arXiv subjects

Omer Tamuz

Publications and source records attributed to Omer Tamuz.

At least 19 recordsLinked to original sources

arXiv2026

Decentralized Equilibrium for Bitcoin Mining

Cryptocurrencies such as Bitcoin are defined by protocols that specify how participants record transactions and create new currency units. These protocols are not enforced by law or any central entity and instead are intended to be incentive compatible. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is known not to constitute an equilibrium (Eyal and Sirer, 2018). This leaves open the question of whether the decentralized outcome intended by Nakamoto can be sustained in equilibrium in the Bitcoin mining game. We propose inertial mining, a novel mining protocol that induces that outcome, i.e., a single longest chain in which each miner's asymptotic share of blocks equals its share of computational power. Our main result establishes that inertial mining constitutes an equilibrium, assuming no miner controls one half or more of the computational power. Inertial mining coincides with Nakamoto's protocol on the equilibrium path, and can be implemented in Bitcoin without any changes to its consensus mechanism or blockchain architecture. When a single miner controls more than half of the computational power, we show that no decentralized equilibrium exists.

cs.CR↗

arXiv2026

Local Global Games and Network Common Learning

We study global games in which agents coordinate locally, with their social network neighbors, contingent on a favorable state. Before acting, agents learn the private signals of all agents within network distance $r$. As $r$ grows, every agent learns the state, but efficient coordination depends on higher-order beliefs, which are shaped by the geometry of the network. We introduce network common learning, a network analogue of common learning, and show that it is attained when neighboring agents' observations differ by many signals, as on the two-dimensional grid, but fails on networks with informational bottlenecks, such as the line, where only the safe action survives in equilibrium.

econ.TH↗

arXiv2026

Monotonicity and Bracketing in Games

We study solution concepts for normal-form games. We obtain a characterization of Nash equilibria and logit quantal response equilibria, as well as generalizations capturing non-expected utility. Our axioms reflect that players are responsive to payoffs induced by the play of others and, whenever several games are played simultaneously, players may consider each separately.

econ.TH↗

arXiv2026

Monotone additive statistics on heavy-tailed convolution semigroups

We study sub-semigroups of the semigroup of probability measures on $\mathbb{R}$ and monotone additive statistics on them, by which we mean maps to the reals that are monotone with respect to the stochastic order and additive under convolution. We show that scalar multiples of the expectation are the unique monotone additive statistics on the semigroup of measures with finite $p$-th moment, for any $1 \le p < \infty$. We also prove that the entire semigroup of probability measures admits no non-zero monotone additive statistic at all.

math.PR↗

arXiv2026

Robust Market Interventions

When can interventions in markets be designed to increase surplus robustly -- i.e., with high probability -- accounting for uncertainty due to imprecise information about economic primitives? In a setting with many strategic firms, each possessing some market power, we present conditions for such interventions to exist. The key condition, recoverable structure, requires large-scale complementarities among families of products. The analysis works by decomposing the incidence of interventions in terms of principal components of a Slutsky matrix. Under recoverable structure, a noisy signal of this matrix reveals enough about these principal components to design robust interventions. Our results demonstrate the usefulness of spectral methods for analyzing imperfectly observed strategic interactions with many agents.

econ.TH↗

arXiv2026

Local Coordination and the Geometry of Social Networks

We study agents playing a pure coordination game on a large social network. Agents are restricted to coordinate locally, without access to a global communication device, and so different regions of the network will converge to different actions, precluding perfect coordination. We show that the extent of this inefficiency depends on the network geometry: on some networks, near-perfect efficiency is achievable, while on others welfare is strictly bounded away from the optimum. We provide a geometric condition on the network structure that characterizes when near-efficiency is attainable. On networks in which it is unattainable, our results more generally preclude high correlations between outcomes in a large spectrum of dynamic games.

econ.TH↗

arXiv2026

Learning Through Imitation: An Experiment

We compare how well agents aggregate information in two repeated social learning environments. In the first setting agents have access to a public data set. In the second they have access to the same data, and also to the past actions of others. Despite the fact that actions contain no additional payoff-relevant information, and despite potential herd behavior, free riding and information overload issues, observing and imitating the actions of others leads agents to take the optimal action more often in the second setting. We also investigate the effect of group size, as well as a setting in which agents observe private data and others' actions.

econ.TH↗

arXiv2026

A Separability Foundation for Random Coefficients Logit

We study stochastic choice across decision problems, each represented as a menu of action labels paired with observable outcome vectors. We propose a consistency condition for behavior in decision problems composed of two separable components: choice probabilities must agree with those obtained when each component is considered in isolation. Together with monotonicity and continuity, this separability requirement characterizes the family of random coefficients logit rules.

econ.TH↗

arXiv2025

Infinite stationary measures of co-compact group actions

Let $Γ$ be a finitely generated group, and let $μ$ be a nondegenerate, finitely supported probability measure on $Γ$. We show that every co-compact $Γ$ action on a locally compact Hausdorff space admits a nonzero $μ$-stationary Radon measure. The main ingredient of the proof is a stationary analogue of Tarski's theorem: we show that for every nonempty subset $A \subseteq Γ$ there is a $μ$-stationary, finitely additive measure on $Γ$ that assigns unit mass to $A$.

math.GR↗

arXiv2025

On the origin of the Boltzmann distribution

The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of polynomials with non-negative coefficients.

math.PR↗

arXiv2025

The Power of Two in Token Systems

In economies without monetary transfers, token systems serve as an alternative to sustain cooperation, alleviate free riding, and increase efficiency. This paper studies whether a token-based economy can be effective in marketplaces with thin exogenous supply. We consider a marketplace in which at each time period one agent requests a service, one agent provides the service, and one token (artificial currency) is used to pay for service provision. The number of tokens each agent has represents the difference between the amount of service provisions and service requests by the agent. We are interested in the behavior of this economy when very few agents are available to provide the requested service. Since balancing the number of tokens across agents is key to sustain cooperation, the agent with the minimum amount of tokens is selected to provide service among the available agents. When exactly one random agent is available to provide service, we show that the token distribution is unstable. However, already when just two random agents are available to provide service, the token distribution is stable, in the sense that agents' token balance is unlikely to deviate much from their initial endowment, and agents return to their initial endowment in finite expected time. Our results mirror the power of two choices paradigm in load balancing problems. Supported by numerical simulations using kidney exchange data, our findings suggest that token systems may generate efficient outcomes in kidney exchange marketplaces by sustaining cooperation between hospitals.

cs.GT↗

arXiv2025

A fixed-point theorem for face maps, or deletion-tolerant random finite sets

We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions. Consequences for various monoids of order-preserving transformations of $\mathbf{N}$ are discussed in an appendix.

math.GR↗

arXiv2025

Private Private Information

Private signals model noisy information about an unknown state. Although these signals are called "private," they may still carry information about each other. Our paper introduces the concept of private private signals, which contain information about the state but not about other signals. To achieve privacy, signal quality may need to be sacrificed. We study the informativeness of private private signals and characterize those that are optimal in the sense that they cannot be made more informative without violating privacy. We discuss implications for privacy in recommendation systems, information design, causal inference, and mechanism design.

econ.TH↗

arXiv2025

A Fourier approach to Levine's hat puzzle

We consider Lionel Levine's notorious hat puzzle with two players. Each player has a stack of hats on their head, and each hat is chosen independently to be either black or white. After observing only the other player's hats, players simultaneously choose one of their own hats. The players win if both chosen hats are black. In this note, we observe an upper bound on the probability of success, using Chang's lemma, a result in Boolean harmonic analysis.

math.PR↗

arXiv2024

Network and timing effects in social learning

We consider a group of agents who can each take an irreversible costly action whose payoff depends on an unknown state. Agents learn about the state from private signals, as well as from past actions of their social network neighbors, which creates an incentive to postpone taking the action. We show that outcomes depend on network structure: on networks with a linear structure patient agents do not converge to the first-best action, while on regular directed tree networks they do.

econ.TH↗

arXiv2024

Learning in Repeated Interactions on Networks

We study how long-lived, rational agents learn in a social network. In every period, after observing the past actions of his neighbors, each agent receives a private signal, and chooses an action whose payoff depends only on the state. Since equilibrium actions depend on higher order beliefs, it is difficult to characterize behavior. Nevertheless, we show that regardless of the size and shape of the network, the utility function, and the patience of the agents, the speed of learning in any equilibrium is bounded from above by a constant that only depends on the private signal distribution.

econ.TH↗

arXiv2024

Asymptotic Renyi Entropies of Random Walks on Groups

We introduce asymptotic Rényi entropies as a parameterized family of invariants for random walks on groups. These invariants interpolate between various well-studied properties of the random walk, including the growth rate of the group, the Shannon entropy, and the spectral radius. They furthermore offer large deviation counterparts of the Shannon-McMillan-Breiman Theorem. We prove some basic properties of asymptotic Rényi entropies that apply to all groups, and discuss their analyticity and positivity for the free group and lamplighter groups.

math.PR↗

arXiv2024

Monotone additive statistics

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of nonexpected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.

econ.TH↗