arXiv subjects

Itai Arieli

Publications and source records attributed to Itai Arieli.

26 records · Page 2Linked to original sources

arXiv2020

Feasible Joint Posterior Beliefs

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state, and who observe some information structure. For two agents we introduce a quantitative version of Aumann's Agreement Theorem, and show that it is equivalent to a characterization of feasible distributions due to Dawid et al. (1995). For any number of agents, we characterize feasible distributions in terms of a "no-trade" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

econ.TH↗

arXiv2020

On social networks that support learning

It is well understood that the structure of a social network is critical to whether or not agents can aggregate information correctly. In this paper, we study social networks that support information aggregation when rational agents act sequentially and irrevocably. Whether or not information is aggregated depends, inter alia, on the order in which agents decide. Thus, to decouple the order and the topology, our model studies a random arrival order. Unlike the case of a fixed arrival order, in our model, the decision of an agent is unlikely to be affected by those who are far from him in the network. This observation allows us to identify a local learning requirement, a natural condition on the agent's neighborhood that guarantees that this agent makes the correct decision (with high probability) no matter how well other agents perform. Roughly speaking, the agent should belong to a multitude of mutually exclusive social circles. We illustrate the power of the local learning requirement by constructing a family of social networks that guarantee information aggregation despite that no agent is a social hub (in other words, there are no opinion leaders). Although the common wisdom of the social learning literature suggests that information aggregation is very fragile, another application of the local learning requirement demonstrates the existence of networks where learning prevails even if a substantial fraction of the agents are not involved in the learning process. On a technical level, the networks we construct rely on the theory of expander graphs, i.e., highly connected sparse graphs with a wide range of applications from pure mathematics to error-correcting codes.

econ.TH↗

arXiv2020

Multi-Issue Social Learning

We consider social learning where agents can only observe part of the population (modeled as neighbors on an undirected graph), face many decision problems, and arrival order of the agents is unknown. The central question we pose is whether there is a natural observability graph that prevents the information cascade phenomenon. We introduce the `celebrities graph' and prove that indeed it allows for proper information aggregation in large populations even when the order at which agents decide is random and even when different issues are decided in different orders.

cs.GT↗

arXiv2019

The Implications of Pricing on Social Learning

We study the implications of endogenous pricing for learning and welfare in the classic herding model . When prices are determined exogenously, it is known that learning occurs if and only if signals are unbounded. By contrast, we show that learning can occur when signals are bounded as long as non-conformism among consumers is scarce. More formally, learning happens if and only if signals exhibit the vanishing likelihood property introduced bellow. We discuss the implications of our results for potential market failure in the context of Schumpeterian growth with uncertainty over the value of innovations.

econ.TH↗

arXiv2018

The One-Shot Crowdfunding Game

The recent success of crowd-funding for supporting new and innovative products has been overwhelming with over 34 Billion Dollars raised in 2015. In many crowd-funding platforms, firms set a campaign goal and contributions are collected only if this goal is reached. At the time of the campaign, consumers are often uncertain as to the ex-post value of the product, the business model viability, or the seller's reliability. Consumer who commit to a contribution therefore gambles. This gamble is effected by the campaign's threshold. Contributions to campaigns with higher thresholds are collected only if a greater number of agents find the offering acceptable. Therefore, high threshold serves as a social insurance and thus in high-threshold campaigns, potential contributors feel more at ease with contributing. We introduce the crowdunding game and explore the contributor's dilemma in the context of experience goods. We discuss equilibrium existence and related social welfare, information aggregation and revenue implications.

cs.GT↗

arXiv2017

The Crowdfunding Game

The recent success of crowdfunding for supporting new and innovative products has been overwhelming with over 34 Billion Dollars raised in 2015. In many crowdfunding platforms, firms set a campaign threshold and contributions are collected only if this threshold is reached. During the campaign, consumers are uncertain as to the ex-post value of the product, the business model viability, and the seller's reliability. Consumer who commit to a contribution therefore gambles. This gamble is effected by the campaign's threshold. Contributions to campaigns with higher thresholds are collected only if a greater number of agents find the offering acceptable. Therefore, high threshold serves as a social insurance and thus in high-threshold campaigns, potential contributors feel more at ease with contributing. We introduce the crowdfunding game and explore the contributor's dilemma in the context of experience goods. We discuss equilibrium existence and related social welfare, information aggregation and revenue implications.

cs.GT↗

arXiv2017

Simple approximate equilibria in games with many players

We consider $ε$-equilibria notions for constant value of $ε$ in $n$-player $m$-actions games where $m$ is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that $ε$-equilibrium is guaranteed to exist over this grid. For Nash equilibrium, we prove that constant grid size (that depends on $ε$ and $m$, but not on $n$) is sufficient to guarantee existence of weak approximate equilibrium. This result implies a polynomial (in the input) algorithm for weak approximate equilibrium. For approximate Nash equilibrium we introduce a closely related question and prove its \emph{equivalence} to the well-known Beck-Fiala conjecture from discrepancy theory. To the best of our knowledge this is the first result introduces a connection between game theory and discrepancy theory. For correlated equilibrium, we prove a $O(\frac{1}{\log n})$ lower-bound on the grid size, which matches the known upper bound of $Ω(\frac{1}{\log n})$. Our result implies an $Ω(\log n)$ lower bound on the rate of convergence of dynamics (any dynamic) to approximate correlated (and coarse correlated) equilibrium. Again, this lower bound matches the $O(\log n)$ upper bound that is achieved by regret minimizing algorithms.

cs.GT↗

arXiv2015

Random Extensive Form Games and its Application to Bargaining

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for binary-trees with increasing depth in various random (or deterministic) assignments of players to nodes. We characterize the assignments under which the asymptotic distribution concentrates around a point. Our analysis provides a natural way to derive from the asymptotic distribution a novel solution concept for two-player bargaining problems with a solid strategic justification.

cs.GT↗