Strategy subsets closed under rational behavior

Basu, Kaushik; Weibull, Jörgen W.

doi:10.1016/0165-1765(91)90179-o

Cited by 213 publications

(181 citation statements)

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“…Thus E(l(f )|f ) = 1 n i l(f i ). 6 For any two vectors x and y, we have x T y ≤ √ x T x · p y T y. where the last inequality follows from Cauchy-Schwarz. Thus, if we set x = l(f ) OP T , the above can be transformed into the inequality x 2 ≤ 12x + 1.…”

Section: Shapley Network Design Gamesmentioning

confidence: 99%

“…Among them are correlated equilibria [2], stable equilibria [45], stochastic adjustment models [39], strategy subsets closed under rational behaviour (CURB set) [6], iterative elimination of dominated strategies, the set of undominated strategies, etc. Convergence and strategic stability of equilibria in evolutionary game theory is also an important subject of study.…”

Section: Background and Related Workmentioning

confidence: 99%

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A Theoretical Examination of Practical Game Playing: Lookahead Search

Mirrokni

Thain

Vetta

2012

Algorithmic Game Theory

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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?Myopic game playing (whose corresponding equilibria are Nash equilibria), where each player can only foresee the immediate effect of her own actions, is the special case of 1-lookahead search. Thus, for the first question, it is natural to ask whether social outcomes improve when players use more foresight than in myopic behaviour. The answer depends on the game played: (i) For the Cournot game, applying 2-lookahead leads to a 12.5% increase in output and a 5.5% increase in social surplus compared with myopic competition. Similar bounds arise as the length k of foresight increases.(ii) In AdWord auctions (or generalized second-price auctions), we show that 2-lookahead game playing results in outcomes that are always optimal to within a constant factor; in contrast, myopic game play can produce arbitrarily poor equilibrium outcomes.(ii) For congestion games, as with myopic game playing, lookahead search leads to constant factor qualitative guarantees. (iv) For basic-utility games, on the other hand, whilst myopic game playing always leads to constant factor approximations, additional foresight can lead to arbitrarily bad solutions! (v) In a simple Shapley network design game, qualitative guarantees improve with the length of foresight. Regarding the second question, a variety of interesting game playing characteristics also arise with lookahead search. Stackelberg leader-follower behaviours can be induced when the players have asymmetric computational power. For example, Stackelberg equilibria can be produced in the Cournot game. Lookahead search can also generate "uncoordinated" cooperative behaviour!

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Section: Shapley Network Design Gamesmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

A Theoretical Examination of Practical Game Playing: Lookahead Search

Mirrokni

Thain

Vetta

2012

Algorithmic Game Theory

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“…A set-valued solution concept assigns to each game a collection of product sets of strategies, i.e., a set of product sets in the strategy space of the game. Set-valued solution concepts include: the set of rationalizable strategies (Bernheim, 1984), persistent retracts (Kalai and Samet, 1984), minimal curb sets (Basu and Weibull, 1991), and minimal prep sets (Voorneveld, 2004(Voorneveld, , 2005.…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…Dufwenberg et al (2001) show by means of examples that a transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games. The minimal curb sets of Basu and Weibull (1991) constitute one such a solution concept. Minimal curb sets are of central importance in the literature on strategic adjustment, since many intuitively appealing adjustment processes eventually settle down in a minimal curb set; cf.…”

Section: Introductionmentioning

confidence: 99%

An axiomatization of minimal curb sets

2005

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An Axiomatization of Minimal Curb SetsVoorneveld, M.; Kets, W.; Norde, Henk General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract. Norde et al. [Games Econ. Behav. 12 (1996)

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“…, n, R i (t) = R * i (see Pearce [19]). The iterative procedure used above to define rationalizability can be interpreted as follows: 3 Suppose every player choosing a strategy behaves according to the following axioms of rationality which I will call the "Rationality Hypothesis." (R1): Every player i has some conjecture s −i regarding the behavior of his opponents.…”

Section: Normal Form Gamesmentioning

confidence: 99%

Rationality and Coherent Theories of Strategic Behavior

Gül

1996

Journal of Economic Theory

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A non-equilibrium model of rational strategic behavior that can be viewed as a refinement of (normal form) rationalizability is developed for both normal form and extensive form games. This solution concept is called a τ -theory and is used to analyze the main concerns of the Nash equilibrium refinements literature such as dominance, iterative dominance, extensive form rationality, invariance, and backward induction. The relationship between τ -theories and dynamic learning is investigated.JEL classification number C72

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Strategy subsets closed under rational behavior

Cited by 213 publications

References 3 publications

A Theoretical Examination of Practical Game Playing: Lookahead Search

A Theoretical Examination of Practical Game Playing: Lookahead Search

An axiomatization of minimal curb sets

Rationality and Coherent Theories of Strategic Behavior

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