When exactly does a preference ordering on acts have an additive state-dependent utility representation per indifference curve? Following the analogy of a sliding balance, a perfect reflection of the well-known betweenness models for lotteries, we find three answers for monetary acts on a finite state space.In the first two, we exploit the axiom of weak decomposability, identified by Grant, Kajii, and Polak (2000) as the key axiom to extend betweenness to acts, but leaving the continuity and monotonicity of state utility in setpoints an open issue. Our first theorem confirms the necessity of continuity, while the second shows that monotonicty in setpoints requires the additional axiom of ratio monotonicity. It formalises the idea that sliding a setpoint towards a gain decreases its momentum compared to losses.This observation, in turn, suggests to extend the primitive of a preference ordering with a benchmark for discerning gains from losses within an act. Thus we arrive at the Additive Sliding Balance Utility model for orderings anchored to such a benchmark. In the third theorem, we characterise this class with an even more straightforward betweenness axiom: the balance point of an act should be in between those of its parts.
We study development traps generated by payoff-mediated coordination between an institutional layer and a private-sector layer. The leading interpretation is the transition from informality to formal-sector participation: institutional effort raises the return to formalisation, while formal participation raises the fiscal, compliance, and legitimacy returns to institutional effort. The paper develops this mechanism through nested continuous-time replicator models. The one-population benchmark gives the familiar critical-mass and hysteresis result. The two-role follower model shows how a scalar threshold becomes a stable saddle branch. The main contribution is a leader–follower phase-plane analysis: we derive local stability conditions for joint poverty, joint prosperity, and decoupled regimes; give sufficient global conditions under which the stable manifold of an interior saddle is the basin boundary; and prove a comparison result showing that payoff-improving reforms weakly expand the basin of joint prosperity. A multi-role extension records local rare-deviation stability and monotone nullcline shifts, without claiming a complete global classification in four dimensions. The analysis implies that unilateral policy interventions do not fail by definition; they fail when the induced state remains in the basin of the low-activity equilibrium.
We examine how the shapes of utility functions, particularly risk attitudes, influence Nash bargaining outcomes, thereby challenging the conventional assumption of risk neutrality. Our comparative static analysis reveals several key insights. (1) Changes in Pie Size: Increasing Absolute Risk Aversion (IARA) introduces an “equality bias,” which elucidates the fair distributions observed in unstructured bargaining experiments by emphasizing the role of participants’ risk attitudes. (2) Changes in Disagreement Point: IARA also results in low sensitivity, referred to as “insensitivity bias,” which contests the interpretation proposed by Anbarci and Feltovich (2013) by showing that concave IARA utility functions can adequately explain this insensitivity. These equality bias and insensitivity bias are closely interconnected phenomena. We propose a novel theoretical framework that elucidates the diverse outcomes of experimental bargaining through the lens of fundamental risk attitudes.
This paper uncovers some of the epistemic implications of stability in the presence of one-sided incomplete information. If it is not common knowledge that an allocation is not stable under complete information, the allocation must be stable under incomplete information, in the sense of Liu et al. (2014), regardless of the agents’ information and preferences. The converse does not necessarily hold, so that there can be common knowledge that an incomplete-information stable allocation is not complete-information stable, but is recovered within familiar information and preference domains. The characterization implies that incomplete-information stability is testable and observationally equivalent to its complete-information counterpart, and carries over to other well-known stability notions proposed in the literature.
In close-knit communities, relationships are often formed and severed through the consent of community members. Inspired by this fact, I consider network formation when individuals need the consent of at least a fraction p of the population to form or sever links. First, I show that a small consent requirement (p=1/(n−1)) is sufficient to stabilize efficient networks in the classical connections model. Second, I establish that altering only one feature of the connections model — type of externalities (positive vs negative) or path-dependence (single vs multiple paths) — has little impact, whereas modifying both features simultaneously produces significant changes in outcomes. My analysis highlights the importance of understanding complementarities between different features of externalities in network formation.
We consider a number of deterministic models of economic growth in which all agents act rationally and the unique perfect foresight equilibrium features a stock price bubble. The key assumptions are that the production technology exhibits decreasing returns to scale (so that firms earn positive profits) and that wage income and dividend income have different growth rates. We relate the latter property to the violation of the Inada conditions for labor. The unique equilibrium fails to satisfy the property of balanced growth.
We introduce a new family of power indices for nodes in graphs with classes. We provide an axiomatic characterization of this family and prove the independence of the axioms. Furthermore, we show that these indices coincide with the Shapley values of a family of subadditive transferable-utility games defined on such graphs. These normative results yield a general framework for quantifying structural influence in complex networks. In particular, we identify the normative conditions under which power in technological sharing networks can be represented by our family of indices. Importantly, the proposed axiomatic framework also applies to influence flows that generate negative effects.
We extend the classical syndicate model to a setting with ambiguous beliefs, where agents face both risk and ambiguity and have heterogeneous smooth ambiguity preferences. Our main theorem generalizes Borch’s seminal result by providing necessary and sufficient conditions for Pareto optimality in this environment: an uncertainty-sharing contract is Pareto-optimal if and only if agents’ marginal utilities, weighted by ambiguity-adjusted belief densities, are proportional across states. The ambiguity-adjusted densities reflect how ambiguity aversion tilts evaluation toward adverse probabilistic models, with weights proportional to the marginal ambiguity attitude. The welfare interpretation is standard: Pareto-optimal contracts coincide with maximizers of a weighted social-welfare functional, and the proportionality constants equal the associated Pareto weights. The characterization nests Borch’s rule, reducing to proportional marginal utilities when beliefs are unambiguous or agents are ambiguity neutral.
This paper analyzes a decentralized matching environment in which agents privately observe their ability but must choose between two mutually exclusive sectors before learning their relative rank. The sectors differ in their payoff distributions, and positions within each are assigned via positive assortative matching. Thus, outcomes depend both on ability and on the endogenous congestion created by agents’ sectoral choices. I characterize the unique symmetric Bayesian Nash equilibrium, which exhibits a cutoff structure: high-ability agents select the high-payoff sector with certainty, while low-ability agents mix to trade off match quality against the risk of being crowded out. The equilibrium choice probability is continuous within groups but displays a discontinuous jump at the sorting threshold. A key welfare finding is that rank uncertainty can raise the expected utility of some low-ability agents relative to a complete information benchmark. The analysis shows how private information induces endogenous discontinuities in strategies and heterogeneous welfare effects across types.
This paper studies equilibria in games in which agents report utility functions or preferences over continuously divisible goods and allocation is determined by maximizing the egalitarian social welfare function. About the game of reporting utility functions, we make an even trivial but practically overlooked point that everybody tries to be seen as unhappier, and hence only ordinal information can be conveyed. We then characterize equilibria of the preference reporting game in which we adopt a wide class of individual welfare measures.
This paper establishes a precise link between the tail behavior of a distribution and the structure of its Virtual Value. We show that the only continuously differentiable distributions whose Virtual Value is linear on an interval coincide, on that interval, with a Generalized Pareto distribution. This equivalence yields explicit expressions for optimal cutoffs and implies that, within this class, comparative statics of allocation and pricing rules are governed by a single primitive, the tail index. Thin tails lead to the familiar monotone adjustment of prices, whereas heavy tails reverse the sign of the response and produce countercyclical pricing. The analysis also demonstrates that widely used textbook distributions acquire an approximately affine Virtual Value in their upper tails whenever their expectations are finite. Under standard regularity conditions from Extreme Value Theory, the tail Virtual Value converges to an affine form, with slope equal to the underlying tail index. These results provide a unified framework for studying allocation, mechanism design and monopoly pricing in environments where high valuations play a central role.
The smooth ambiguity model (Klibanoff et al., 2005) or second-order subjective expected utility (SOSEU) model (Nau, 2006; Seo, 2009; Giraud, 2014) has two characteristics that contribute to its success: it is an iterated expected utility and, under certain conditions, it is smooth. These characteristics allow for the use of standard analytical techniques from expected utility theory, including optimization calculus. In this paper, we utilize the continuous differentiability (C1) of the SOSEU functional to offer an axiomatic characterization of this model. First, we define C1 preferences and provide a representation for them. Then, assuming that preferences are C1, the primary axiom that delivers the iterated expected utility form essentially states that if decision makers are more sensitive to perturbations of one portfolio of assets than another one when the probability distribution is known, then they are still more sensitive when it is not.
Gul and Pesendorfer (2015) introduce subjective sources in Hurwicz expected utility: event domains on which binary bets are ranked as if by a prior and this “as if” behavior varies continuously with the event. Motivated by the certainty effect, I relax continuity only at the extremes, allowing discontinuities at impossible and certain events while maintaining continuity for non-degenerate bets. I characterize these non-extreme-outcome (neo)-continuous sources by a conditional power-series link between source probability and inner probability on an ideal core event. On acts measurable with respect to a neo-continuous source, the Hurwicz functional admits a rank-dependent representation on non-extreme ranks together with an extreme-outcome term.
We give weak conditions for a continuous time optimal control problem with one-dimensional state space to have monotone optimal trajectories. These conditions include a concavity condition on the Lagrange function. If that condition is changed to strict concavity, then all optimal trajectories are monotone.
A subset of economic agents in a society is aware of the existence of an economic opportunity, and compete to exploit it. We study incentives to communicate about the existence of this economic opportunity when its exploitation by the winner generates externalities to other agents. We characterize the equilibria of the communication game, identify conditions under which stronger externalities generate more communication, and highlight the tension between equilibrium and efficient communication.
We establish a mean-field stochastic framework for analyzing institutional lock-in driven by asymmetric belief updating. A continuum of agents update confidence levels s(t) through success/failure experiences, with update functions F-S, F-F exhibiting negativity bias: failures impact beliefs more strongly than successes of equal magnitude. Aggregate confidence I-t influences the success probability pi(I-t), creating feedback between individual psychology and collective outcomes. We prove existence of stationary equilibria via Schauder's fixed-point theorem on the space of probability measures P([0,1]), establishing compactness through Prokhorov's theorem. Stability is characterized via spectral analysis of Frechet derivatives in the bounded-Lipschitz metric, with operator decomposition into push-forward L-mu, and rank-one feedback R-mu* components. Under negativity bias and positive feedback, we establish multiplicity: generically three equilibria (low, middle, high) with stable-unstable-stable pattern. For escape dynamics from stable equilibria, we establish a large deviation principle on Skorokhod space D([0, infinity), P([0, 1])) with rate function determined by a quasi-potential computed via action functional minimization. Expected escape times scale as exp(N center dot V) where N is population size and V is the quasi-potential, confirming exponential rarity: for calibrated parameters with N = 10(6) agents, escape times exceed 10(63,900) periods. We derive comparative statics for reform policy through optimal control: value function concavity implies optimal sequencing places high-success-probability reforms first. Material investments M and psychological interventions P exhibit strategic complementarity (partial derivative I-2*(;)/partial derivative M partial derivative P > 0), verified through implicit function theorem analysis. Numerical verification with 10(6) Monte Carlo simulations confirms all theoretical predictions, with robustness checks across alternative functional specifications. The framework provides a rigorous foundation for understanding institutional persistence as emerging from collective psychological dynamics rather than material coordination failures, with implications for development economics, political economy, and organizational change.
This paper investigates the strategic implications of the uniform rank-minimizing mechanism (URM), which selects uniformly from the set of deterministic assignments minimizing the total reported rank. We focus on settings in which agents may refuse their assigned object and instead receive an outside option. Without the refusal option, we show that truth-telling is not strategically dominated under any rank-minimizing mechanism satisfying equal treatment of equals and independence of irrelevant rankings. However, introducing the refusal option significantly changes strategic incentives: specific manipulations, called outside option demotion strategies, strategically dominate truth-telling under the URM. Moreover, such manipulations can lead to inefficient outcomes, as desirable objects may be refused by misreporting agents and consequently remain unassigned. To address this issue, we propose a modification of the URM that restores undominated truth-telling, although it introduces incentives to underreport acceptable objects. Our results highlight a trade-off in the design of fair rank-minimizing mechanisms when agents can refuse their assigned objects.
