4: Rock, Paper, Scissors
RPS is a common childhood game that is often used by adults to come to a decision when none can agree. It is fundamentally the same as a coin toss or a roll of dice - a method of random choice - and is believed to remain popular because each "player" makes a voluntary choice (so has a sense of participation and commitment to the outcome) and enters into an explicit agreement to abide by the outcome.
In terms of game theory, there's not much strategy involved. Arguably, you can use your expectation of the other person's choice to make an informed decision. All the same, there have been situations in which there have been fairly high stakes (an RPS contest between two auction houses) that resulted in a rather silly amount of statistics and psychology to predict the other side's choice.
The author dwells a bit on the difficulty of playing RPS with more than two people - the outcome may not have one clear winner or loser. (EN: but in truth, there is general an impromptu solution, such as a "tournament" or "odd man out" approach - need not get too caught up in the details so long as the "spirit" of the game is preserved.)
The author refers to a few examples in nature - lizards and bacteria - where the same strategy is used: there are three tactics for mating or claiming territory, each of which defeats one of the others while being defeated by the third. The result is a sustainable balance. However, if one of the groups should "disappear," the balance of power would be disrupted and one of the remaining two groups would also become extinct.
As a sidebar, the author suggests that the best approach to RPS is to adopt a truly random strategy. This will not make you more likely to "win", but it will make you less likely to lose more often that you should by virtue of being predictable.
Opting Out
Cooperation is more evident in groups where there is voluntary membership. The author reasons that this reduces the clutter of people who participate in a discussion when they aren't interested in achieving the outcome and end up subverting the communal purpose in order to serve other interests.
An experiment as done to observe the effect of opting out: subjects were presented a game in which they could earn a small amount for opting out altogether, a chance at a larger amount by playing cooperatively, and a chance at getting an even larger amount if they could successfully free-ride (though the amount would be diminished by the number of free riders).
The appeal of opting-out is a certain reward, as opposed to an uncertain return for playing. It's reasoned that a free-rider seeks to gain something for nothing and, given that he expects others will have the same motivation, estimated that the small prize for opting-out would be better than the share to be split among free-riders who participated (which would take more effort to earn).
The Truel
The author presents a logic puzzle of a three-way duel, in which the worst shot goes first. The appropriate strategy for the worst shooter is to fire his first shot into the air. If you hit either one of your opponents, the remaining person will shoot you (as you are his only target) - but if you purposefully miss, then the next shooter will aim at the other person, who is more skilled and therefore a bigger threat. Getting one of your opponents to eliminate the other increases your chances of ultimate success.
The same is true in double-elimination tournaments. Players who lose in the first round are pitted against one another - so if you're a strong player who intentionally throws the first match, you will be pitted against weaker players until the final round - and if your estimation is correct and no other strong player user the same strategy, then you've an excellent chance of making second place, even if you're not the second-best player in the tournament.
The basic strategy here is to let the strong competitors fight among themselves before entering the fray, which is an effective strategy. The author claims success with it in committee meetings, waiting to introduce his argument until the last minute, when the people are tired of arguing over the other alternatives.
Even the potential for a truel is often enough to dissuade people from combating. For example, it's largely assumed that the nuclear standoff between the USA and USSR was because of a balance of power when, in truth, credit for the stalemate was more attributable to China. The USSR might have been convinced that it could beat the USA, but refrained from attacking because it would have been left in a weakened position, easily overtaken by China, and so refrained.