Peer prediction refers to a collection of mechanisms for eliciting information from human agents when direct verification of the obtained information is unavailable. They are designed to have a game-theoretic equilibrium where everyone reveals their private information truthfully. This result holds under the assumption that agents are Bayesian and they each adopt a fixed strategy across all tasks. Human agents however are observed in many domains to exhibit learning behavior in sequential settings. In this paper, we explore the dynamics of sequential peer prediction mechanisms when participants are learning agents. We first show that the notion of no regret alone for the agents’ learning algorithms cannot guaran- tee convergence to the truthful strategy. We then focus on a family of learning algorithms where strategy updates only depend on agents’ cumulative rewards and prove that agents’ strategies in the popular Correlated Agreement (CA) mechanism converge to truthful reporting when they use algorithms from this family. This fam- ily of algorithms is not necessarily no-regret, but includes several familiar no-regret learning algorithms (e.g multiplicative weight update and Follow the Perturbed Leader) as special cases. Simulation of several algorithms in this family as well as the ε-greedy algorithm, which is outside of this family, shows convergence to the truthful strategy in the CA mechanism.
more »
« less
False Consensus, Information Theory, and Prediction Markets
We study a setting where Bayesian agents with a common prior have private information related to an event’s outcome and sequentially make public announcements relating to their information. Our main result shows that when agents' private information is independent conditioning on the event’s outcome whenever agents have similar beliefs about the outcome, their information is aggregated. That is, there is no false consensus.
Our main result has a short proof based on a natural information-theoretic framework. A key ingredient of the framework is the equivalence between the sign of the "interaction information" and a super/sub-additive property of the value of people’s information. This provides an intuitive interpretation and an interesting application of the interaction information, which measures the amount of information shared by three random variables.
We illustrate the power of this information-theoretic framework by reproving two additional results within it: 1) that agents quickly agree when announcing (summaries of) beliefs in round-robin fashion [Aaronson 2005], and 2) results from [Chen et al 2010] on when prediction market agents should release information to maximize their payment. We also interpret the information-theoretic framework and the above results in prediction markets by proving that the expected reward of revealing information is the conditional mutual information of the information revealed.
more »
« less
- PAR ID:
- 10526183
- Editor(s):
- Tauman_Kalai, Yael
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Volume:
- 251
- ISSN:
- 1868-8969
- ISBN:
- 978-3-95977-263-1
- Page Range / eLocation ID:
- 251-251
- Subject(s) / Keyword(s):
- Agreeing to disagree false consensus information theory prediction market Theory of computation → Algorithmic game theory and mechanism design
- Format(s):
- Medium: X Size: 23 pages; 1119574 bytes Other: application/pdf
- Size(s):
- 23 pages 1119574 bytes
- Right(s):
- Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)We exhibit a natural environment, social learning among heterogeneous agents, where even slight misperceptions can have a large negative impact on long‐run learning outcomes. We consider a population of agents who obtain information about the state of the world both from initial private signals and by observing a random sample of other agents' actions over time, where agents' actions depend not only on their beliefs about the state but also on their idiosyncratic types (e.g., tastes or risk attitudes). When agents are correct about the type distribution in the population, they learn the true state in the long run. By contrast, we show, first, that even arbitrarily small amounts of misperception about the type distribution can generate extreme breakdowns of information aggregation, where in the long run all agents incorrectly assign probability 1 to some fixed state of the world, regardless of the true underlying state. Second, any misperception of the type distribution leads long‐run beliefs and behavior to vary only coarsely with the state, and we provide systematic predictions for how the nature of misperception shapes these coarse long‐run outcomes. Third, we show that how fragile information aggregation is against misperception depends on the richness of agents' payoff‐relevant uncertainty; a design implication is that information aggregation can be improved by simplifying agents' learning environment. The key feature behind our findings is that agents' belief‐updating becomes “decoupled” from the true state over time. We point to other environments where this feature is present and leads to similar fragility results.more » « less
-
Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome of an uncertain event, is an increasingly popular way for robots to act under uncertainty. In this work we take a game-theoretic perspective on contingency planning, tailored to multi-agent scenarios in which a robot’s actions impact the decisions of other agents and vice versa. The resulting contingency game allows the robot to efficiently interact with other agents by generating strategic motion plans conditioned on multiple possible intents for other actors in the scene. Contingency games are parameterized via a scalar variable which represents a future time when intent uncertainty will be resolved. By estimating this parameter online, we construct a game-theoretic motion planner that adapts to changing beliefs while anticipating future certainty. We show that existing variants of game-theoretic planning under uncertainty are readily obtained as special cases of contingency games. Through a series of simulated autonomous driving scenarios, we demonstrate that contingency games close the gap between certainty-equivalent games that commit to a single hypothesis and non-contingent multi-hypothesis games that do not account for future uncertainty reduction.more » « less
-
Abstract We develop a novel bounded rationality model of imperfect reasoning as the interaction between automatic (System 1) and analytical (System 2) thinking. In doing so, we formalize the empirical consensus of cognitive psychology using a structural, constrained-optimal economic framework of mental information acquisition about the unknown optimal policy function. A key result is that agents reason less (more) when facing usual (unusual) states of the world, producing state- and history-dependent behavior. Our application is an otherwise standard incomplete-markets model with no a priori behavioral biases. The ergodic distribution of actions and beliefs is characterized by endogenous learning traps, where locally stable state dynamics generate familiar regions of the state space within which behavior appears to follow memory-based heuristics. This results in endogenous behavioral biases that have many empirically desirable properties: the marginal propensity to consume is high even for unconstrained agents, hand-to-mouth status is more frequent and persistent, and there is more wealth inequality than in the standard model.more » « less
-
Bringmann, Karl ; Grohe, Martin ; Puppis, Gabriele ; Svensson, Ola (Ed.)We study information design in click-through auctions, in which the bidders/advertisers bid for winning an opportunity to show their ads but only pay for realized clicks. The payment may or may not happen, and its probability is called the click-through rate (CTR). This auction format is widely used in the industry of online advertising. Bidders have private values, whereas the seller has private information about each bidder’s CTRs. We are interested in the seller’s problem of partially revealing CTR information to maximize revenue. Information design in click-through auctions turns out to be intriguingly different from almost all previous studies in this space since any revealed information about CTRs will never affect bidders' bidding behaviors - they will always bid their true value per click - but only affect the auction’s allocation and payment rule. In some sense, this makes information design effectively a constrained mechanism design problem. Our first result is an FPTAS to compute an approximately optimal mechanism under a constant number of bidders. The design of this algorithm leverages Bayesian bidder values which help to "smooth" the seller’s revenue function and lead to better tractability. The design of this FPTAS is complex and primarily algorithmic. Our second main result pursues the design of "simple" mechanisms that are approximately optimal yet more practical. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works. When bidders' CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a parameter termed optimal signal ratio. The constructed scheme provably obtains a good approximation as long as the maximum and minimum of bidders' value density functions do not differ much.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.4230/LIPIcs.ITCS.2023.81
