arXiv subjects

Florian Brandl

Publications and source records attributed to Florian Brandl.

At least 19 recordsLinked to original sources

arXiv2026

Equilibrium Play Without Mutual Knowledge of Rationality

Equilibrium play in two-player zero-sum games is usually justified via epistemic assumptions, such as mutual knowledge of rationality and beliefs, that go far beyond the rationality of the players. We propose a justification that dispenses with these assumptions. To this end, we consider solution concepts that assign to every subgame of a given game a set of plausible actions for each player, and we impose two conditions. Rationality requires that the plausible sets are supports of undominated strategies or, equivalently, that all plausible actions are best responses to a common belief about the opponent. Inheritance requires that plausible actions remain plausible when implausible actions are discarded. In two-player games, the two conditions characterize the solution concepts that consistently select supports of Nash equilibria. Zero-sum payoffs ensure that Nash equilibria -- and hence the selection -- are generically unique. Equilibrium play thus emerges from individual rationality and the mutual understanding that plausibility judgments persist when implausible actions are discarded.

econ.TH↗

arXiv2026

Fair Division with Binary Valuations: Characterizations

We consider the fair allocation of indivisible goods with binary valuations. In this setting, the maximum Nash welfare rule, the leximin rule, and all additive welfarist rules with a strictly concave function coincide. We show that for any number of agents, this rule is the only rule that satisfies envy-freeness up to one good, strategyproofness, neutrality, minimal completeness, and invariance under disapproving unassigned goods (IDU). Moreover, we present an alternative characterization for two agents, where we replace IDU with non-redundancy and resource-monotonicity. In both characterizations, all axioms are necessary.

econ.TH↗

arXiv2026

Axioms for Correlated Equilibrium

We characterize correlated equilibrium in finite normal-form games. Interpreting correlated strategies as action recommendations, we show that correlated equilibrium is the unique solution concept that never recommends a pure-strategy dominated action, treats payoff-equivalent actions interchangeably, and respects the sure-thing principle under uncertainty about payoffs and the correlation device. A parallel characterization identifies coarse correlated equilibrium among solution concepts that recommend dominant actions whenever they exist and treat payoff-equivalent actions as strongly interchangeable.

econ.TH↗

arXiv2026

Consistent Probabilistic Social Choice Revisited

Brandt et al. (2016) characterized a probabilistic social choice function known as maximal lotteries within a framework based on fractional preference profiles, which abstracts away from individual voters. While this modeling assumption enables a more elegant and transparent proof, it complicates comparison with other results in the literature. The purpose of this note is to transfer their results to the standard model of social choice, where each preference profile is defined for a finite number of voters. Along the way, we prove a slightly stronger version of their main theorem that uses a weaker continuity condition and allows for real-valued (rather than only rational-valued) probabilities.

econ.TH↗

arXiv2026

On the Inefficiency of Social Learning

We study whether a social planner can improve the efficiency of learning, measured by the expected total welfare loss, in a sequential decision-making environment. Agents arrive in order and each makes a binary action based on their private signal and the social information they observe. The planner can intervene by jointly designing the social information disclosed to agents and offering monetary transfers contingent on agents' actions. We show that, despite such flexibility, efficient learning cannot be restored with a finite budget: whenever learning is inefficient without intervention, no combination of information disclosure and transfers can achieve efficient learning while keeping total expected transfers finite.

econ.TH↗

arXiv2025

The Social Learning Barrier

We consider long-lived agents who interact repeatedly in a social network. In each period, each agent learns about an unknown state by observing a private signal and her neighbors' actions from the previous period before choosing her own action. Our main result shows that the learning rate of the slowest-learning agent is bounded from above by a constant that only depends on the marginal distributions of the agents' private signals and not on the number of agents, the network structure, correlations between the private signals, and the agents' strategies. Applying this result to equilibrium learning with rational agents shows that the learning rate of all agents in any equilibrium is bounded under general conditions. This extends recent findings on equilibrium learning and demonstrates that the limitation stems from an information-theoretic tradeoff between optimal action choices and information revelation, rather than strategic considerations. We also show that a social planner can achieve almost optimal learning by designing strategies for which each agent's learning rate is close to the upper bound.

econ.TH↗

arXiv2025

High-$Q$ superconducting resonators fabricated in an industry-scale semiconductor-fabrication facility

Universal quantum computers promise to solve computational problems that are beyond the capabilities of known classical algorithms. To realize such quantum hardware on a superconducting material platform, a vast number of physical qubits has to be manufactured and integrated at high quality and uniformity on a chip. Anticipating the benefits of semiconductor industry processes in terms of process control, uniformity and repeatability, we set out to manufacture superconducting quantum circuits in a semiconductor fabrication facility. In order to set a baseline for the process quality, we report on the fabrication of coplanar waveguide resonators in a 200 mm production line, making use of a two-layer superconducting circuit technology. We demonstrate high material and process quality by cryogenic Q-factor measurements exceeding $10^6$ in the single-photon regime, for microwave resonators made of both Niobium and Tantalum. In addition, we demonstrate the incorporation of superconducting Niobium air bridges in our process, while maintaining the high quality factor of Niobium resonators.

quant-ph↗

arXiv2025

Dividing a cake for the irrationally entitled

A perfectly divisible cake is to be divided among a group of agents. Each agent is entitled to a share between zero and one, and these entitlements are compatible in that they sum to one. The mediator does not know the preferences of the agents, but can query the agents to make cuts and appraise slices in order to learn. We prove that if one of the entitlements is irrational, then the mediator must use a protocol that involves an arbitrarily large number of queries in order to construct an allocation that respects the entitlements regardless of preferences.

econ.TH↗

arXiv2025

Patience ensures fairness

We revisit the problem of fairly allocating a sequence of time slots when agents may have different levels of patience (Mackenzie and Komornik 2023). For each number of agents, we provide a lower threshold and an upper threshold on the level of patience such that (i) if each agent is at least as patient as the lower threshold, then there is a proportional allocation, and (ii) if each agent is at least as patient as the upper threshold and moreover has weak preference for earlier time slots, then there is an envy-free allocation. In both cases, the proof is constructive.

econ.TH↗

arXiv2024

A Robust Characterization of Nash Equilibrium

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability, (ii) if a strategy profile is played in two games, it is also played in every convex combination of these games, and (iii) players can shift probability arbitrarily between two indistinguishable actions, and deleting one of these actions has no effect. Our theorem implies that every equilibrium refinement violates at least one of these axioms. Moreover, every solution concept that approximately satisfies these axioms returns approximate Nash equilibria, even in natural subclasses of games, such as two-player zero-sum games, potential games, and graphical games.

econ.TH↗

arXiv2024

A Natural Adaptive Process for Collective Decision-Making

Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the collective decision, put both balls back into the urn, and repeat. Once in a while, relabel a randomly drawn ball with a random collective decision. We prove that the empirical distribution of collective decisions produced by this process approximates a maximal lottery, a celebrated probabilistic voting rule proposed by Peter C. Fishburn (Rev. Econ. Stud., 51(4), 1984). In fact, the probability that the collective decision in round $n$ is made according to a maximal lottery increases exponentially in $n$. The proposed procedure is more flexible than traditional voting rules and bears strong similarities to natural processes studied in biology, physics, and chemistry as well as algorithms proposed in machine learning.

econ.TH↗

arXiv2021

Funding Public Projects: A Case for the Nash Product Rule

We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents report linear utility functions over projects together with the amount of their contributions, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism -- the Nash product rule -- which picks the distribution that maximizes the product of the agents' utilities. This rule is Pareto efficient, and we prove that it satisfies attractive incentive properties: it spends each agent's contribution only on projects the agent finds acceptable, and agents are strongly incentivized to participate.

cs.GT↗

arXiv2021

Efficient, Fair, and Incentive-Compatible Healthcare Rationing

Rationing of healthcare resources has emerged as an important issue, which has been discussed by medical experts, policy-makers, and the general public. We consider a rationing problem where medical units are to be allocated to patients. Each unit is reserved for one of several categories and each category has a priority ranking of the patients. We present an allocation rule that respects the priorities, complies with the eligibility requirements, allocates the largest feasible number of units, and does not incentivize agents to hide that they qualify through a category. The rule characterizes all possible allocations that satisfy the first three properties and is polynomial-time computable.

cs.GT↗

arXiv2021

Belief-Averaged Relative Utilitarianism

We consider social welfare functions when the preferences of individual agents and society maximize subjective expected utility in the tradition of Savage. A system of axioms is introduced whose unique solution is the social welfare function that averages the agents' beliefs and sums up their utility functions, normalized to have the same range. The first distinguishing axiom requires positive association of society's preferences with the agents' preferences for acts about which beliefs agree. The second is a weakening of Arrow's independence of irrelevant alternatives that only applies to non-redundant acts.

econ.TH↗

arXiv2021

The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints

We consider the problem of probabilistic allocation of objects under ordinal preferences. We devise an allocation mechanism, called the vigilant eating rule (VER), that applies to nearly arbitrary feasibility constraints. It is constrained ordinally efficient, can be computed efficiently for a large class of constraints, and treats agents equally if they have the same preferences and are subject to the same constraints. When the set of feasible allocations is convex, we also present a characterization of our rule based on ordinal egalitarianism. Our results about VER do not just apply to allocation problems but to all collective choice problems in which agents have ordinal preferences over discrete outcomes. As a case study, we assume objects have priorities for agents and apply VER to sets of probabilistic allocations that are constrained by stability. VER coincides with the (extended) probabilistic serial rule when priorities are flat and the agent proposing deterministic deferred acceptance algorithm when preferences and priorities are strict. While VER always returns a stable and constrained efficient allocation, it fails to be strategyproof, unconstrained efficient, and envy-free. We show, however, that each of these three properties is incompatible with stability and constrained efficiency.

econ.TH↗

arXiv2019

Arrovian Aggregation of Convex Preferences

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.

cs.GT↗

arXiv2017

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable. In this paper, we provide a computer-aided proof of a sweeping impossibility using these two conditions for randomized aggregation mechanisms. More precisely, we show that every efficient aggregation mechanism can be manipulated for all expected utility representations of the agents' preferences. This settles an open problem and strengthens a number of existing theorems, including statements that were shown within the special domain of assignment. Our proof is obtained by formulating the claim as a satisfiability problem over predicates from real-valued arithmetic, which is then checked using an SMT (satisfiability modulo theories) solver. In order to verify the correctness of the result, a minimal unsatisfiable set of constraints returned by the SMT solver was translated back into a proof in higher-order logic, which was automatically verified by an interactive theorem prover. To the best of our knowledge, this is the first application of SMT solvers in computational social choice.

cs.GT↗

arXiv2017

The Distribution of Optimal Strategies in Symmetric Zero-sum Games

Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is given by the corresponding matrix entry, the column player receives the negative of the row player. A randomized strategy is optimal if it guarantees an expected payoff of at least 0 for a player independently of the strategy of the other player. We determine the probability that an optimal strategy randomizes over a given set of actions when the game is drawn from a distribution that satisfies certain regularity conditions. The regularity conditions are quite general and apply to a wide range of natural distributions.

cs.GT↗