Presh Talwalkar

a best response is a strategy that one player would choose in response to the given strategy profile of another player, or a group of players.

As desirable as this outcome is, it is not sustainable. The reason is that each stand has an incentive to deviate. Either one could choose to locate closer to the center and gain more than half the customers. The other stand would retaliate by moving closer to the center as well, and the game would go on until both end up in the center.

the Bertrand Duopoly. It is characterized by two firms competing solely on price to customers that have no loyalty and simply pick the firm with the lowest price.

There is an obvious lesson from game theory: never choose a dominated action

Dominated strategies are not just bad decisions; they are the worst possible decisions. Buying lottery tickets is a losing bet and generally not smart, but even then you have a chance to win. So you can think of playing a dominated strategy as worse than buying a lottery ticket. You are always better off avoiding dominated strategies.

The people who wrote down the winning numbers told the class they suspected some people would deviate for irrational reasons. And they were rewarded for not confusing theory with practice.

A dominated strategy is one that you should never play. The flip side is a dominant strategy, a strategy that always makes sense and should be played. A dominant strategy is one that gives you the best outcome, regardless of what your other choices are and what other people are doing.

A focal point is a time or strategy that is natural or special in some way. Focal points are important because they allow people to coordinate without communication.

Suppose two people are arguing over a garment. One claims half belongs to him while the other claims the whole is his. A judge is asked to decide who gets what. What would you do?
There are naturally various answers. One could propose an even split (1/2, 1/2) or a proportional split (1/3, 2/3).
But the Talmud offers a different answer, an answer that turns out to be an equal division of the contested sum (1/4, 3/4). How does this principle work? There are three stages. First, decide what portion of the cloth is being disputed. In this case, exactly half of the garment is being claimed by both parties. Second, split the disputed division among both parties—so 1/4 of the cloth is awarded to each. And third, give the remaining cloth—the “undisputed” portion—entirely to the person whose claim is not disputed.
This logic yields a split of 1/4 for the person claiming half of the garment and 3/4 for the person claiming the whole.

But it is not always the case that attractive choices are useful in all games. In competitive games, it is often the naturally appealing choice that creates conflict.