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This chapter describes the theory of two-person, zero-sum games invented by John Von Neumann in 1928. It begins with an application to the computation of economic shadow prices. It shows that a two-person game is strictly competitive if, and only if, it has a zero-sum representation. Such a game can be represented using only the first player's payoff matrix. The minimax and maximin values of the matrix are defined and linked to the concept of a saddle point. The ideas are then related to a player's security level in a game. An inductive proof of Von Neumann's minimax theorem is offered. The connexion between the minimax theorem and the duality theorem of linear programming is explained. The method of solving certain two-person, zero-sum games geometrically with the help of the theorem of the separating hyperplane is introduced. The Hide-and-Seek Game is used as a non-trivial example.

This chapter reviews the strategic framework that integrates options and competitive games to de-bias decision making, and recaps the main conclusions and strategy implications. It provides empirical evidence that acquisitions are driven by growth options and behavioral economics, discusses examples of option game applications beyond acquisitions, and lists promising directions for future research. Most important, it provides a decision framework for directly integrating finance and acquisition strategy in uncertain environments. The authors hope that this book helps readers apply an options perspective to significant nonfinancial decisions, including such vital life decisions such as the design of one's education strategy or career plan, or more common problems such how to plan holiday journeys. They believe valuable lessons can be learned as the reader applies the insights in this book to a broader set of uncertainty problems, although they are impossible to quantify.

This chapter describes a novel behavioral bias not previously documented in a competitive situation: psychological pressure in a dynamic competitive environment arising from the state of the competition. Drawing on a data set comprising 1,001 penalty shoot-outs with 10,431 penalty kicks over the period 1970–2013, it collects information on the date of every shoot-out of every competition, the identity of the teams kicking first and second, the final outcome of the shoot-out, the outcomes of each of the kicks in the sequence, the geographical location of the game (that is, whether the game was played in a home ground, a visiting ground, or in a neutral field); and variables that measure the quality of the teams, such as their previous experience in shoot-outs, their official FIFA and UEFA rankings (for national teams), and the division, category, and standings (for club teams).

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.

This chapter examines the choice behaviours of rhesus monkeys during two different computerized competitive games in order to understand how decision-making strategies are adjusted during social interactions in nonhuman primates. The monkeys were trained to perform free-choice tasks modelled after matching pennies and rock–paper–scissors games. The findings reveal that the choice behaviour of the monkeys during both games is consistent with the predictions of reinforcement learning models and that the prefrontal cortex plays a key role in dynamically updating the animals' decision-making strategies.