Monte Carlo approximation in incomplete information, sequential auction games

We model sequential, possibly multiunit, sealed bid auctions as a sequential game with imperfect and incomplete information. We develop an agent that constructs a bidding policy by sampling the valuation space of its opponents, solving the resulting complete information game, and aggregating the samples into a policy. The constructed policy takes advantage of information learned in the early stages of the game and is flexible with respect to assumptions about the other bidders\u27 valuations. Because the straightforward expansion of the complete information game is intractable, we develop a more concise representation that takes advantage of the sequential auctions\u27 natural structure. We examine the performance of our agent versus agents that play perfectly, agents that also create policies using Monte Carlo, and other benchmarks. The technique performs quite well in these empirical studies, although the tractability of the problem is bounded by the ability to solve component games

The constraints of the valuation distribution for solving a class of games by using a best response algorithm

Infinite games with incomplete information are common in practice. First-price, sealed-bid auctions are a prototypical example. To solve this kind of infinite game, a heuristic approach is to discretise the strategy spaces and enumerate to approximate the equilibrium strategies. However, an approximate algorithm might not be guaranteed to converge. This paper discusses the utilisation of a best response algorithm in solving infinite games with incomplete information. We show the constraints of the valuation distributions define the necessary conditions of the convergence of the best response algorithm for several classes of infinite games, including auctions. A salient feature of the necessary convergence conditions lies in that they can be employed to compute the exact Nash equilibria without discretising the strategy space if the best response algorithm converges

Composing Efficient, Robust Tests for Policy Selection

Modern reinforcement learning systems produce many high-quality policies throughout the learning process. However, to choose which policy to actually deploy in the real world, they must be tested under an intractable number of environmental conditions. We introduce RPOSST, an algorithm to select a small set of test cases from a larger pool based on a relatively small number of sample evaluations. RPOSST treats the test case selection problem as a two-player game and optimizes a solution with provable $k$-of-$N$ robustness, bounding the error relative to a test that used all the test cases in the pool. Empirical results demonstrate that RPOSST finds a small set of test cases that identify high quality policies in a toy one-shot game, poker datasets, and a high-fidelity racing simulator.Comment: 26 pages, 13 figures. To appear in Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI 2023

Computing Price Trajectories in Combinatorial Auctions with Proxy Bidding

Proxy bidding has proven useful in a variety of real auction formats---most notably eBay--- and has been proposed for the nascent field of combinatorial auctions. Previous work on proxy bidding in combinatorial auctions requires the auctioneer to run the auction with myopic bidders to determine the outcome. In this paper we present a radically different approach that computes the bidders' allocation of their attention across the bundles only at "inflection points." Inflections are caused by the introduction of a new bundle into an agent's demand set, a change in the set of currently competitive allocations, or the withdrawal of an agent from the set of active bidders. This approach has several advantages over alternatives, including that it computes exact solutions and is invariant to the magnitude of the bids

Analysis and Observations from the First Amazon Picking Challenge

This paper presents a overview of the inaugural Amazon Picking Challenge along with a summary of a survey conducted among the 26 participating teams. The challenge goal was to design an autonomous robot to pick items from a warehouse shelf. This task is currently performed by human workers, and there is hope that robots can someday help increase efficiency and throughput while lowering cost. We report on a 28-question survey posed to the teams to learn about each team's background, mechanism design, perception apparatus, planning and control approach. We identify trends in this data, correlate it with each team's success in the competition, and discuss observations and lessons learned based on survey results and the authors' personal experiences during the challenge

Agent-Based Markov Modeling for Improved COVID-19 Mitigation Policies

You are currently viewing a research paper that was included in the August 2021 Good Systems Network Digest.Office of the VP for Researc

Auction Protocols for Decentralized Scheduling

Scheduling is the problem of allocating resources to alternate possible uses over designated periods of time. Several have proposed (and some have tried) market-based approaches to decentralized versions of the problem, where the competing uses are represented by autonomous agents. Market mechanisms use prices derived through distributed bidding protocols to determine an allocation, and thus solve the scheduling problem. To analyze the behavior of market schemes, we formalize decentralized scheduling as a discrete resource allocation problem, and bring to bear some relevant economic concepts. Drawing on results from the literature, we discuss the existence of equilibrium prices for some general classes of scheduling problems, and the quality of equilibrium solutions. To remedy the potential nonexistence of price equilibria due to complementarity in preference, we introduce additional markets in combinations of basic goods. We present some auction mechanisms and bidding protocols corresponding to the two market structures, and analyze their computational and economic properties. Finally, we consider direct revelation mechanisms, and compare to the market-based approach.http://deepblue.lib.umich.edu/bitstream/2027.42/50443/1/gebfinal.pd

Some Economics of Market-Based Distributed Scheduling

Market mechanisms solve distributed scheduling problems by allocating the scheduled resources according to market prices. We model distributed scheduling as a discrete resource allocation problem, and demonstrate the applicability of economic analysis to this framework. Drawing on results from the literature, we discuss the existence of equilibrium prices for some general classes of scheduling problems, and the quality of equilibrium solutions. We then present two protocols for implementing market solutions, and analyze their computational and economic properties.http://deepblue.lib.umich.edu/bitstream/2027.42/60422/1/mb-scheduling-extended.pd