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December 2, 2019 - January 22, 2020
game table or payoff table.
When a simultaneous-move game has this special feature, namely that for a player the best choice is the same regardless of what the other player or players choose, it greatly simplifies the players’ thinking and the game theorists’ analysis. Therefore it is worth making a big deal of it, and looking for it to simplify the solution of the game. The name given by game theorists for this property is dominant strategy. A player is said to have a dominant strategy if that same strategy is better for him than all of his other available strategies no matter what strategy or strategy combination the
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RULE 2: If you have a dominant strategy, use it.
In the general context, the two strategies available to each player are labeled “Cooperate” and “Defect” (or sometimes “Cheat”),
TIT FOR TAT
Tit for tat is a variation of the eye for an eye rule of behavior: Do unto others as they have done onto you.* More precisely, the strategy cooperates in the first period and from then on mimics the rival’s action from the previous period.
Axelrod argues that tit for tat embodies four principles that should be present in any effective strategy for the repeated prisoners’ dilemma: clarity, niceness, provocability, and forgivingness.
Suppose you started by acting nicely. Then the other player, even if he is not a reciprocator, would think it possible that you are one of the few nice people around. There are real gains to be had by cooperating for a while, and the other player would plan to reciprocate your niceness to achieve these gains. That helps you, too. Of course you are planning to sneak in a defection near the end of the game, just as the other player is. But you two can still have an initial phase of mutually beneficial cooperation. While each side is waiting to take advantage of the other, both are benefiting
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HOW TO ACHIEVE COOPERATION
philosopher Immanuel Kant: “Take only such actions as you would like to see become a universal law.”
The actions of one player have no effect whatsoever on the other player in the game. Still people think that somehow their actions can influence the choice of others, even when their actions are invisible.
“quasi-magical” thinking—the idea that by taking some action, you can influence what the other side will do. People realize they can’t change what the other side has done once they’ve been told what the other side has done. But if it remains open or undisclosed, then they imagine that their actions might have some influence—or that the other side will somehow be employing the same reasoning chain and reach the same outcome they do.
First, there must be clear rules that identify who is a member of the group of players in the game—those who have the right to use the resource.
Gerald Wilkinson explored the basis of this behavior by collecting bats from different locations and putting them together. Then he systematically withheld blood from some of them and saw whether others shared with them. He found that sharing occurred only when the bat was on the verge of death, and not earlier. Bats seem to be able to distinguish real need from mere temporary bad luck. More interesting, he found that sharing occurred only among bats that already knew each other from their previous group, and that a bat was much more likely to share with another bat that had come to its aid in
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The game we have here is a cousin to the prisoners’ dilemma, a life and death case of the “stag hunt” game analyzed by the philosopher Jean-Jacques Rousseau.
In the stag hunt, if everyone works together to capture the stag, they succeed and all eat well. A problem arises if some hunters come across a hare along the way. If too many hunters are sidetracked chasing after hares, there won’t be enough hunters left to capture the stag. In that case, everyone will do better chasing after rabbits. The best strategy is to go after the stag if and only if you can be confident that most everyone is doing the same thing. You have no reason not to chase after the stag, except if you lack confidence in what others will do.
The result is a confidence game. There are two ways it can be played. Everyone works together and life is good. Or everyone looks out for themselves and life is nasty, brutish, and short. This is not the classic prisoners’ dilemma in which each person has an incentive to cheat no matter what others do. Here, there is no incentive to cheat, so long as you can trust others to do the same. But can you trust them? And even if you do, can you trust them to trust you? Or can you trust them to trust you to trust them? As FDR famously said (in a different context), we have nothing to fear but fear
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BIG GAME OF COORDINATION
where the action of each player is best for him given his beliefs about the other’s action, and the action of each is consistent with the other’s beliefs about it, neatly squares the circle of thinking about thinking. Therefore it has a good claim to be called a resting point of the players’ thought processes, or an equilibrium of the game. Indeed, this is just a definition of Nash equilibrium.
If an equilibrium is obvious ad infinitum in this way, that is, if the players’ expectations converge upon it, we call it a focal point.
Anything that distinguishes becomes a focal point and allows people’s expectations to converge. For this reason, we should not be surprised that many of the world’s top models do not have perfect features; rather, they are almost perfect but have some interesting flaw that gives their look a personality and a focal point.
conflict is sharper in chicken, in the sense that if each player tries to achieve his preferred equilibrium, both end up in their worst outcome.
chicken shows a general point about games: even though the players are perfectly symmetric as regards their strategies and payoffs, the Nash equilibria of the game can be asymmetric, that is, the players choose different actions.
When one strategy, say A, is uniformly worse for a player than another, say B, we say that A is dominated by B. If such is the case, that player will never use A, although whether he uses B remains to be seen. The other player can confidently proceed in thinking on this basis; in particular, he need not consider playing a strategy that is the best response only to A. When solving the game, we can remove dominated strategies from consideration. This reduces the size of the game table and simplifies the analysis.*
there are zones of commonality of interests as well as of conflict and so, there can be combinations of mutually gainful or mutually harmful strategies.
game tree.
In a game with simultaneous moves, there is a logical circle of reasoning: I think that he thinks that I think that…and so on. This circle must be squared; one must see through the rival’s action even though one cannot see it when making one’s own move. To tackle such a game, construct a table that shows the outcomes corresponding to all conceivable combinations of choices. Then proceed in the following steps.
Begin by seeing if either side has a dominant strategy—one that outperforms all of that side’s other strategies, irrespective of the rival’s choice. This leads to Rule 2: If you have a dominant strategy, use it. If you don’t have a dominant strategy, but your rival does, then count on his using it, and choose your best response accordingly. Next, if neither side has a dominant strategy, see if either has a dominated strategy—one that is uniformly worse for the side playing it than all the rest of its strategies. If so, apply Rule 3: Eliminate dominated strategies from consideration. Go on
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RULE 5: In a game of pure conflict (zero-sum game), if it would be disadvantageous for you to let the opponent see your actual choice in advance, then you benefit by choosing at random from your available pure strategies. The proportions in your mix should be such that the opponent cannot exploit your choice by pursuing any particular pure strategy from the ones available to him—that is, you get the same average payoff when he plays any of his pure strategies against your mixture.
www.worldrps.com,
The purpose of the coupons is to expand market share. But each firm realizes that to be successful, it has to offer promotions when the other is not offering similar promotions.
actions that change the game to ensure a better outcome for the player taking the actions are called strategic moves.
You could establish a reputation as someone who never swerves. However, to do that you must have won similar games in the past, so the question just transfers itself to what you could have done in those games.
two aspects of commitments and credibility: what and how. The “what” part is the scientific or game-theoretic aspect—seizing first-mover advantage. The “how” part is the practical aspect or the art—thinking up devices for making strategic moves credible in a specific situation.
But the very purpose of a strategic move is to alter the other player’s choice, not to take it as given.
A threat is a response rule that punishes others who fail to act as you would like them to. A promise is an offer to reward other players who act as you would like them to.
Therefore such moves require you to change the game in more complex ways. You must seize the first-mover status in the matter of putting the response rule in place and communicating it to the other player.
You must ensure that your response rule is credible, namely that if and when the time comes for you to make the stated response, you will actually choose it. This may require changing the game in some way to ensure that the choice is in fact best for you in that situation. But in the game that follows, you must then have the second move so you will have the ability to respond to the other’s choice. This may require you to restructure the order of moves in the game, and that adds its own difficulties to your making the strategic move.
DETERRENCE AND COMPELLENCE
useful to classify the overall purpose into two distinct categories. When you want to stop the others from doing something they would otherwise do, that is deterrence. Its mirror image, namely to compel the others to do something they would not otherwise do, can then be termed compellence.
WARNINGS AND ASSURANCES
When it is in your interest to carry out a promise, we call this an assurance.
Strategic moves, therefore, contain two elements: the planned course of action and the associated actions that make this course credible.
CLARITY AND CERTAINTY
LARGE THREATS
BRINKMANSHIP
We argued in the previous section that there are good reasons for keeping the size of a threat down to the smallest level that will have the desired effect. But you may not know in advance the smallest effective size of a threat. That is why it makes sense to
start small, and increase it gradually to find out when it works.
brinkmanship.* The term is often interpreted as taking an adversary to the brink of disaster in order to get him to blink first.
