Approximate Analysis of Large Simulation-Based Games.

Game theory offers powerful tools for reasoning about agent behavior and incentives in multi-agent systems. Traditional approaches to game-theoretic analysis require enumeration of all possible strategies and outcomes. This often constrains game models to small numbers of agents and strategies or simple closed-form payoff descriptions. Simulation-based game theory extends the reach of game-theoretic analysis through the use of agent-based modeling. In the simulation-based approach, the analyst describes an environment procedurally and then computes payoffs by simulation of agent interactions in that environment. I use simulation-based game theory to study a model of credit network formation. Credit networks represent trust relationships in a directed graph and have been proposed as a mechanism for distributed transactions without a central currency. I explore what information is important when agents make initial decisions of whom to trust, and what sorts of networks can result from their decisions. This setting demonstrates both the value of simulation-based game theory—extending game-theoretic analysis beyond analytically tractable models—and its limitations—simulations produce prodigious amounts of data, and the number of simulations grows exponentially in the number of agents and strategies. I propose several techniques for approximate analysis of simulation-based games with large numbers of agents and large amounts of simulation data. First, I show how bootstrap-based statistics can be used to estimate confidence bounds on the results of simulation-based game analysis. I show that bootstrap confidence intervals for regret of approximate equilibria are well-calibrated. Next, I describe deviation-preserving reduction, which approximates an environment with a large number of agents using a game model with a small number of players, and demonstrate that it outperforms previous player reductions on several measures. Finally, I employ machine learning to construct game models from sparse data sets, and provide evidence that learned game models can produce even better approximate equilibria in large games than deviation-preserving reduction.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113587/1/btwied_1.pd

Data Structures for Deviation Payoffs

We present new data structures for representing symmetric normal-form games. These data structures are optimized for efficiently computing the expected utility of each unilateral pure-strategy deviation from a symmetric mixed-strategy profile. The cumulative effect of numerous incremental innovations is a dramatic speedup in the computation of symmetric mixed-strategy Nash equilibria, making it practical to represent and solve games with dozens to hundreds of players. These data structures naturally extend to role-symmetric and action-graph games with similar benefits.Comment: AAMAS 2023 + appendice

Drawing Isoglosses Algorithmically

Abstract In this paper, we apply algorithms for defining regions from sets of points to the problem of drawing isoglosses, the boundaries between dialect regions. We discuss the justifications for our method, and alternative models that could be constructed from this data. We evaluate the resultant model by comparison to the traditional method of drawing isoglosses, by hand

Learning Deviation Payoffs in Simulation-Based Games

We present a novel approach for identifying approximate role-symmetric Nash equilibria in large simulation-based games. Our method uses neural networks to learn a mapping from mixed-strategy profiles to deviation payoffs—the expected values of playing pure-strategy deviations from those profiles. This learning can generalize from data about a tiny fraction of a game’s outcomes, permitting tractable analysis of exponentially large normal-form games. We give a procedure for iteratively refining the learned model with new data produced by sampling in the neighborhood of each candidate Nash equilibrium. Relative to the existing state of the art, deviation payoff learning dramatically simplifies the task of computing equilibria and more effectively addresses player asymmetries. We demonstrate empirically that deviation payoff learning identifies better approximate equilibria than previous methods and can handle more difficult settings, including games with many more players, strategies, and roles

Strategic Formation of Credit Networks

Credit networks are an abstraction for modeling trust between agents in a network. Agents who do not directly trust each other can transact through exchange of IOUs (obligations) along a chain of trust in the network. Credit networks are robust to intrusion, can enable transactions between strangers in exchange economies, and have the liquidity to support a high rate of transactions. We study the formation of such networks when agents strategically decide how much credit to extend each other. When each agent trusts a fixed set of other agents, and transacts directly only with those it trusts, the formation game is a potential game and all Nash equilibria are social optima. Moreover, the Nash equilibria of this game are equivalent in a very strong sense: the sequences of transactions that can be supported from each equilibrium credit network are identical. When we allow transactions over longer paths, the game may no

SmartK: Efficient, Scalable, And Winning Parallel MCTS

SmartK is our efficient and scalable parallel algorithm for Monte Carlo Tree Search (MCTS), an approximation technique for game searches. MCTS is also used to solve problems as diverse as planning under uncertainty, combinatorial optimization, and high-energy physics. In these problems, the solution search space is significantly large, necessitating parallel solutions. Shared memory parallel approaches do not scale well beyond the size of a single node\u27s RAM. SmartK is a distributed memory parallelization that takes advantage of both inter-node and intra-node parallelism and a large cumulative RAM found in clusters. SmartK\u27s novel selection algorithm combined with its ability to efficiently search the solution space, results in better solutions than other MCTS parallel approaches. Results of an MPI implementation of SmartK for the game of Hex, show SmartK yields a better win percentage than other parallel algorithms, and that its performance scales to larger search spaces and high degrees of parallelism