Avg. Model Size vs. Changes No. Model Size Error vs. Changes No

model of its opponent's strategy based on its past behavior, and uses the model to predict its future behavior. We represent an interaction between agents by a repeated-game and restrict our attention to opponent strategies that can be represented by DFA. Learning a minimal DFA without a teacher was proved to be hard. We presented an unsu-pervised algorithm, US-L , based on Angluin's L algorithm. The algorithm maintains a model consistent with its past examples. When a new counterexample arrives it tries to extend the model in a minimal fashion. We presented a method for constructing an optimal strategy against the learned automaton. We conducted a set of experiments where random automata that represent diierent strategies were generated, and the algorithm tried to learn them based on a random set of game-histories. The algorithm managed to learn very compact models with high accuracy. The experimental results suggest that for random preex-closed samples the algorithm behaves well. However, following Angluin's result on the diiculty of learning almost uniform complete samples Ang78], it is obvious that our algorithm does not solve the complexity issue of inferring a DFA from a general preex-closed sample. We are currently looking for classes of preex-closed samples where US-L behaves well. The work presented here is only a rst step in the area of opponent modeling. The US-L algorithm enables an adaptive player to model an other agent's strategy in order to nd a proper response. The tasks of modeling adaptive players, modeling players that hide their interactive strategies, or avoiding other agent's attempts to model your strategy, are extremely diicult and deserve further research. The complexity of computing a best response automaton in repeated games with mixed strategies. Figure 7: The average model size learned by US-L , and the average error of the learned models, as a function of the changes number. In the third experiment we tested US-L with non-random automata. We repeated the famous tournament managed by Axelrod Axe84] for the Iterated Prisoner's Dilemma game (IPD) and allowed our adaptive player to observe the tournament and build models for all the attendees. In the original tournament, fteen attendees (strategies) competed in a round robin tournament, where any interaction was based on 200 repetitions of the PD game. In our tournament we allowed only deterministic players to participate (10 players). After building the models, the adaptive player joined the tournament and played against the …