Do Prices Coordinate Markets?

Walrasian equilibrium prices can be said to coordinate markets: They support a welfare optimal allocation in which each buyer is buying bundle of goods that is individually most preferred. However, this clean story has two caveats. First, the prices alone are not sufficient to coordinate the market, and buyers may need to select among their most preferred bundles in a coordinated way to find a feasible allocation. Second, we don't in practice expect to encounter exact equilibrium prices tailored to the market, but instead only approximate prices, somehow encoding "distributional" information about the market. How well do prices work to coordinate markets when tie-breaking is not coordinated, and they encode only distributional information? We answer this question. First, we provide a genericity condition such that for buyers with Matroid Based Valuations, overdemand with respect to equilibrium prices is at most 1, independent of the supply of goods, even when tie-breaking is done in an uncoordinated fashion. Second, we provide learning-theoretic results that show that such prices are robust to changing the buyers in the market, so long as all buyers are sampled from the same (unknown) distribution

Binocular fusion and invariant category learning due to predictive remapping during scanning of a depthful scene with eye movements

How does the brain maintain stable fusion of 3D scenes when the eyes move? Every eye movement causes each retinal position to process a different set of scenic features, and thus the brain needs to binocularly fuse new combinations of features at each position after an eye movement. Despite these breaks in retinotopic fusion due to each movement, previously fused representations of a scene in depth often appear stable. The 3D ARTSCAN neural model proposes how the brain does this by unifying concepts about how multiple cortical areas in the What and Where cortical streams interact to coordinate processes of 3D boundary and surface perception, spatial attention, invariant object category learning, predictive remapping, eye movement control, and learned coordinate transformations. The model explains data from single neuron and psychophysical studies of covert visual attention shifts prior to eye movements. The model further clarifies how perceptual, attentional, and cognitive interactions among multiple brain regions (LGN, V1, V2, V3A, V4, MT, MST, PPC, LIP, ITp, ITa, SC) may accomplish predictive remapping as part of the process whereby view-invariant object categories are learned. These results build upon earlier neural models of 3D vision and figure-ground separation and the learning of invariant object categories as the eyes freely scan a scene. A key process concerns how an object's surface representation generates a form-fitting distribution of spatial attention, or attentional shroud, in parietal cortex that helps maintain the stability of multiple perceptual and cognitive processes. Predictive eye movement signals maintain the stability of the shroud, as well as of binocularly fused perceptual boundaries and surface representations.Published versio

The hippocampus and cerebellum in adaptively timed learning, recognition, and movement

The concepts of declarative memory and procedural memory have been used to distinguish two basic types of learning. A neural network model suggests how such memory processes work together as recognition learning, reinforcement learning, and sensory-motor learning take place during adaptive behaviors. To coordinate these processes, the hippocampal formation and cerebellum each contain circuits that learn to adaptively time their outputs. Within the model, hippocampal timing helps to maintain attention on motivationally salient goal objects during variable task-related delays, and cerebellar timing controls the release of conditioned responses. This property is part of the model's description of how cognitive-emotional interactions focus attention on motivationally valued cues, and how this process breaks down due to hippocampal ablation. The model suggests that the hippocampal mechanisms that help to rapidly draw attention to salient cues could prematurely release motor commands were not the release of these commands adaptively timed by the cerebellum. The model hippocampal system modulates cortical recognition learning without actually encoding the representational information that the cortex encodes. These properties avoid the difficulties faced by several models that propose a direct hippocampal role in recognition learning. Learning within the model hippocampal system controls adaptive timing and spatial orientation. Model properties hereby clarify how hippocampal ablations cause amnesic symptoms and difficulties with tasks which combine task delays, novelty detection, and attention towards goal objects amid distractions. When these model recognition, reinforcement, sensory-motor, and timing processes work together, they suggest how the brain can accomplish conditioning of multiple sensory events to delayed rewards, as during serial compound conditioning.Air Force Office of Scientific Research (F49620-92-J-0225, F49620-86-C-0037, 90-0128); Advanced Research Projects Agency (ONR N00014-92-J-4015); Office of Naval Research (N00014-91-J-4100, N00014-92-J-1309, N00014-92-J-1904); National Institute of Mental Health (MH-42900

Learning Existing Social Conventions via Observationally Augmented Self-Play

In order for artificial agents to coordinate effectively with people, they must act consistently with existing conventions (e.g. how to navigate in traffic, which language to speak, or how to coordinate with teammates). A group's conventions can be viewed as a choice of equilibrium in a coordination game. We consider the problem of an agent learning a policy for a coordination game in a simulated environment and then using this policy when it enters an existing group. When there are multiple possible conventions we show that learning a policy via multi-agent reinforcement learning (MARL) is likely to find policies which achieve high payoffs at training time but fail to coordinate with the real group into which the agent enters. We assume access to a small number of samples of behavior from the true convention and show that we can augment the MARL objective to help it find policies consistent with the real group's convention. In three environments from the literature - traffic, communication, and team coordination - we observe that augmenting MARL with a small amount of imitation learning greatly increases the probability that the strategy found by MARL fits well with the existing social convention. We show that this works even in an environment where standard training methods very rarely find the true convention of the agent's partners.Comment: Published in AAAI-AIES2019 - Best Pape

Efficient Dynamic Coordination with Individual Learning

We study how the presence of multiple participation opportunities coupled with individual learning about payoff affects the ability of agents to coordinate efficiently in global coordination games. Two players face the option to invest irreversibly in a project in one of many rounds. The project succeeds if some underlying state variable theta is positive and both players invest, possibly asynchronously. In each round they receive informative private signals about theta, and asymptotically learn the true value of theta. Players choose in each period whether to invest or to wait for more precise information about theta. We show that with sufficiently many rounds, both players invest with arbitrarily high probability whenever investment is socially efficient, and delays in investment disappear when signals are precise. This result stands in sharp contrast to the usual static global game outcome in which players coordinate on the risk-dominant action. We provide a foundation for these results in terms of higher order beliefs.

Monotone and bounded interval equilibria in a coordination game with information aggregation

We analyze how private learning in a class of games with common stochastic payoffs affects the form of equilibria, and how properties such as player welfare and the extent of strategic miscoordination relate across monotone and non-monotone equilibria. Researchers typically focus on monotone equilibria. We provide conditions under which non-monotone equilibria also exist, where players attempt to coordinate to obtain the stochastic payoff whenever signals are in a bounded interval. In bounded interval equilibria (BIE), an endogenous fear of miscoordination discourages players from coordinating to obtain the stochastic payoff when their signals suggest coordination is most beneficial. In contrast to monotone equilibria, expected payoffs from successful coordination in BIE are lower than the ex-ante expected payoff from ignoring signals and always trying to coordinate to obtain the stochastic payoff. We show that BIE only exist when, absent private information, the game would be a coordination game

One Step at a Time: Does Gradualism Build Coordination?

We study how gradualism -- increasing required levels (“thresholds”) of contributions slowly over time rather than requiring a high level of contribution immediately -- affects individuals’ decisions to contribute to a public project. Using a laboratory binary choice minimum-effort coordination game, we randomly assign participants to three treatments: starting and continuing at a high threshold, starting at a low threshold but jumping to a high threshold after a few periods, and starting at a low threshold and gradually increasing the threshold over time (the “gradualism” treatment). We find that individuals coordinate most successfully at the high threshold in the gradualism treatment relative to the other two groups. We propose a theory based on belief updating to explain why gradualism works. We also discuss alternative explanations such as reinforcement learning, conditional cooperation, inertia, preference for consistency, and limited attention. Our findings point to a simple, voluntary mechanism to promote successful coordination when the capacity to impose sanctions is limited.Gradualism; Coordination; Cooperation; Public Goods; Belief-based Learning; Laboratory Experiment