Minimax strategies for Bernoulli two-armed bandit on a moderate control horizon

2021 ◽  
pp. 1-9
Author(s):  
Alexander Kolnogorov ◽  
Denis Grunev
Keyword(s):  
Minimax Strategies

Mapping Minimax in the Brain

2014 ◽  
Author(s):  
Ignacio Palacios-Huerta
Keyword(s):  
Decision Making ◽  
Mixed Strategies ◽  
Interactive Decision Making ◽  
Minimax Strategies ◽  
Experimental Subjects ◽  
Competitive Games ◽  
Zero Sum ◽  
Increased Activity ◽  
The Brain

This chapter is concerned with mixed strategies. Using fMRI techniques, it peers inside the brain when experimental subjects play the penalty kick game. As we have noted already, minimax is considered a cornerstone of interactive decision-making analysis. More importantly, the minimax strategies have not been mapped in the brain previously by studying simultaneously the two testable implications of equilibrium. The results show increased activity in various bilateral prefrontal regions during the decision period. Two inferior prefrontal nodes appear to jointly contribute to the ability to optimally play the study's asymmetric zero-sum penalty kick game by ensuring the appropriate equating of payoffs across strategies and the generating of random choices within the game, respectively. This evidence contributes to the neurophysiological literature studying competitive games.

scholarly journals Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables

2018 ◽  
Vol 20 (01) ◽  
pp. 1750030 ◽  
Author(s):  
Atsuhiro Satoh ◽  
Yasuhito Tanaka
Keyword(s):  
Nash Equilibrium ◽  
Objective Function ◽  
The Other ◽  
Minimax Strategy ◽  
Equilibrium Strategies ◽  
Minimax Strategies ◽  
Nash Equilibrium Strategies ◽  
Special Case ◽  
Maximin Strategy

We examine maximin and minimax strategies for players in a two-players game with two strategic variables, [Formula: see text] and [Formula: see text]. We consider two patterns of game; one is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s, and the other is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s. We call two players Players A and B, and will show that the maximin strategy and the minimax strategy in the [Formula: see text]-game, and the maximin strategy and the minimax strategy in the [Formula: see text]-game are all equivalent for each player. However, the maximin strategy for Player A and that for Player B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the [Formula: see text]-game nor the [Formula: see text]-game. But, in a special case, where the objective function of Player B is the opposite of the objective function of Player A, the maximin strategy for Player A and that for Player B are equivalent, and they constitute the Nash equilibrium both in the [Formula: see text]-game and the [Formula: see text]-game.

Design of Vehicle Semi-Active Suspension System Control Unit

2012 ◽  
Vol 220-223 ◽  
pp. 1995-1999
Author(s):  
Hong Kun Zhang ◽  
Wen Jun Li
Keyword(s):  
Embedded System ◽  
Control Strategy ◽  
Ride Comfort ◽  
Integrated Control ◽  
Control Unit ◽  
Active Suspension ◽  
Suspension System ◽  
System Control ◽  
Control Effect ◽  
Minimax Strategies

This paper researches on embedded system design based on MC9s12Dp256 microcontroller for vehicle semi-active suspension. The hardware design of suspension control unit (SCU) is introduced. The integrated control strategy which integrates Skyhook and MiniMax strategies is proposed. The hardware-in-the-loop simulation (HILS) test on a two-degree-of-freedom quarter car semi-active suspension system model is carried out. The functions of SUC are verified and the performance of passive suspension and semi-active suspension is compared. The simulation results indicate that the performance of SCU achieves design requirement. In comparison with passive system, the control effect of integrated control strategy can be improved in ride comfort and drive safety.

Symmetric Spatial Games Without Majority Rule Equilibria

1976 ◽  
Vol 70 (4) ◽  
pp. 1172-1184 ◽  
Author(s):  
Richard D. McKelvey ◽  
Peter C. Ordeshook
Keyword(s):  
General Class ◽  
Majority Rule ◽  
Pure Strategy ◽  
Spatial Models ◽  
Strategy Space ◽  
Spatial Games ◽  
Minimax Strategies ◽  
Zero Sum

The assumptions imposed in spatial models of election competition generally are restrictive in that they require either unidimensional issue spaces or symmetrically distributed electorate preferences. We attribute such assumptions to the reliance of these models on a single concept of a solution to the election game—pure strategy equilibria—and to the fact that such equilibria do not exist in general under less severe restrictions. This essay considers, then, the possibility that candidates adopt mixed minimax strategies. We show, for a general class of symmetric zero-sum two-person games, that the domain of these minimax strategies is restricted to a subset of the strategy space and that for spatial games this set not only exists, but if preferences are characterized by continuous densities, it is typically small. Thus, the hypothesis that candidates abide by mixed minimax strategies can limit considerably our expectation as to the policies candidates eventually advocate. Additionally, we examine the frequently blurred distinction between spatial conceptualizations of two-candidate elections and of committees, and we conclude that if pure strategy equilibria do not exist, this distinction is especially important since committees and elections can produce entirely different outcomes.

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