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Pure Nash Equilibria: Hard and Easy Games
"... In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then s ..."
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Cited by 66 (3 self)
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In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NPhard, while deciding whether a game has a strong Nash equilibrium is Stcomplete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's move depends on moves of other players. We say that a game has small neighborhood if the " utility function for each player depends only on (the actions of) a logarithmically small number of other players, The dependency structure of a game G can he expressed by a graph G(G) or by a hypergraph II(G). Among other results, we show that if jC has small neighborhood and if II(G) has botmdecl hypertree width (or if G(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFLcomplete and thus in the class _NC ~ of highly parallelizable problems. 1 Introduction and Overview of Results The theory of strategic games and Nash equilibria has important applications in economics and decision making [31, 2]. Determining whether Nash equilibria exist, and effectively computing
Networks of Influence Diagrams: A Formalism for Reasoning about Agents’ Decisionmaking Processes
"... Traditional gametheoretic analysis for decisionmaking takes a normative approach, in which agents derive rational decisions from the game description. This approach cannot naturally and compactly capture agents that are uncertain about the structure of the game, the strategies of other agents or w ..."
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Cited by 8 (0 self)
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Traditional gametheoretic analysis for decisionmaking takes a normative approach, in which agents derive rational decisions from the game description. This approach cannot naturally and compactly capture agents that are uncertain about the structure of the game, the strategies of other agents or whether agents may deviate from their optimal strategy. This paper presents Networks of Influence Diagrams (NID), a compact, natural and highly expressive language for reasoning about agents ’ beliefs and decisionmaking processes. NIDs are graphical structures in which agents ’ mental models are represented as nodes in a network; a mental model for an agent may itself use descriptions of the mental models of other agents. NIDs are demonstrated by examples, showing how they can be used to describe conflicting and cyclic belief structures, and certain forms of bounded rationality. In an opponent modeling domain, NIDs were able to outperform other computational agents whose strategies were not known in advance. A novel equilibrium concept is defined that makes a distinction between agents ’ optimal strategies, and how they actually behave in reality. It is also shown that NIDs are more compact and structured than Bayesian games, the traditional formalism used to model uncertainty in multiagent decisionmaking problems.
Using iterated reasoning to predict opponent strategies
 In AAMAS
, 2011
"... The field of multiagent decision making is extending its tools from classical game theory by embracing reinforcement learning, statistical analysis, and opponent modeling. For example, behavioral economists conclude from experimental results that people act according to levels of reasoning that form ..."
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Cited by 6 (2 self)
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The field of multiagent decision making is extending its tools from classical game theory by embracing reinforcement learning, statistical analysis, and opponent modeling. For example, behavioral economists conclude from experimental results that people act according to levels of reasoning that form a “cognitive hierarchy ” of strategies, rather than merely following the hyperrational Nash equilibrium solution concept. This paper expands this model of the iterative reasoning process by widening the notion of a level within the hierarchy from one single strategy to a distribution over strategies, leading to a more general framework of multiagent decision making. It provides a measure of sophistication for strategies and can serve as a guide for designing good strategies for multiagent games, drawing it’s main strength from predicting opponent strategies. We apply these lessons to the recently introduced Lemonadestand Game, a simple setting that includes both collaborative and competitive elements, where an agent’s score is critically dependent on its responsiveness to opponent behavior. The opening moves are significant to the end result and simple heuristics have achieved faster cooperation than intricate learning schemes. Using results from the past two realworld tournaments, we show how the submitted entries fit naturally into our model and explain why the top agents were successful.
Networks of Influence Diagrams: A Formalism for Reasoning about Agents ’ Decisionmaking Processes
"... Traditional gametheoretic analysis for decisionmaking takes a normative approach, in which agents derive rational decisions from the game description. This approach cannot naturally and compactly capture agents that are uncertain about the structure of the game, the strategies of other agents or w ..."
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Cited by 3 (0 self)
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Traditional gametheoretic analysis for decisionmaking takes a normative approach, in which agents derive rational decisions from the game description. This approach cannot naturally and compactly capture agents that are uncertain about the structure of the game, the strategies of other agents or whether agents may deviate from their optimal strategy. This paper presents Networks of Influence Diagrams (NID), a compact, natural and highly expressive language for reasoning about agents ’ beliefs and decisionmaking processes. NIDs are graphical structures in which agents ’ mental models are represented as nodes in a network; a mental model for an agent may itself use descriptions of the mental models of other agents. NIDs are demonstrated by examples, showing how they can be used to describe conflicting and cyclic belief structures, and certain forms of bounded rationality. In an opponent modeling domain, NIDs were able to outperform other computational agents whose strategies were not known in advance. A novel equilibrium concept is defined that makes a distinction between agents ’ optimal strategies, and how they actually behave in reality. It is also shown that NIDs are more compact and structured than Bayesian games, the traditional formalism used to model uncertainty in multiagent decisionmaking problems. 1
Coherence and Rationality in Grounding
"... This paper analyses dialogues where understanding and agreement are problematic. We argue that pragmatic theories can account for such dialogues only by models that combine linguistic principles of discourse coherence and cognitive models of practical rationality. 1 ..."
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This paper analyses dialogues where understanding and agreement are problematic. We argue that pragmatic theories can account for such dialogues only by models that combine linguistic principles of discourse coherence and cognitive models of practical rationality. 1
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"... An emerging empirical methodology bridges the gap between game theory and simulation for practical strategic reasoning. GameTheoretic Analysis Gametheoretic analysis typically takes at its starting point, most naturally, a description of its subject—the game, a formal model of a multiagent interac ..."
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An emerging empirical methodology bridges the gap between game theory and simulation for practical strategic reasoning. GameTheoretic Analysis Gametheoretic analysis typically takes at its starting point, most naturally, a description of its subject—the game, a formal model of a multiagent interaction. The recent surge in interest among AI researchers in game theory has led to numerous advances in game modeling (Gal & Pfeffer 2004;
unknown title
"... An emerging empirical methodology bridges the gap between game theory and simulation for practical strategic reasoning. GameTheoretic Analysis Gametheoretic analysis typically takes at its starting point, most naturally, a description of its subject—the game, a formal model of a multiagent interac ..."
Abstract
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An emerging empirical methodology bridges the gap between game theory and simulation for practical strategic reasoning. GameTheoretic Analysis Gametheoretic analysis typically takes at its starting point, most naturally, a description of its subject—the game, a formal model of a multiagent interaction. The recent surge in interest among AI researchers in game theory has led to numerous advances in game modeling (Gal & Pfeffer 2004;