arXiv subjects

Amir Ban

Publications and source records attributed to Amir Ban.

14 recordsLinked to original sources

arXiv2025

Unending Sequential Auctions

Sequential auctions for identical items with unit-demand, private-value buyers are common and often occur periodically without end, as new bidders replace departing ones. We model bidder uncertainty by introducing a probability that a bidder must exit the auction in each period. Treating the sequential auction as a Markov process, we demonstrate the existence of a unique steady state. In the absence of uncertainty, the steady state resembles a posted-price mechanism: bidders with values above a threshold almost surely win items by repeatedly bidding the threshold price, while those below the threshold almost surely do not. The equilibrium price corresponds to the threshold value that balances supply (bidders with values above the threshold) and demand (auction winners). When uncertainty is introduced, the threshold value persists but becomes less precise, growing "fuzzier" as uncertainty increases. This uncertainty benefits low-value bidders, those below the threshold, by giving them a significant chance of winning. Surprisingly, high-value bidders also benefit from uncertainty, up to a certain value limit, as it lowers equilibrium bids and increases their expected utility. On the other hand, this bidder uncertainty often reduces the auctioneer's utility.

cs.GT↗

arXiv2022

Budget-Constrained Reinforcement of Ranked Objects

Commercial entries, such as hotels, are ranked according to score by a search engine or recommendation system, and the score of each can be improved upon by making a targeted investment, e.g., advertising. We study the problem of how a principal, who owns or supports a set of entries, can optimally allocate a budget to maximize their ranking. Representing the set of ranked scores as a probability distribution over scores, we treat this question as a game between distributions. We show that, in the general case, the best ranking is achieved by equalizing the scores of several disjoint score ranges. We show that there is a unique optimal reinforcement strategy, and provide an efficient algorithm implementing it.

cs.GT↗

arXiv2021

Simple Economies are Almost Optimal

Consider a seller that intends to auction some item. The seller can invest money and effort in advertising in different market segments in order to recruit $n$ bidders to the auction. Alternatively, the seller can have a much cheaper and focused marketing operation and recruit the same number of bidders from a single market segment. Which marketing operation should the seller choose? More formally, let $D=\{\mathcal D_1,\ldots, \mathcal D_n\}$ be a set of distributions. Our main result shows that there is always $\mathcal D_i\in D$ such that the revenue that can be extracted from $n$ bidders, where the value of each is independently drawn from $\mathcal D_i$, is at least $\frac 1 2 \cdot (1-\frac 1 e)$ of the revenue that can be obtained by any possible mix of bidders, where the value of each bidder is drawn from some (possibly different) distribution that belongs to $D$. We next consider situations in which the auctioneer cannot use the optimal auction and is required to use a second price auction. We show that there is always $\mathcal D_i\in D$ such that if the value of all bidders is independently drawn from $\mathcal D_i$ then running a second price auction guarantees a constant fraction of the revenue that can be obtained by a second-price auction by any possible mix of bidders. Finally, we show that for any $\varepsilon>0$ there exists a function $f$ that depends only on $\varepsilon$ (in particular, the function does not depend on $n$ or on the set $D$), such that recruiting $n$ bidders which have at most $f(\varepsilon)$ different distributions, all from $D$, guarantees $(1-\varepsilon)$-fraction of the revenue that can be obtained by a second-price auction by any possible mix of bidders.

cs.GT↗

arXiv2020

Sequential Fundraising and Mutual Insurance

Seed fundraising for ventures often takes place by sequentially approaching potential contributors, who make observable decisions. The fundraising succeeds when a target number of investments is reached. Though resembling classic information cascades models, its behavior is radically different, exhibiting surprising complexities. Assuming a common distribution for contributors' levels of information, we show that participants rely on {\em mutual insurance}, i.e., invest despite unfavorable information, trusting future player strategies to protect them from loss. {\em Delegation} occurs when contributors invest unconditionally, empowering the decision to future players. Often, all early contributors delegate, in effect empowering the last few contributors to decide the outcome. Similar dynamics hold in sequential voting, as in voting in committees.

cs.GT↗

arXiv2020

A Practical Approach to Social Learning

Models of social learning feature either binary signals or abstract signal structures often deprived of micro-foundations. Both models are limited when analyzing interim results or performing empirical analysis. We present a method of generating signal structures which are richer than the binary model, yet are tractable enough to perform simulations and empirical analysis. We demonstrate the method's usability by revisiting two classical papers: (1) we discuss the economic significance of unbounded signals Smith and Sorensen (2000); (2) we use experimental data from Anderson and Holt (1997) to perform econometric analysis. Additionally, we provide a necessary and sufficient condition for the occurrence of action cascades.

econ.TH↗

arXiv2019

Strategy-Proof Incentives for Predictions

Our aim is to design mechanisms that motivate all agents to reveal their predictions truthfully and promptly. For myopic agents, proper scoring rules induce truthfulness. However, as has been described in the literature, when agents take into account long-term effects of their actions, deception and reticence may appear. No simple rules exist to distinguish between the truthful and the untruthful situations, and a determination has been done in isolated cases only. This is of relevance to prediction markets, where the market value is a common prediction, and more generally in informal public prediction forums, such as stock-market estimates by analysts. We describe three mechanisms that are strategy-proof with non-myopic considerations, and show that one of them meets all our requirements from a mechanism in almost all prediction settings. We formulate rules to distinguish truthful from untruthful settings, and use them to extensively classify prediction settings with continuous outcomes. We show how our proposed mechanism restores prompt truthfulness where incumbent mechanisms fail, and offer guidelines to implementing it in a prediction market.

cs.GT↗

arXiv2018

Are All Experts Equally Good? A Study of Analyst Earnings Estimates

We investigate whether experts possess differential expertise when making predictions. We note that this would make it possible to aggregate multiple predictions into a result that is more accurate than their consensus average, and that the improvement prospects grow with the amount of differentiation. Turning this argument on its head, we show how differentiation can be measured by how much weighted aggregation improves on simple averaging. Taking stock-market analysts as experts in their domain, we do a retrospective study using historical quarterly earnings forecasts and actual results for large publicly traded companies. We use it to shed new light on the Sinha et al. (1997) result, showing that analysts indeed possess individual expertise, but that their differentiation is modest. On the other hand, they have significant individual bias. Together, these enable a 20%-30% accuracy improvement over consensus average.

cs.CY↗

arXiv2017

The Strategy of Experts for Repeated Predictions

We investigate the behavior of experts who seek to make predictions with maximum impact on an audience. At a known future time, a certain continuous random variable will be realized. A public prediction gradually converges to the outcome, and an expert has access to a more accurate prediction. We study when the expert should reveal his information, when his reward is based on a proper scoring rule (e.g., is proportional to the change in log-likelihood of the outcome). In Azar et. al. (2016), we analyzed the case where the expert may make a single prediction. In this paper, we analyze the case where the expert is allowed to revise previous predictions. This leads to a rather different set of dilemmas for the strategic expert. We find that it is optimal for the expert to always tell the truth, and to make a new prediction whenever he has a new signal. We characterize the expert's expectation for his total reward, and show asymptotic limits

cs.GT↗

arXiv2017

Truthfulness in Repeated Predictions

Proper scoring rules elicit truth-telling when making predictions, or otherwise revealing information. However, when multiple predictions are made of the same event, telling the truth is in general no longer optimal, as agents are motivated to distort early predictions to mislead competitors. We demonstrate this, and then prove a significant exception: In a multi-agent prediction setting where all agent signals belong to a jointly multivariate normal distribution, and signal variances are common knowledge, the (proper) logarithmic scoring rule will elicit truthful predictions from every agent at every prediction, regardless of the number, order and timing of predictions. The result applies in several financial models.

cs.GT↗

arXiv2017

Decomposing Weighted Graphs

We solve the following problem: Can an undirected weighted graph G be parti- tioned into two non-empty induced subgraphs satisfying minimum constraints for the sum of edge weights at vertices of each subgraph? We show that this is possible for all constraints a(x), b(x) satisfying d_G(x) >= a(x) + b(x) + 2W_G(x), for every vertex x, where d_G(x), W_G(x) are, respectively, the sum and maximum of incident edge weights.

math.CO↗

arXiv2016

When should an expert make a prediction?

We consider a setting where in a known future time, a certain continuous random variable will be realized. There is a public prediction that gradually converges to its realized value, and an expert that has access to a more accurate prediction. Our goal is to study {\em when} should the expert reveal his information, assuming that his reward is based on a logarithmic market scoring rule (i.e., his reward is proportional to the gain in log-likelihood of the realized value). Our contributions are: (1) we characterize the expert's optimal policy and show that it is threshold based. (2) we analyze the expert's asymptotic expected optimal reward and show a tight connection to the Law of the Iterated Logarithm, and (3) we give an efficient dynamic programming algorithm to compute the optimal policy.

cs.GT↗

arXiv2014

Market Share Indicates Quality

Market share and quality, or customer satisfaction, go together. Yet inferring one from the other appears difficult. Indeed, such an inference would need detailed information about customer behavior, and might be clouded by modes of behavior such as herding (following popularity) or elitism, where customers avoid popular products. We investigate a fixed-price model where customers are informed about their history with products and about market share data. We find that it is in fact correct to make a Bayesian inference that the product with the higher market share has the better quality under few and unrestrictive assumptions on customer behavior.

cs.GT↗

arXiv2013

Internal Partitions of Regular Graphs

An internal partition of an $n$-vertex graph $G=(V,E)$ is a partition of $V$ such that every vertex has at least as many neighbors in its own part as in the other part. It has been conjectured that every $d$-regular graph with $n>N(d)$ vertices has an internal partition. Here we prove this for $d=6$. The case $d=n-4$ is of particular interest and leads to interesting new open problems on cubic graphs. We also provide new lower bounds on $N(d)$ and find new families of graphs with no internal partitions. Weighted versions of these problems are considered as well.

math.CO↗

arXiv2011

Strong Convergence in Posets

We consider the following solitaire game whose rules are reminiscent of the children's game of leapfrog. The player is handed an arbitrary ordering $\pi=(x_1,x_2,...,x_n)$ of the elements of a finite poset $(P,\prec)$. At each round an element may "skip over" the element in front of it, i.e. swap positions with it. For example, if $x_i \prec x_{i+1}$, then it is allowed to move from $\pi$ to the ordering $(x_1,x_2,...,x_{i-1},x_{i+1},x_i,x_{i+2},...,x_n)$. The player is to carry out such steps as long as such swaps are possible. When there are several consecutive pairs of elements that satisfy this condition, the player can choose which pair to swap next. Does the order of swaps matter for the final ordering or is it uniquely determined by the initial ordering? The reader may guess correctly that the latter proposition is correct. What may be more surprising, perhaps, is that this question is not trivial. The proof works by constructing an appropriate system of invariants.

math.CO↗