Brown's original fictitious play

Berger, Ulrich

doi:10.1016/j.jet.2005.12.010

Cited by 70 publications

(44 citation statements)

References 18 publications

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“…In evolutionary game theory, this problem is addressed by developing dynamic learning models that converge to the equilibria [24]. One of the simplest classes of such learning models is fictitious play [25][26][27]. In fictitious play, it is assumed that the other player plays with a stationary strategy, which is estimated by the hitherto observed empirical choice frequencies.…”

Section: A Risk-sensitive Model Of Interactionmentioning

confidence: 99%

The effect of model uncertainty on cooperation in sensorimotor interactions

Grau-Moya

Hez

Pezzulo³

et al. 2013

J. R. Soc. Interface.

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Decision-makers have been shown to rely on probabilistic models for perception and action. However, these models can be incorrect or partially wrong in which case the decision-maker has to cope with model uncertainty. Model uncertainty has recently also been shown to be an important determinant of sensorimotor behaviour in humans that can lead to risk-sensitive deviations from Bayes optimal behaviour towards worst-case or best-case outcomes. Here, we investigate the effect of model uncertainty on cooperation in sensorimotor interactions similar to the stag-hunt game, where players develop models about the other player and decide between a pay-off-dominant cooperative solution and a risk-dominant, non-cooperative solution. In simulations, we show that players who allow for optimistic deviations from their opponent model are much more likely to converge to cooperative outcomes. We also implemented this agent model in a virtual reality environment, and let human subjects play against a virtual player. In this game, subjects' pay-offs were experienced as forces opposing their movements. During the experiment, we manipulated the risk sensitivity of the computer player and observed human responses. We found not only that humans adaptively changed their level of cooperation depending on the risk sensitivity of the computer player but also that their initial play exhibited characteristic risksensitive biases. Our results suggest that model uncertainty is an important determinant of cooperation in two-player sensorimotor interactions.

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Section: A Risk-sensitive Model Of Interactionmentioning

confidence: 99%

The effect of model uncertainty on cooperation in sensorimotor interactions

Grau-Moya

Hez

Pezzulo³

et al. 2013

J. R. Soc. Interface.

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“…An ǫ-saddle-point for (20) is an ǫ-equilibrium for this game. One could, in principle, use fictitious play [4] or similar methods to compute such an ǫ-equilibrium. Since the general methods for computing ǫ-equilibria in minimax games rely on subgradient descent and the primaldual objective functions are non-smooth, these general methods need O(ǫ −2 ) iterations to converge [34].…”

Section: Solving the Saddle-point Problemmentioning

confidence: 99%

Approximating Semidefinite Packing Programs

Iyengar¹,

Phillips²,

Stein³

2011

SIAM J. Optim.

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In this paper we define semidefinite packing programs and describe an algorithm to approximately solve these problems. Semidefinite packing programs arise in many applications such as semidefinite programming relaxations for combinatorial optimization problems, sparse principal component analysis, and sparse variance unfolding technique for dimension reduction. Our algorithm exploits the structural similarity between semidefinite packing programs and linear packing programs.

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“…For more recent results on the issue of convergence and nonconvergence of fictitious play and the best response dynamics see Berger (2005Berger ( , 2007aBerger ( , 2007bBerger ( , 2008, Hofbauer and Sandholm (2009), Hahn (2010), and van Strien (2011).…”

Section: Introductionmentioning

confidence: 99%

Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play

Berger¹

2011

Dyn Games Appl

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In this technical note we use insights from the theory of projective geometry to provide novel and non-algebraic proofs of convergence of continuous-time fictitious play for a class of games. As a corollary we obtain a kind of equilibrium selection result, whereby continuous-time fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4×4 zero-sum games.Journal of Economic Literature classification numbers: C72.

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Brown's original fictitious play

Cited by 70 publications

References 18 publications

The effect of model uncertainty on cooperation in sensorimotor interactions

The effect of model uncertainty on cooperation in sensorimotor interactions

Approximating Semidefinite Packing Programs

Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play

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