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

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.

Mapping Minimax in 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.

A generalization of Nash's theorem with higher-order functionals

The recent theory of sequential games and selection functions by Escardó & Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalized to games defined by selection functions. A normal form construction is given, which generalizes the game-theoretic normal form, and its soundness is proved. Minimax strategies also generalize to the new class of games, and are computed by the Berardi–Bezem–Coquand functional, studied in proof theory as an interpretation of the axiom of countable choice.

Design of Vehicle Semi-Active Suspension System Control Unit

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.