Abstract
Lookahead search is perhaps the most natural and widely used game playing strategy. Given the practical importance of the method, the aim of this paper is to provide a theoretical performance examination of lookahead search in a wide variety of applications. To determine a strategy play using lookahead search, each agent predicts multiple levels of possible re-actions to her move (via the use of a search tree), and then chooses the play that optimizes her future payoff accounting for these re-actions. There are several choices of optimization function the agents can choose, where the most appropriate choice of function will depend on the specifics of the actual game - we illustrate this in our examples. Furthermore, the type of search tree chosen by computationally-constrained agent can vary. We focus on the case where agents can evaluate only a bounded number, k, of moves into the future. That is, we use depth k search trees and call this approach k-lookahead search. We apply our method in five well-known settings: industrial organization (Cournot’s model); AdWord auctions; congestion games; valid-utility games and basic-utility games; cost-sharing network design games. We consider two questions. First, what is the expected social quality of outcome when agents apply lookahead search? Second, what interactive behaviours can be exhibited when players use lookahead search? We demonstrate how the answer depends on the game played.
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References
Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. Journal of the ACM 55(6) (2008)
Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: STOC (2005)
Awerbuch, B., Azar, Y., Epstein, A., Mirrokni, V., Skopalik, A.: Fast convergence to nearly-optimal solutions in potential games. In: EC, pp. 264–273 (2008)
Blum, A., Hajiaghayi, M., Ligett, K., Roth, A.: Regret minimization and the price of total anarchy. In: STOC, pp. 373–382 (2008)
Bu, T., Deng, X., Qi, Q.: Forward looking Nash equilibrium for keyword auction. Information Processing Letters 105(2), 41–46 (2008)
Cary, M., Das, A., Edelman, B., Giotis, I., Heimerl, K., Karlin, A., Mathieu, C., Schwarz, M.: Greedy bidding strategies for keyword auctions. In: EC (2007)
Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. Games and Economic Behavior 71(2), 315–327 (2011)
Christodoulou, G., Mirrokni, V.S., Sidiropoulos, A.: Convergence and Approximation in Potential Games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 349–360. Springer, Heidelberg (2006)
Cournot, A.: Recherces sur les Principes Mathématiques de la Théorie des Richesse, Paris (1838)
Fabrikant, A., Papadimitriou, C.: The complexity of game dynamics: BGP oscillations, sink equlibria, and beyond. In: SODA, pp. 844–853 (2008)
Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure Nash equilibria. In: STOC, pp. 604–612 (2004)
Fanelli, A., Flammini, M., Moscardelli, L.: The Speed of Convergence in Congestion Games under Best-Response Dynamics. In: Aceto, L., DamgĂ¥rd, I., Goldberg, L.A., HalldĂ³rsson, M.M., IngĂ³lfsdĂ³ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 796–807. Springer, Heidelberg (2008)
Friedman, M.: The methodology of positive economics. In: Friedman, M. (ed.) Essays in Positive Economics, pp. 3–43. University of Chicago Press (1953)
Goemans, M., Li, L., Mirrokni, V., Thottan, M.: Market sharing games applied to content distribution in ad-hoc networks. In: MOBIHOC (2004)
Goemans, M., Mirrokni, V., Vetta, A.: Sink equilibria and convergence. In: FOCS, pp. 142–154 (2005)
de Groot, A.: Thought and Choice in Chess, 2nd edn. Mouton (1978), Original Version: Het denken van den Schaker, een experimenteel-psychologische studie, Ph.D. thesis, University of Amsterdam (1946)
de Kleer, J., Raiman, O., Shirley, M.: One step lookahead is pretty good. In: Hamscher, W., Console, L., de Kleer, J. (eds.) Readings in Model-Based Diagnosis, pp. 138–142. Morgan Kaufmann (1992)
Koutsoupias, E., Papadimitriou, C.: Worst-Case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Paes Leme, R., Tardos, E.: Pure and Bayes-Nash price of anarchy for generalized second price auction. In: FOCS (2010)
Markakis, E., Telelis, O.: Discrete Strategies in Keyword Auctions and Their Inefficiency for Locally Aware Bidders. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 523–530. Springer, Heidelberg (2010)
Mirrokni, V., Skopalik, A.: On the complexity of Nash dynamics and sink equilibria. In: EC (2009)
Mirrokni, V.S., Vetta, A.: Convergence Issues in Competitive Games. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) APPROX and RANDOM 2004. LNCS, vol. 3122, pp. 183–194. Springer, Heidelberg (2004)
Nagel, R.: Unraveling in guessing games: an experimental study. The American Economic Review 85(5), 1313–1326 (1995)
Nau, D.: An investigation of the causes of pathology in games. Artificial Intelligence 19, 257–278 (1982)
Nau, D.: Decision quality as a function of search depth on game trees. Journal of the ACM 30(4), 687–708 (1983)
Newell, A., Simon, H.: Human Problem Solving. Prentice-Hall (1972)
Pearl, J.: Heuristics: Intelligent Search Strategies for Computer Problem Solving. Addison-Wesley (1984)
Rubenstein, A.: Modeling Bounded Rationality. MIT Press (1998)
Sefer, E., Kuter, U., Nau, D.: Real-time A* Search with Depth-k Lookahead. In: Proceedings of the International Symposium on Combinatorial Search (2009)
Selten, R.: What is bounded rationality? In: Gigerenzer, G., Selten, R. (eds.) Bounded Rationality: the Adaptive Toolbox, pp. 13–36. MIT Press (2001)
Shannon, C.: Programming a computer for playing chess. Philosophical Magazine, Series 7 41(314), 256–275 (1950)
Simon, H.: A behavioral model of rational choice. Psychological Review 63, 129–138 (1955)
Skopalik, A., Vöcking, B.: Inapproximability of pure Nash equilibria. In: STOC, pp. 355–364 (2008)
Stahl, D., Wilson, P.: Experimental evidence on players’ models of other players. Journal of Economic Behavior and Organization 25(3), 309–327 (1994)
Tirole, J.: The Theory of Industrial Organization. MIT Press (1988)
Varian, H.: Position auctions. International Journal of Industrial Organization 25, 1163–1178 (2007)
Vetta, A.: Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In: FOCS, pp. 416–425 (2002)
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Mirrokni, V., Thain, N., Vetta, A. (2012). A Theoretical Examination of Practical Game Playing: Lookahead Search. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_22
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DOI: https://doi.org/10.1007/978-3-642-33996-7_22
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