/wp-content/uploads/2016/07/SRG-black-background.png 0 0 wellman /wp-content/uploads/2016/07/SRG-black-background.png wellman2010-03-27 22:59:022016-08-22 16:08:09Stochastic Search Methods for Nash Equilibrium Approximation in Simulation-Based Games
We define the class of games called simulation-based games, in which the payoffs are available as an output of an oracle (simulator), rather than specified analytically or using a payoff matrix. We then describe a convergent algorithm based on a hierarchical application of simulated annealing for estimating Nash equilibria in simulation-based games with finite-dimensional strategy sets. Additionally, we present alternative algorithms for best response and Nash equilibrium estimation, with a particular focus on one-shot infinite games of incomplete information. Our experimental results demonstrate that all the approaches we introduce are efficacious, albeit some more so than others. We show, for example, that while iterative best response dynamics has relatively weak convergence guarantees, it outperforms our convergent method experimentally. Additionally, we provide considerable evidence that a method based on random search outperforms gradient descent in our setting.
/wp-content/uploads/2016/07/SRG-black-background.png 0 0 wellman /wp-content/uploads/2016/07/SRG-black-background.png wellman2010-03-27 22:56:322016-08-22 16:07:56Selecting Strategies using Empirical Game Models: An Experimental Analysis of Meta-Strategies
In many complex multi-agent domains it is impractical to compute exact analytic solutions. An alternate means of analysis applies computational tools to derive and analyze empirical game models. These models are noisy approximations, which raises questions about how to account for uncertainty when analyzing the model. We develop a novel experimental framework and apply it to benchmark meta-strategies – general algorithms for selecting strategies based on empirical game models. We demonstrate that modeling noise is important; a naïve approach that disregards noise and plays according to Nash equilibrium yields poor choices. We introduce three parameterized algorithms that factor noise into the analysis by predicting distributions of opponent play. As observation noise increases, rational players generally make less specific outcome predictions. Our comparison of the algorithms identifies logit equilibrium as the best method for making these predictions. Logit equilibrium incorporates a form of noisy decision-making by players. Our evidence shows that this is a robust method for approximating the effects of uncertainty in many contexts. This result has practical relevance for guiding analysis of empirical game models. It also offers an intriguing rationale for behavioral findings that logit equilibrium is a better predictor of human behavior than Nash equilibrium.
/wp-content/uploads/2016/07/SRG-black-background.png 0 0 wellman /wp-content/uploads/2016/07/SRG-black-background.png wellman2010-03-27 22:52:592016-08-22 16:07:43Searching for Approximate Equilibria in Empirical Games
When exploring a game over a large strategy space, it may not be feasible or cost-effective to evaluate the payoff of every relevant strategy profile. For example, determining a profile payoff for a procedurally defined game may require Monte Carlo simulation or other costly computation. Analyzing such games poses a search problem, with the goal of identifying equilibrium profiles by evaluating payoffs of candidate solutions and potential deviations from those candidates. We propose two algorithms, applicable to distinct models of the search process. In the revealed-payoff model, each search step determines the exact payoff for a designated pure-strategy profile. In the noisy-payoff model, a step draws a stochastic sample corresponding to such a payoff. We compare our algorithms to previous proposals from the literature for these two models, and demonstrate performance advantages.
/wp-content/uploads/2016/07/SRG-black-background.png 0 0 wellman /wp-content/uploads/2016/07/SRG-black-background.png wellman2010-03-27 22:41:482016-08-15 14:41:18Knowledge Combination in Graphical Multiagent Models
A graphical multiagent model (GMM) represents a joint distribution over the behavior of a set of agents. One source of knowledge about agents' behavior may come from game-theoretic analysis, as captured by several graphical game representations developed in recent years. GMMs generalize this approach to express arbitrary distributions, based on game descriptions or other sources of knowledge bearing on beliefs about agent behavior. To illustrate the flexibility of GMMs, we exhibit game-derived models that allow probabilistic deviation from equilibrium, as well as models based on heuristic action choice. We investigate three different methods of integrating these models into a single model representing the combined knowledge sources. To evaluate the predictive performance of the combined model, we treat as actual outcome the behavior produced by a reinforcement learning process. We find that combining the two knowledge sources, using any of the methods, provides better predictions than either source alone. Among the combination methods, mixing data outperforms the opinion pool and direct update methods investigated in this empirical trial.
/wp-content/uploads/2016/07/SRG-black-background.png 0 0 wellman /wp-content/uploads/2016/07/SRG-black-background.png wellman2010-03-27 22:31:252016-08-15 14:41:10CUI Networks: A Graphical Representation for Conditional Utility Independence
We introduce CUI networks, a compact graphical representation of utility functions over multiple attributes. CUI networks model multiattribute utility functions using the well-studied and widely applicable utility independence concept. We show how conditional utility independence leads to an effective functional decomposition that can be exhibited graphically, and how local, compact data at the graph nodes can be used to calculate joint utility. We discuss aspects of elicitation, network construction, and optimization, and contrast our new representation with previous graphical preference modeling.
/wp-content/uploads/2016/07/SRG-black-background.png 0 0 wellman /wp-content/uploads/2016/07/SRG-black-background.png wellman2010-03-27 22:27:592016-08-22 16:07:12Bidding Strategies for Simultaneous Ascending Auctions
Simultaneous ascending auctions present agents with various strategic problems, depending on preference structure. As long as bids represent non-repudiable offers, submitting non-contingent bids to separate auctions entails an exposure problem: bidding to acquire a bundle risks the possibility of obtaining an undesired subset of the goods. With multiple goods (or units of a homogeneous good) bidders also need to account for their own effects on prices. Auction theory does not provide analytic solutions for optimal bidding strategies in the face of these problems. We present a new family of decision-theoretic bidding strategies that use probabilistic predictions of final prices: self-confirming distribution-prediction strategies. Bidding based on these is provably not optimal in general. But evidence using empirical game-theoretic methods we developed indicates the strategy is quite effective compared to other known methods when preferences exhibit complementarities. When preferences exhibit substitutability, simpler demand-reduction strategies address the own price effect problem more directly and perform better.