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New results on the verification of nash refinements for extensive–form games
, 2012
"... The computational study of strategic interaction situations has recently deserved a lot of attention in multi–agent systems. A number of results on strategic–form games and zero–sum extensive–form games are known in the literature, while general–sum extensive–form games are not studied in depth. We ..."
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The computational study of strategic interaction situations has recently deserved a lot of attention in multi–agent systems. A number of results on strategic–form games and zero–sum extensive–form games are known in the literature, while general–sum extensive–form games are not studied in depth. We focus on the problem to decide whether or not a solution is a refinement of the Nash equilibrium (NE) for extensive–form games. Refinements are needed because the NE concept is not satisfactory for this game class. While verifying whether a solution is an NE is in P, verifying whether it is a NE refinement may be not (all the results known so far showNP–hardness). In this paper, we provide the first positive result, showing that verifying a sequential equilibrium with any number of agents and a quasi perfect equilibrium with two agents are inP. We show also that when the input is expressed in (non–perturbed) sequence form even the problem to verify a subgame perfect equilibrium isNP–complete and that sequence form, if applicable, must be rethought to verify (and therefore to compute) an extensive–form perfect equilibrium.
Effectiveness of GameTheoretic Strategies in ExtensiveForm GeneralSum Games
"... Abstract. Game theory is a descriptive theory defining the conditions for the strategies of rational agents to form an equilibrium (a.k.a. the solution concepts). From the prescriptive viewpoint, game theory generally fails (e.g., when multiple Nash equilibria exist) and can only serve as a heurist ..."
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Abstract. Game theory is a descriptive theory defining the conditions for the strategies of rational agents to form an equilibrium (a.k.a. the solution concepts). From the prescriptive viewpoint, game theory generally fails (e.g., when multiple Nash equilibria exist) and can only serve as a heuristic for agents. Extensiveform generalsum games have a plethora of solution concepts, each posing specific assumptions about the players. Unfortunately, there is no comparison of the effectiveness of the solutionconcept strategies that would serve as a guideline for selecting the most effective algorithm for a given domain. We provide this comparison and evaluate the effectiveness of solutionconcept strategies and strategies computed by Counterfactual regret minimization (CFR) and Monte Carlo Tree Search in practice. Our results show that (1) CFR strategies perform typically the best, (2) the effectiveness of the Nash equilibrium and its refinements is closely related to the correlation between the utilities of players, and (3) that the strong assumptions about the opponent in Strong Stackelberg equilibrium typically cause ineffective strategies when not met. 1
Auton Agent MultiAgent Syst DOI 10.1007/s1045801291985
"... Bilateral bargaining with onesided uncertain reserve prices ..."
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