee a utility that is arbitrarily close to the principal's optimal utility in the classic non-learning model with commitment; if the agent uses contextual no-swap-regret learning algorithms, then the principal cannot obtain any utility significantly more than the optimal utility in the non-learning model with commitment. The difference between the principal's obtainable utility in the learning model and the non-learning model is bounded by the agent's regret (swap-regret). If the agent uses mean-based learning algorithms (which can be no-regret but not no-swap-regret), then the principal can do significantly better than the non-learning model. These conclusions hold not only for Bayesian persuasion, but also for any generalized principal-agent problem with complete information, including Stackelberg games and contract design. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.09721&r=upt |
| By: | van Cranenburgh, Sander; Meyerhoff, Jürgen; Rehdanz, Katrin; Wunsch, Andrea |
| Abstract: | Efficient experimental designs aim to maximise the information obtained from stated choice data to estimate discrete choice models' parameters statistically efficiently. Almost without exception efficient experimental designs assume that decision-makers use a Random Utility Maximisation (RUM) decision rule. When using such designs, researchers (implicitly) assume that the decision rule used to generate the design has no impact on respondents' choice behaviour. This study investigates whether the decision rule assumption underlying an experimental design affects respondents' choice behaviour. We use four stated choice experiments on coastal adaptation to climate change: Two are based on experimental designs optimised for utility maximisation and two are based on experimental designs optimised for a mixture of RUM and Random Regret Minimisation (RRM). Generally, we find that respondents place value on adaptation measures (e.g., dykes and beach nourishments). We evaluate the models' fits and investigate whether some choice tasks particularly invoke RUM or RRM decision rules. For the latter, we develop a new sampling-based approach that avoids the confounding between preference and decision rule heterogeneity. We find no evidence that RUM-optimised designs invoke RUM-consistent choice behaviour. However, we find a relationship between some of the attributes and decision rules, and compelling evidence that some choice tasks invoke RUM consistent behaviour while others invoke RRM consistent behaviour. This implies that respondents’ choice behaviour and choice modelling outcomes are not exogenous to the choice tasks, which can be particularly critical when information on preferences is used to inform actual decision-making on a sensitive issue of common interest as climate change. |
| Keywords: | Coastal adaptation, Climate change, Experimental design theory, Decision rules, Random regret minimisation |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwkie:281987&r=upt |
| By: | Martin Herdegen; David Hobson; Alex S. L. Tse |
| Abstract: | The Merton investment-consumption problem is fundamental, both in the field of finance, and in stochastic control. An important extension of the problem adds transaction costs, which is highly relevant from a financial perspective but also challenging from a control perspective because the solution now involves singular control. A further significant extension takes us from additive utility to stochastic differential utility (SDU), which allows time preferences and risk preferences to be disentangled. In this paper, we study this extended version of the Merton problem with proportional transaction costs and Epstein-Zin SDU. We fully characterise all parameter combinations for which the problem is well posed (which may depend on the level of transaction costs) and provide a full verification argument that relies on no additional technical assumptions and uses primal methods only. The case with SDU requires new mathematical techniques as duality methods break down. Even in the special case of (additive) power utility, our arguments are significantly simpler, more elegant and more far-reaching than the ones in the extant literature. This means that we can easily analyse aspects of the problem which previously have been very challenging, including comparative statics, boundary cases which heretofore have required separate treatment and the situation beyond the small transaction cost regime. A key and novel idea is to parametrise consumption and the value function in terms of the shadow fraction of wealth, which may be of much wider applicability. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.08387&r=upt |
| By: | Simina Br\^anzei; MohammadTaghi Hajiaghayi; Reed Phillips; Suho Shin; Kun Wang |
| Abstract: | We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at a point of her choice, while Bob chooses the left piece or the right piece, leaving the remainder for Alice. We consider two versions: sequential, where Bob observes Alice's cut point before choosing left/right, and simultaneous, where he only observes her cut point after making his choice. The simultaneous version was first considered by Aumann and Maschler (1995). We observe that if Bob is almost myopic and chooses his favorite piece too often, then he can be systematically exploited by Alice through a strategy akin to a binary search. This strategy allows Alice to approximate Bob's preferences with increasing precision, thereby securing a disproportionate share of the resource over time. We analyze the limits of how much a player can exploit the other one and show that fair utility profiles are in fact achievable. Specifically, the players can enforce the equitable utility profile of $(1/2, 1/2)$ in the limit on every trajectory of play, by keeping the other player's utility to approximately $1/2$ on average while guaranteeing they themselves get at least approximately $1/2$ on average. We show this theorem using a connection with Blackwell approachability. Finally, we analyze a natural dynamic known as fictitious play, where players best respond to the empirical distribution of the other player. We show that fictitious play converges to the equitable utility profile of $(1/2, 1/2)$ at a rate of $O(1/\sqrt{T})$. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.08547&r=upt |
| By: | Stelios Arvanitis; Olivier Scaillet; Nikolas Topaloglou |
| Abstract: | We develop and implement methods for determining whether relaxing sparsity constraints on portfolios improves the investment opportunity set for risk-averse investors. We formulate a new estimation procedure for sparse second-order stochastic spanning based on a greedy algorithm and Linear Programming. We show the optimal recovery of the sparse solution asymptotically whether spanning holds or not. From large equity datasets, we estimate the expected utility loss due to possible under-diversification, and find that there is no benefit from expanding a sparse opportunity set beyond 45 assets. The optimal sparse portfolio invests in 10 industry sectors and cuts tail risk when compared to a sparse mean-variance portfolio. On a rolling-window basis, the number of assets shrinks to 25 assets in crisis periods, while standard factor models cannot explain the performance of the sparse portfolios. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.01951&r=upt |
| By: | Connor R. Forsythe; Cristian Arteaga; John P. Helveston |
| Abstract: | This paper introduces the Heterogeneous Aggregate Valence Analysis (HAVAN) model, a novel class of discrete choice models. We adopt the term "valence'' to encompass any latent quantity used to model consumer decision-making (e.g., utility, regret, etc.). Diverging from traditional models that parameterize heterogeneous preferences across various product attributes, HAVAN models (pronounced "haven") instead directly characterize alternative-specific heterogeneous preferences. This innovative perspective on consumer heterogeneity affords unprecedented flexibility and significantly reduces simulation burdens commonly associated with mixed logit models. In a simulation experiment, the HAVAN model demonstrates superior predictive performance compared to state-of-the-art artificial neural networks. This finding underscores the potential for HAVAN models to improve discrete choice modeling capabilities. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.00184&r=upt |
| By: | Takeshi Kato |
| Abstract: | Based on interactions between individuals and others and references to social norms, this study reveals the impact of heterogeneity in time preference on wealth distribution and inequality. We present a novel approach that connects the interactions between microeconomic agents that generate heterogeneity to the dynamic equations for capital and consumption in macroeconomic models. Using this approach, we estimate the impact of changes in the discount rate due to microeconomic interactions on capital, consumption and utility and the degree of inequality. The results show that intercomparisons with others regarding consumption significantly affect capital, i.e. wealth inequality. Furthermore, the impact on utility is never small and social norms can reduce this impact. Our supporting evidence shows that the quantitative results of inequality calculations correspond to survey data from cohort and cross-cultural studies. This study's micro-macro connection approach can be deployed to connect microeconomic interactions, such as exchange, interest and debt, redistribution, mutual aid and time preference, to dynamic macroeconomic models. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.08905&r=upt |
| By: | Alireza Fallah; Michael I. Jordan; Ali Makhdoumi; Azarakhsh Malekian |
| Abstract: | We study a three-layer data market comprising users (data owners), platforms, and a data buyer. Each user benefits from platform services in exchange for data, incurring privacy loss when their data, albeit noisily, is shared with the buyer. The user chooses platforms to share data with, while platforms decide on data noise levels and pricing before selling to the buyer. The buyer selects platforms to purchase data from. We model these interactions via a multi-stage game, focusing on the subgame Nash equilibrium. We find that when the buyer places a high value on user data (and platforms can command high prices), all platforms offer services to the user who joins and shares data with every platform. Conversely, when the buyer's valuation of user data is low, only large platforms with low service costs can afford to serve users. In this scenario, users exclusively join and share data with these low-cost platforms. Interestingly, increased competition benefits the buyer, not the user: as the number of platforms increases, the user utility does not improve while the buyer utility improves. However, increasing the competition improves the overall utilitarian welfare. Building on our analysis, we then study regulations to improve the user utility. We discover that banning data sharing maximizes user utility only when all platforms are low-cost. In mixed markets of high- and low-cost platforms, users prefer a minimum noise mandate over a sharing ban. Imposing this mandate on high-cost platforms and banning data sharing for low-cost ones further enhances user utility. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.09697&r=upt |
| By: | Guibril Zerbo |
| Abstract: | This article examines the determinants of willingness to pay (WTP) for flood insurance, focusing on the role of information and information sources. We use data from a September 2022 field survey of 593 individuals in urban Burkina Faso. We find that 71.3% of individuals are willing to spend money on insurance. But many individuals have a lower willingness to pay than the expected loss. This suggests that individuals would appreciate insurance cover, but do not have sufficient income to pay the insurance premium. We also find that being well informed about flood risk increases the likelihood of paying the expected loss for insurance. However, obtaining flood information from television increases WTP whereas radio does not. These results suggest the need to take information sources into account when developing effective communication policies against these risks. Another result is that recourse to the family and risk aversion reduce PAD. Finally, trust in insurers and ambiguity aversion increase individuals' chances of paying the expected loss for insurance. |
| Keywords: | Natural disasters, Flood risk; Insurance, Willingness to pay; Information |
| JEL: | D81 D83 G22 Q54 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2024-7&r=upt |
| By: | Shoka Hayaki (Faculty of Economics, Kagawa University and Research Institute for Economics and Business Administration, Kobe University, JAPAN) |
| Abstract: | Traditional frameworks often fail to adequately explain the observed procyclical nature of the risk-return trade-off associated with aggregate risk aversion in recent years. This study introduces a simple model incorporating the concepts of loss aversion and state-dependent preferences. The model suggests an initial positive adjustment to the risk-return trade-off when the shock occurs, followed by a negative adjustment once the shock fully manifests. Essentially, the risk-return trade-off temporarily becomes procyclical as the shock spreads. In this study, the nonlinear structure of the risk-return trade-off is approximated using natural cubic splines with several constraints. Estimation results based on market excess returns in the United States indicate that a nonlinear risk-return trade-off, consistent with the model, offers valuable insights for pricing. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2024-05&r=upt |
| By: | Asier Estevan; Roberto Maura; Oscar Valero |
| Abstract: | In this paper we focus our efforts on studying how a preorder and topology can be made compatible. Thus we provide a characterization of those that are continuous-compatible. Such a characterization states that such topologies must be finer than the so-called upper topology induced by the preorder and, thus, it clarifies which topology is the smallest one among those that make the preorder continuous. Moreover, we provide sufficient conditions that allows us to discard in an easy way the continuity of a preference. In the light of the obtained results, we provide possibility counterparts of the a few celebrate impossibility theorems for continuous social social intergenerational preferences due to P. Diamond, L.G. Svensson and T. Sakai. Furthermore, we suggest quasi-pseudo-metrics as appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric type method which is able to guarantee possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. We also show that our method makes always the intergenerational preferences semi-continuous multi-utility representables in the sense of \"{O}zg\"{u} Evern and Efe O. Ok. Finally, in order to keep close to the classical way of measuring in the literature, a refinement of the previous method is presented in such a way that metrics are involved. |
| Date: | 2024–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.01699&r=upt |
| By: | Nastasi, Federico; Spagano, Salvatore |
| Abstract: | The Brazilian economist Celso Furtado escapes from the traditional distinctions among different schools of thought. Indeed, he made large use of tools from various proveniences according to a pragmatic approach. Nonetheless, this paper shows that his work also contains several characteristic elements of the institutionalist tradition. In the early 1960s, Furtado placed institutions at the centre of his analysis of the evolution of the economic history. Moreover, he rejected the kind of determinism that follows a concept of choice entirely dependent on the utility-maximizing rationality. Coherently, he opposed the New Institutional Economics as an example of neoclassical retread of institutional issues. Finally, and especially, even without theorizing it, he adopted the institutionalised individual as an economic agent. This choice, rather than that of the homo oeconomicus, implied assuming an agent able to shape institutions that, in turn, influence human behaviours according to a downward cumulative causation. |
| Keywords: | Furtado, Structuralism, Institutionalism |
| JEL: | B2 |
| Date: | 2023–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120242&r=upt |
| By: | Andrea Teglio (Department of Economics, Ca’ Foscari University of Venice); Michele Catalano (Department of Economics, Ca’ Foscari University of Venice); Marko Petrovic (University of Valencia) |
| Abstract: | The neoclassical growth model is extended to include limitations in the forecasting capability of a rational individual, who can predict the future state of the economy only for a short time horizon. Long-term predictions are formulated according to uninformed expectations, relying solely on myopic information about short-run dynamics, such as assuming a future persistent growth rate. Steady-state results are obtained in the case of iso-elastic utility and Cobb-Douglas technology. The model, characterized by forecasting errors and subsequent corrections, exhibits global stability and has relevant implications for welfare and policy. It is analyzed in comparison to the Solow–Swan model and the Ramsey model. Our approach, incorporating behavioral assumptions within a standard optimization rule, successfully yields explicit analytical solutions for the policy function in the neoclassical model. This strategy may also be extended to various modeling streams, including DSGE and HANK models. |
| Keywords: | Expectations, Neoclassical growth, Bounded rationality, Myopic behavior, Dynamic optimization, Time inconsistency |
| JEL: | C61 D83 D84 E21 E25 E71 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2024:05&r=upt |
| By: | Qixin Zhan (China Economics and Management Academy, Central University of Finance and Economics); Heng-fu Zou (The World Bank; Institute for Advanced Study, Wuhan University; Institute for Advanced Study, Shenzhen University) |
| Abstract: | This paper delves into the theoretical underpinnings of how freedom, grounded in the rule of law and property rights, shapes wealth accumulation and economic growth. By integrating liberty into the neoclassical growth model, we introduce the innovative concepts of "liberty consumption" and "liberty capital" and define utility and production functions on them. Through theoretical analysis and simulations, we ascertain that a robust preference for liberty nurtures sustained prosperity and heightened productivity. However, in scenarios where the costs associated with liberty consumption are substantial and liberty capital depreciates rapidly—indicating an environment inhospitable or constraining to liberty -- it adversely affects economic output and overall well-being. These insights underscore the significance of examining liberty dynamics in economic growth and development. Without the presence of liberty, property rights, and the rule of law within utility and production functions, society faces the peril of descending into either a Hobbesian state of "war of all against all" or a totalitarian state ruled by a singular authority. In either case, life becomes solitary, poor, nasty, brutish, and potentially short. |
| Date: | 2024–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:cuf:wpaper:619&r=upt |
| By: | Nazif Durmaz; Henry Thompson |
| Abstract: | This paper simulates the constant cost trade model with labor inputs for three and five regions and products aggregated from the World Input-Output Database. The regions start with America, Asia, and Europe trading Resources, Manufactures, and Services. Each region maximizes Cobb-Douglas utility based on global consumption shares subject to balanced trade and global material balance. Simulated autarky and trade with the rest of the world lead to the full model with multiple potential equilibria. Diversified exports and import competition characterize the trade patterns with the gains from trade relative to autarky up to 20% for the five regions. |
| Keywords: | comparative advantage; relative prices; simulation; constant cost trade |
| JEL: | F10 F14 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:abn:wpaper:auwp2024-03&r=upt |
| By: | Bardey, David (Universidad de los Andes); De Donder , Philippe (TSE - CNRS); Zaporozhets , Vera (TSE - INRAe) |
| Abstract: | We review the medico-economic literature assessing the economic value of diagnostic tests. We first present the health technology assessment methods, as applied to generic health interventions. We then define our object of study, diagnostic and prognostic tests, and relate them to various definitions of personalized medicine. We then review the empirical assessments of diagnostic tests related to personalized medicine and of companion tests. We summarize systematic reviews which are not performing quantitative meta-analyses, but rather provide a descriptive synthesis of the results reviewed. We find no evidence that such tests perform better than more traditional approaches, such as pharmaceutical interventions. At the same time, there is a lot of heterogeneity in the cost per QALY (Quality-Adjusted Life Year) gained, so that some genetic testing procedures may perform better than non-genetic ones. Finally, we focus on imperfect tests and show how to optimize, from an economic perspective, their accuracy levels, and how to take accuracy levels into considerations when assessing their economic value. |
| Keywords: | genetic tests; companion tests; cost-benefit analysis (CBA); cost-effectiveness analysis (CEA); cost-utility analysis (CUA); and cost-minimization analysis (CMA); personalized medicine; Receiver-Operator (ROC) curve; Incremental cost-effectiveness ration (ICER). |
| JEL: | H51 I18 J17 |
| Date: | 2024–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:col:000089:021041&r=upt |
| By: | Kroll, Yoram; Marchioni, Andrea; Ben-Horin, Moshe |
| Abstract: | A portfolio’s Sortino ratio is strongly affected by the risk-free vs. risky assets mix, except for the case where the threshold, T is equal to the risk-free rate. Therefore, if T differs from the risk-free rate, the portfolio’s Sortino ratio could potentially be increased by merely changing the mix of the risk-free and the risky components. The widely used Sharpe ratio, on the other hand, does not share this caveat. We introduce a modified Sortino ratio, Sortino(γ), which is invariant with respect to the portfolio’s risk-free vs. risky assets mix, and hence eliminates the above deficiency. The selected threshold T(γ), mimics the portfolio composition in the sense that it equals to the risk-free rate plus γ times the portfolio’s equity risk premium. Higher selected γ reflects higher risk/loss aversion. We propose a procedure for optimizing the composition of the risky portion of the portfolio to maximize the Sortino(γ) ratio. In addition, we show that Sortino(γ) is consistent with first and second order stochastic dominance with riskless asset rules. |
| Keywords: | Performance ratios; Sortino ratio; Risk aversion; Loss aversion; FSDR rule; SSDR rule |
| JEL: | C0 G0 |
| Date: | 2024–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120203&r=upt |
| By: | Nathan I. N. Henry; Mangor Pedersen; Matt Williams; Jamin L. B. Martin; Liesje Donkin |
| Abstract: | The value-loading problem is a significant challenge for researchers aiming to create artificial intelligence (AI) systems that align with human values and preferences. This problem requires a method to define and regulate safe and optimal limits of AI behaviors. In this work, we propose HALO (Hormetic ALignment via Opponent processes), a regulatory paradigm that uses hormetic analysis to regulate the behavioral patterns of AI. Behavioral hormesis is a phenomenon where low frequencies of a behavior have beneficial effects, while high frequencies are harmful. By modeling behaviors as allostatic opponent processes, we can use either Behavioral Frequency Response Analysis (BFRA) or Behavioral Count Response Analysis (BCRA) to quantify the hormetic limits of repeatable behaviors. We demonstrate how HALO can solve the 'paperclip maximizer' scenario, a thought experiment where an unregulated AI tasked with making paperclips could end up converting all matter in the universe into paperclips. Our approach may be used to help create an evolving database of 'values' based on the hedonic calculus of repeatable behaviors with decreasing marginal utility. This positions HALO as a promising solution for the value-loading problem, which involves embedding human-aligned values into an AI system, and the weak-to-strong generalization problem, which explores whether weak models can supervise stronger models as they become more intelligent. Hence, HALO opens several research avenues that may lead to the development of a computational value system that allows an AI algorithm to learn whether the decisions it makes are right or wrong. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.07462&r=upt |