This thesis develops equilibrium asset pricing models in incomplete markets with a large number of heterogeneous agents using mean field game theory. The market equilibrium is characterized by a novel form of mean field backward stochastic differential equations (BSDEs). First, we propose a theoretical model that endogenously derives the equilibrium risk premium. Agents with exponential preferences are heterogeneous in initial wealth, risk aversion, and unspanned stochastic terminal liability. We solve the optimal investment problem using the optimal martingale principle. The equilibrium is characterized by a mean field BSDE whose driver has quadratic growth in both the stochastic integrands and their conditional expectations. We prove the existence of solutions and show that the risk premium clears the market in the large population limit. Second, we extend the model to include consumption and habit formation, relaxing the time-separability assumption of utility functions. A similar mean field BSDE is derived, and its well-posedness and asymptotic behavior are examined. We also introduce an exponential quadratic Gaussian (EQG) reformulation to obtain equilibrium solutions in semi-analytic form. Finally, the model is extended to partially observable markets where agents must infer the risk premium from stock price observations to determine trading strategies. We provide semi-analytic expressions for the equilibrium via the EQG framework, and the equilibrium risk-premium process is constructed endogenously using Kalman-Bucy filtering theory. Numerical simulations are included to visualize the resulting market dynamics.

This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic differential equations (BSDEs). These equations encapsulate the equilibrium value function essential for resolving cases where the present state affecting the target functional triggers the inconsistency. Additionally, the paper offers an application exemplifying this theory through the time-inconsistent linear--quadratic regulator.

A number of recent contributions have put forward the topological structure of production networks as a key determinant of macro-economic dynamics. However, firm-to-firm production networks data is generally not available. Against this background, reconstruction method based on firms' size have been developed. This paper enriches this set of reconstruction methods by integrating input-output sectoral flows in the reconstruction process. We derive analytical expressions for the maximum entropy solutions to the firm network reconstruction problem with sectoral input-output constraints, first for binary networks and then for weight reconstruction. We perform a numerical analysis comparing standard and input-output based reconstruction methods using Hungarian production network data. Our results show that adding input-output constraints substantially reduces deviations from the input-output structure compared with standard methods. Our augmented method provides an almost perfect fit to input-output data, though all methods have difficulties reproducing other structural characteristics.

We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approximate the total implied variance as a function of log-moneyness and maturity. Our approach generates candidate parametrizations directly from market data without imposing a predefined functional form. We compare the resulting formulas with the widely used SVI parametrization in terms of accuracy and simplicity. Numerical experiments indicate that symbolic regression can identify compact parametrizations with competitive fitting performance.

We study the associations between everyday economic decision-making quality and people's emotional states. Using high-frequency, highly disaggregated consumer "scanner" data, we show that the cost of poor decision-making is substantial, on average equal to around half of day-to-day consumption budgets. While material circumstances help explain decision-making quality, how people feel about those circumstances is equally important. Contrary to evidence that stress and worry impair performance in settings where distraction is costly, we find these same feelings are associated with improved decision-making for frequently made consumption choices. This is consistent with worry increasing attentiveness to decisions within households' locus of control.

We study an information acquisition problem in which an informed trader acquires costly information prior to trading in the Kyle equilibrium. The cost of information acquisition is represented by an entropy cost. Regardless of the prior distribution of the asset payoff, continuous signals are optimal. Moreover, any continuously distributed signal, together with an associated logit type posterior distribution of the payoff, yields the same ex-ante value for the informed trader, the same distribution of posterior expected payoff, and the same unconditional distribution of the informed trader's trading strategy. Consequently, a normally distributed signal can be adopted without loss of generality. We further show that when the information acquisition cost increases or the volatility of noise trades decreases, the variance of the posterior expected payoff declines, the profit potential from trading diminishes, meanwhile the posterior expected payoff increasingly resembles a normal distribution, and the information leakage cost from trading decreases.

As large language models (LLMs) and vision-language-action models (VLAs) become widely deployed, the tokens consumed by AI inference are evolving into a new type of commodity. This paper systematically analyzes the commodity attributes of tokens, arguing for their transition from intelligent service outputs to compute infrastructure raw materials, and draws comparisons with established commodities such as electricity, carbon emission allowances, and bandwidth. Building on the historical experience of electricity futures markets and the theory of commodity financialization, we propose a complete design for standardized token futures contracts, including the definition of a Standard Inference Token (SIT), contract specifications, settlement mechanisms, margin systems, and market-maker regimes. By constructing a mean-reverting jump-diffusion stochastic process model and conducting Monte Carlo simulations, we evaluate the hedging efficiency of the proposed futures contracts for application-layer enterprises. Simulation results show that, under an application-layer demand explosion scenario, token futures can reduce enterprise compute cost volatility by 62%-78%. We also explore the feasibility of GPU compute futures and discuss the regulatory framework for token futures markets, providing a theoretical foundation and practical roadmap for the financialization of compute resources.

This paper develops a novel multi-agent reinforcement learning (MARL) framework for reinsurance treaty bidding, addressing long-standing inefficiencies in traditional broker-mediated placement processes. We pose the core research question: Can autonomous, learning-based bidding systems improve risk transfer efficiency and outperform conventional pricing approaches in reinsurance markets? In our model, each reinsurer is represented by an adaptive agent that iteratively refines its bidding strategy within a competitive, partially observable environment. The simulation explicitly incorporates institutional frictions including broker intermediation, incumbent advantages, last-look privileges, and asymmetric access to underwriting information. Empirical analysis demonstrates that MARL agents achieve up to 15% higher underwriting profit, 20% lower tail risk (CVaR), and over 25% improvement in Sharpe ratios relative to actuarial and heuristic baselines. Sensitivity tests confirm robustness across hyperparameter settings, and stress testing reveals strong resilience under simulated catastrophe shocks and capital constraints. These findings suggest that MARL offers a viable path toward more transparent, adaptive, and risk-sensitive reinsurance markets. The proposed framework contributes to emerging literature at the intersection of algorithmic market design, strategic bidding, and AI-enabled financial decision-making.

This study presents a comparative analysis of deep learning methodologies such as BERT, FinBERT and ULMFiT for sentiment analysis of earnings call transcripts. The objective is to investigate how Natural Language Processing (NLP) can be leveraged to extract sentiment from large-scale financial transcripts, thereby aiding in more informed investment decisions and risk management strategies. We examine the strengths and limitations of each model in the context of financial sentiment analysis, focusing on data preprocessing requirements, computational efficiency, and model optimization. Through rigorous experimentation, we evaluate their performance using key metrics, including accuracy, precision, recall, and F1-score. Furthermore, we discuss potential enhancements to improve the effectiveness of these models in financial text analysis, providing insights into their applicability for real-world financial decision-making.

Algorithms increasingly automate bidding in online auctions, raising concerns about tacit bid suppression and revenue shortfalls. Prior work identifies individual mechanisms behind algorithmic bid suppression, but it remains unclear which factors matter most and how they interact, and policy conclusions rest on algorithms unlike those deployed in practice. This paper develops a computational laboratory framework, based on factorial experimental designs and large-scale Monte Carlo simulation, that addresses bid suppression across multiple algorithm classes within a common methodology. Each simulation is treated as a black-box input-output observation; the framework varies inputs and ranks factors by association with outcomes, without explaining algorithms' internal mechanisms. Across six sub-experiments spanning Q-learning, contextual bandits, and budget-constrained pacing, the framework ranks the relative importance of auction format, competitive pressure, learning parameters, and budget constraints on seller revenue. The central finding is that structural market parameters dominate algorithmic design choices. In unconstrained settings, competitive pressure is the strongest predictor of revenue; under budget constraints, budget tightness takes over. The auction-format effect is context-dependent, favouring second-price under learning algorithms but reversing to favour first-price under budget-constrained pacing. Because the optimal format depends on the prevailing bidding technology, no single auction format is universally superior when bidders are algorithms, and applying format recommendations from one algorithm class to another leads to counterproductive design interventions.

When organisations adopt commercial AI systems for decision support, they inherit value judgements embedded by vendors that are neither transparent nor renegotiable. The governance puzzle is not whether AI can support decisions but which recommendations the system can actually produce given how its vendor has configured it. I formalise this as a behavioural feasible set, the range of recommendations reachable under vendor-imposed alignment constraints, and characterise diagnostic thresholds for when organisational requirements exceed the system's flexibility. In scenario-based experiments using binary decision scenarios and multi-stakeholder ranking tasks, I show that alignment materially compresses this set. Comparing pre- and post-alignment variants of an open-weight model isolates the mechanism: alignment makes the system substantially less able to shift its recommendation even under legitimate contextual pressure. Leading commercial models exhibit comparable or greater rigidity. In multi-stakeholder tasks, alignment shifts implied stakeholder priorities rather than neutralising them, meaning organisations adopt embedded value orientations set upstream by the vendor. Organisations thus face a governance problem that better prompting cannot resolve: selecting a vendor partially determines which trade-offs remain negotiable and which stakeholder priorities are structurally embedded.

We present FinRL-X, a modular and deployment-consistent trading architecture that unifies data processing, strategy construction, backtesting, and broker execution under a weight-centric interface. While existing open-source platforms are often backtesting- or model-centric, they rarely provide system-level consistency between research evaluation and live deployment. FinRL-X addresses this gap through a composable strategy pipeline that integrates stock selection, portfolio allocation, timing, and portfolio-level risk overlays within a unified protocol. The framework supports both rule-based and AI-driven components, including reinforcement learning allocators and LLM-based sentiment signals, without altering downstream execution semantics. FinRL-X provides an extensible foundation for reproducible, end-to-end quantitative trading research and deployment. The official FinRL-X implementation is available at https://github.com/AI4Finance-Foundation/FinRL-Trading.

We present an approximate dynamic programming framework for designing degradation-aware market participation policies for battery energy storage systems. The approach employs a tailored value function approximation that reduces the state space to state of charge and battery health, while performing dynamic programming along a pseudo-time axis encoded by state of health. This formulation enables an offline/online computation split that separates long-term degradation dynamics (months to years) from short-term market dynamics (seconds to minutes) -- a timescale mismatch that renders conventional predictive control and dynamic programming approaches computationally intractable. The main computational effort occurs offline, where the value function is approximated via coarse-grained backward induction along the health dimension. Online decisions then reduce to a real-time tractable one-step predictive control problem guided by the precomputed value function. This decoupling allows the integration of high-fidelity physics-informed degradation models without sacrificing real-time feasibility. Backtests on historical market data show that the resulting policy outperforms several benchmark strategies with optimized hyperparameters.

This paper investigates the barriers to gender convergence using Japan as a salient environment to explore the interactive effects of labor market structures and social norms. I develop a quantitative model of household labor supply where couples jointly decide their occupations and working hours. The model features a labor market with inflexible "regular" jobs with convex pay schedules and flexible "non-regular" jobs, interacting with social norms regarding spousal earnings. The calibrated model successfully reproduces observed gender gaps in participation, occupation, and working hours, and explains 48% of the gender wage gap. The model also accounts for cross-regional differences in gender gaps solely through variation in social norms. Counterfactual simulations show that while increasing job flexibility substantially reduces wage and occupational gaps, the working hours gap persists due to the unequal burden of domestic work. Closing this remaining gap requires policies such as affordable household services. Furthermore, the model suggests that the effects of structural reforms can depend on the strength of gender norms, with larger reductions in gender gaps in more conservative environments.

The Nobel Memorial Prize in Economics has been awarded annually since 1969. Who wins the prize is a topic of much interest and tracks the whole course of the academic discipline over the last 57 years. Explaining who wins the prize in any given year is a complex process, which involves the subtle endogeneity of the choice of the field and the individual(s) who should be honoured. Citations, track records, networks of past winners, institutional factors along with field rotation and Economic Prize Committee composition may all play a role. A dynamic sample involving a changing stock of would-be candidates along with a moving flow -- both into and out of the sample -- add complexities to the modelling. We find robust evidence that the Nobel Prize rotates in a semi-regular way between the fields of economics. Earlier awards were for a single paper, later ones for a body of work. Networks do not matter, but having a Nobel student or co-author does. There is some evidence that the personal preferences of Committee members had an effect on either field or individual winner. The Committee's decisions changed after Lindbeck retired.

Contemporary societies face a severe crisis of demographic reproduction. Global fertility rates continue to decline precipitously, with East Asian nations exhibiting the most dramatic trends -- China's total fertility rate (TFR) fell to approximately 1.0 in 2023, while South Korea's dropped below 0.72. Simultaneously, the institution of marriage is undergoing structural disintegration: educated women rationally reject unions lacking both emotional fulfillment and economic security, while a growing proportion of men at the lower end of the socioeconomic spectrum experience chronic sexual deprivation, anxiety, and learned helplessness. This paper proposes a computational framework for modeling and evaluating a Stratified Polyamory System (SPS) using techniques from agent-based modeling (ABM), multi-agent reinforcement learning (MARL), and large language model (LLM)-empowered social simulation. The SPS permits individuals to maintain a limited number of legally recognized secondary partners in addition to one primary spouse, combined with socialized child-rearing and inheritance reform. We formalize the A/B/C stratification as heterogeneous agent types in a multi-agent system and model the matching process as a MARL problem amenable to Proximal Policy Optimization (PPO). The mating network is analyzed using graph neural network (GNN) representations. Drawing on evolutionary psychology, behavioral ecology, social stratification theory, computational social science, algorithmic fairness, and institutional economics, we argue that SPS can improve aggregate social welfare in the Pareto sense. Preliminary computational results demonstrate the framework's viability in addressing the dual crisis of female motherhood penalties and male sexlessness, while offering a non-violent mechanism for wealth dispersion analogous to the historical Chinese Grace Decree (Tui'en Ling).

Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally modeled by stochastic differential equations (SDEs), whose forward and reverse density evolution closely parallels the forward noising and reverse denoising structure of diffusion models. In this paper, we develop a framework for using DDPMs to generate risk-neutral asset price dynamics for derivative valuation. Starting from log-return dynamics under the physical measure, we analyze the associated forward diffusion and derive the reverse-time SDE. We show that the change of measure from the physical to the risk-neutral measure induces an additive shift in the score function, which translates into a closed-form risk-neutral epsilon shift in the DDPM reverse dynamics. This correction enforces the risk-neutral drift while preserving the learned variance and higher-order structure, yielding an explicit bridge between diffusion-based generative modeling and classical risk-neutral SDE-based pricing. We show that the resulting discounted price paths satisfy the martingale condition under the risk-neutral measure. Empirically, the method reproduces the risk-neutral terminal distribution and accurately prices both European and path-dependent derivatives, including arithmetic Asian options, under a GBM benchmark. These results demonstrate that diffusion-based generative models provide a flexible and principled approach to simulation-based derivative pricing.

We consider the problem of active portfolio management, where an investor seeks the portfolio with maximal expected utility of the difference between the terminal wealth of their strategy and a proportion of the benchmark's, subject to a budget and a deviation constraint from the benchmark portfolio. As the investor aims at outperforming the benchmark, they choose a divergence that asymmetrically penalises gains and losses as well as penalises underperforming the benchmark more than outperforming it. This is achieved by the recently introduced $α$-Bregman-Wasserstein divergence, subsuming the Bregman-Wasserstein and the popular Wasserstein divergence. We prove existence and uniqueness, characterise the optimal portfolio strategy, and give explicit conditions when the divergence constraints and the budget constraints are binding. We conclude with a numerical illustration of the optimal quantile function in a geometric Brownian motion market model.

Economic decision-making depends not only on structured signals such as prices and taxes, but also on unstructured language, including peer dialogue and media narratives. While multi-agent reinforcement learning (MARL) has shown promise in optimizing economic decisions, it struggles with the semantic ambiguity and contextual richness of language. We propose LAMP (Language-Augmented Multi-Agent Policy), a framework that integrates language into economic decision-making and narrows the gap to real-world settings. LAMP follows a Think-Speak-Decide pipeline: (1) Think interprets numerical observations to extract short-term shocks and long-term trends, caching high-value reasoning trajectories; (2) Speak crafts and exchanges strategic messages based on reasoning, updating beliefs by parsing peer communications; and (3) Decide fuses numerical data, reasoning, and reflections into a MARL policy to optimize language-augmented decision-making. Experiments in economic simulation show that LAMP outperforms both MARL and LLM-only baselines in cumulative return (+63.5%, +34.0%), robustness (+18.8%, +59.4%), and interpretability. These results demonstrate the potential of language-augmented policies to deliver more effective and robust economic strategies.

Bond markets respond differently to macroeconomic news compared to equity markets, yet most sentiment models are trained primarily on general financial or equity news data. However, bond prices often move in the opposite direction to economic optimism, making general or equity-based sentiment tools potentially misleading. We introduce BondBERT, a transformer-based language model fine-tuned on bond-specific news. BondBERT can act as the perception and reasoning component of a financial decision-support agent, providing sentiment signals that integrate with forecasting models. We propose a generalisable framework for adapting transformers to low-volatility, domain-inverse sentiment tasks by compiling and cleaning 30,000 UK bond market articles (2018-2025). BondBERT's sentiment predictions are compared against FinBERT, FinGPT, and Instruct-FinGPT using event-based correlation, up/down accuracy analyses, and LSTM forecasting across ten UK sovereign bonds. We find that BondBERT consistently produces positive correlations with bond returns, and achieves higher alignment and forecasting accuracy than the three baseline models. These results demonstrate that domain-specific sentiment adaptation better captures fixed income dynamics, bridging a gap between NLP advances and bond market analytics.

We organize existing empirical regularities of cryptocurrencies into seven stylized facts and analyze cryptocurrencies through the lens of empirical asset pricing. We find important similarities with traditional markets--risk-adjusted performance so far is broadly comparable, and the cross-section of returns can be summarized by a small set of factors. However, cryptocurrency also has its own distinct character: jumps are frequent and large, and blockchain information helps drive prices. This common set of stylized facts provides evidence that cryptocurrency is emerging as an investable asset class. Additionally, we discuss potential data quality issues and possible changes in future regulations and the cryptocurrency environment.

Electricity distribution companies deploy battery storage to defer grid upgrades by reducing peak demand. In deregulated jurisdictions, such storage often sits idle because regulatory constraints bar participation in electricity markets. Here, we develop an optimization framework that, to our knowledge, provides the first formal model of market participation constraints within storage investment and operation planning. Applying the framework to a Massachusetts case study, we find that market participation delivers similar savings as peak demand reduction. Under current conditions, market participation does not increase storage investment, but at very low storage costs, could incentivize deployment beyond local distribution needs. This might run contrary to the separation of distribution from generation in deregulated markets. Our framework can mitigate this concern by identifying investment levels appropriate for local distribution needs.

We propose the Financial Connectome, a new scientific discipline that models financial markets through the lens of brain functional architecture. Inspired by the foundational work of group independent component analysis (groupICA) in neuroscience, we reimagine markets not as collections of assets, but as high-dimensional dynamic systems composed of latent market modules. Treating stocks as functional nodes and their co-fluctuations as expressions of collective cognition, we introduce dynamic Market Network Connectivity (dMNC), the financial analogue of dynamic functional connectivity (dFNC). This biologically inspired framework reveals structurally persistent market subnetworks, captures regime shifts, and uncovers systemic early warning signals all without reliance on predictive labels. Our results suggest that markets, like brains, exhibit modular, self-organizing, and temporally evolving architectures. This work inaugurates the field of financial connectomics, a principled synthesis of systems neuroscience and quantitative finance aimed at uncovering the hidden logic of complex economies.

We develop the information geometry of Lévy processes. Deriving $α$-divergences directly in terms of the Lévy triplets of the Lévy processes, we identify Fisher information matrix and $α$-connection on the statistical manifold. In addition, we discuss statistical implications of this information geometry, including bias reduction estimation and Bayesian predictive priors. Several Lévy processes, broadly used for financial modeling such as tempered stable processes, the CGMY model, variance gamma processes, and the Merton model, are investigated through their differential-geometric structures as illustrative examples.

Integrating electric mobility, including electric vehicles (EVs), electric trucks (ETs), and renewable energy sources (RES) with the power grid is paramount for decarbonization, efficiency, and stability. A critical gap remains, however: existing smart-grid and e-mobility cost-benefit analysis (CBA) approaches do not yet provide a unified framework for appraising AI-driven operational digital platforms (ODPs) that jointly coordinate EV/ET charging, renewable generation, and grid operations across sectoral and national boundaries. This paper develops a seven-step CBA framework tailored to this class of platform. The framework maps each layer of a multi-layered AI architecture to traceable, monetizable benefit streams-panning economic efficiency, grid reliability, and environmental externalities--while explicitly accounting for AI-specific capital and operational expenditures that conventional appraisals omit. Applied to a ten-year, three-country deployment across Austria, Hungary, and Slovenia, the analysis indicates a robust positive investment case under the modeled assumptions, confirmed through scenario sensitivity analysis, one-way parameter ranking, and probabilistic simulation. Benefit composition and country-level drivers differ systematically across national contexts, yet the economic rationale is preserved in each, reflecting the framework's adaptability to heterogeneous electrification trajectories. The findings indicate the economic viability of AI-driven digital platforms for cross-sectoral energy--mobility integration and highlight the critical role of ODPs in advancing decarbonization in the mobility--power nexus. To that end, they have direct implications for the design and appraisal of digital infrastructure investments under the EU's Fit for 55 and REPowerEU programmes.

This note outlines an approach to stress testing of covariance of financial time series, in the context of financial risk management. It discusses how the geodesic distance between covariance matrices implies a notion of plausibility of covariance stress tests. In this approach, correlation stress tests span a submanifold of constant determinant of the Fisher--Rao manifold of covariance matrices. A parsimonious geometrically invariant definition of arbitrarily large correlation stress tests is proposed, and a few examples are discussed.

We consider an $N$-player game where the states of the players evolve with time as Stochastic Differential Equations (SDEs) with interaction only in the drift terms. Each player controls the drift of the SDE satisfied by her state process, aiming to minimize the expected value of a cost that depends on the paths of the player's state and the empirical measure of the states of all the players until a terminal time. When $N \to \infty$, previous works have established Central Limit Theorems and Large Deviation Principles for the state processes when the game is in Nash Equilibrium (the Nash states), by using the Master Equation to construct approximations of those processes that evolve with time as SDEs with classical Mean-Field interaction. Staying in this framework, we improve an existing $L^{1}$ estimate for the total error of approximating all the Nash states to an $L^{\infty}$ one, and we also establish the $N \to \infty$ asymptotic behavior of the upper order statistics of the Nash states. The latter initiates the development of an Extreme Value Theory for Stochastic Differential Games.

We investigate the impact of judges' gender on the outcome of domestic violence cases. Using data from São Paulo, Brazil, between 2011 and 2019, we find that a domestic violence case assigned to a female judge is 28% (9.7 p.p.) more likely to result in a conviction than a case assigned to a male judge with similar career characteristics. To show that this decision gap rises due to different gender perspectives about domestic violence and not because female judges are stricter than their male counterparts in all rulings, we compare it against the gender conviction-rate gap in similar types of crime. We find that this gap for domestic violence cases is larger than the same gap for other physical assault cases (8.5 p.p.). Furthermore, we find evidence that at least two channels explain this gender conviction-rate gap for domestic violence cases: gender-based differences in evidence interpretation and gender-based sentencing criteria. We also find that female judges write longer sentences, schedule more hearings, and write more judicial documents than their male peers when analyzing domestic violence cases. Lastly, we find that the gender conviction-rate gap has no significant impact on the probability of appeals, ruling reversals, or recidivism.

Flexibility is a cornerstone of operations management, crucial to hedge stochasticity in product demands, service requirements, and resource allocation. In two-sided platforms, flexibility is also two-sided and can be viewed as the compatibility of agents on one side with agents on the other side. Platform actions often influence the flexibility on either the demand or the supply side. But how should flexibility be jointly allocated across different sides? Whereas the literature has traditionally focused on only one side at a time, our work initiates the study of two-sided flexibility in matching platforms. We propose an abstract matching model in random graphs and identify the flexibility allocation that optimizes the expected size of a maximum matching. Our findings reveal that flexibility allocation is a first-order issue: for a given flexibility budget, the resulting matching size can vary greatly depending on how the budget is allocated. Moreover, even in the simple and symmetric settings we study, the quest for the optimal allocation is complicated. In particular, easy and costly mistakes can be made if the flexibility decisions on the demand and supply sides are optimized independently (e.g., by two different teams in the company), rather than jointly. To guide the search for optimal flexibility allocation, we uncover two effects - flexibility cannibalization and flexibility asymmetry - that govern when the optimal design places the flexibility budget only on one side or equally on both sides. In doing so we identify the study of two-sided flexibility as a significant aspect of platform efficiency.

This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space $Δ$ of probabilities, a probability weighting function $ψ$, generating the measure $ν_ψ$ by transforming an objective probability measure, and a utility function $ϕ$, such that, for all $\tilde{v},\tilde{u}\in\tilde{V}$, \begin{align*} \tilde{v}\succeq\tilde{u} \Leftrightarrow \min_{Q \in Δ} \left\{\mathbb{E}_Q\left[\intϕ\left(\tilde{v}^{\centerdot}\right)\,\mathrm{d}ν_ψ\right]+c(Q)\right\} \geq \min_{Q \in Δ} \left\{\mathbb{E}_Q\left[\intϕ\left(\tilde{u}^{\centerdot}\right)\,\mathrm{d}ν_ψ\right]+c(Q)\right\}. \end{align*} Our theory extends the rank-dependent utility model of Quiggin (1982) for decision under risk to risk and ambiguity, reduces to the variational preferences model when $ψ$ is the identity, and is dual to variational preferences when $ϕ$ is affine in the same way as the theory of Yaari (1987) is dual to expected utility. As a special case, we obtain a preference axiomatization of a decision theory that is a rank-dependent generalization of the popular maxmin expected utility theory. We characterize ambiguity aversion in our theory.