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Unformatted text preview: Nau: Game Theory 1 Updated 11/14/11 CMSC 498T, Game Theory 7b. Synthesizing Strategies from Interaction Traces Dana Nau University of Maryland Nau: Game Theory 2 Updated 11/14/11 Conditions for a Bayesian Game Recall the two conditions that a Bayesian game G must satisfy Condition 1 : The games in G have the same number of agents, and the same strategy space for each agent. The only difference is in the payoffs of the strategies. Condition 2 : the prior probability distribution over the games in G is common knowledge Well now look at an example that satisfies Condition 1 but not Condition 2 A repeated 2x2 game where we know nothing about the other agents payoffs Nau: Game Theory 3 Updated 11/14/11 A Repeated NonBayesian Game Consider a game where we know nothing about the other agents payoffs Not even a common prior Weve discussed two kinds of strategies for this situation Maximin strategy: maximizes your worstcase outcome Minimaxregret strategy: minimizes your worstcase regret Suppose its a repeated game You can learn something about the other agents strategies by watching how they act With this information, you may be able to do much better Estimate what strategy is most likely to get the responses you want Nau: Game Theory 4 Updated 11/14/11 Learning from Interaction Traces More work by TszChiu Au: Suppose the agents are competent members of their society Then their interactions probably produce payoffs that they find acceptable Observe their interactions, collect interaction traces action histories, without the payoffs See which interaction traces produce outcomes that we prefer i.e., high payoff for us if we interact with those agents Combine those traces into a composite strategy Composite Strategy Synthesis Interaction Traces a 1 a 5 a 2 a 4 a 3 Nau: Game Theory 5 Updated 11/14/11 Results Necessary and sufficient conditions for combining interaction traces into a composite strategy The CIT algorithm selects the best set (i.e., highest expected utility) of combinable interaction traces, and combines them Modified composite agent augments an agent to use the composite strategy to enhance its performance Crossvalidated experimental results Composite strategy M odified C omposite A gent Interaction traces Evaluation in tournaments a 1 a n . . . Nau: Game Theory...
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