In the former the players move in sequence, each aware of the others' previous actions. In the latter the players act at the same time, each ignorant of the others' actions.
A general principle for a player in a sequential-move game is to look ahead and reason back. Each player should figure out how the other players will respond to his current move, how he will respond in turn, and so on.
The player anticipates where his initial decisions will ultimately lead, and uses this information to calculate his current best choice. When thinking about how others will respond, one must put oneself in their shoes and think as they would; one should not impose one's own reasoning on them.
In principle, any sequential game that ends after a finite sequence of moves can be "solved" completely. We determine each player's best strategy by looking ahead to every possible outcome. Simple games, such as tic-tac-toe, can be solved in this way and are therefore not challenging.
For many other games, such as chess, the calculations are too complex to perform in practice—even with computers. Therefore, the players look a few moves ahead and try to evaluate the resulting positions on the basis of experience. In contrast to the linear chain of reasoning for sequential games, a game with simultaneous moves involves a logical circle. Although the players act at the same time, in ignorance of the others' current actions, each must be aware that there are other players who, in turn, are similarly aware, and so on.
The thinking goes: "I think that he thinks that I think His own best action is an integral part of this overall calculation. This logical circle is squared the circular reasoning is brought to a conclusion using a concept of equilibrium developed by the Princeton mathematician John Nash. We look for a set of choices, one for each player, such that each person's strategy is best for him when all others are playing their stipulated best strategies.
In other words, each picks his best response to what the others do. Sometimes one person's best choice is the same no matter what the others do. This is called a dominant strategy for that player. At other times, one player has a uniformly bad choice—a dominated strategy—in the sense that some other choice is better for him no matter what the others do.
The search for an equilibrium should begin by looking for dominant strategies and eliminating dominated ones. When we say that an outcome is an equilibrium, there is no presumption that each person's privately best choice will lead to a collectively optimal result. Indeed, there are notorious examples, such as the prisoners' dilemma see below , where the players are drawn into a bad outcome by each following his best private interests.
Nash's notion of equilibrium remains an incomplete solution to the problem of circular reasoning in simultaneous-move games. Some games have many such equilibria while others have none.
And the dynamic process that can lead to an equilibrium is left unspecified. But in spite of these flaws, the concept has proved extremely useful in analyzing many strategic interactions. The following examples of strategic interaction illustrate some of the fundamentals of game theory: The prisoners' dilemma. Two suspects are questioned separately, and each can confess or keep silent.
If suspect A keeps silent, then suspect B can get a better deal by confessing. If A confesses, B had better confess to avoid especially harsh treatment. However, working through such conflict together and not giving up on others is the best possible strategy to follow.
It is more productive to invest time in our relationships at work rather than ignoring or abusing them. While individuals may seem to benefit from acting selfishly, the benefits are limited and inevitably hurt them.
We are considering the field of biology. These are in fact cancerous cells. A tumour grows when a cell is very unhealthy, but instead of dying, it gets out of control and makes endless copies of itself at the expense of the rest of the body. The outcome of this selfishness is that the cell and its copies damage and can eventually kill the very thing that was keeping them alive. Cancerous cells are thus removed or killed off by treatments such as chemotherapy.
On the other hand, everyone benefits from cooperation and avoiding proliferating negativity. It is also interesting to note that the vast majority of cells have an autodestruct gene, meaning that they simply die out of their own if there is something wrong with them.
In the end, most unhealthy cells do not last long. We may just need to be patient, wait it out, and continue to pursue happiness and cooperation in our lives and work as best we can. Eventually, most trouble-makers leave. If they are still around, seek shelter and foster good relationships in your team and co-workers.
For example, an extended warranty is a credible signal to the consumer that the firm believes it is producing a high-quality product. Recent advances in game theory have succeeded in describing and prescribing appropriate strategies in several situations of conflict and cooperation. But the theory is far from complete, and in many ways the design of successful strategy remains an art. Avinash Dixit is the John J. They are coauthors of Thinking Strategically. Categories: Basic Concepts.
Further Reading Introductory Ankeny, Nesmith. Poker Strategy: Winning with Game Theory. New York: Basic Books, Brandenburger, Adam, and Barry Nalebuff. New York: Doubleday, Davis, Morton. Game Theory: A Nontechnical Introduction. Dixit, Avinash, and Barry Nalebuff. New York: W. Norton, Dixit, Avinash, and Susan Skeath. Games of Strategy. Luce, Duncan, and Howard Raiffa. Games and Decisions. New York: Wiley, McDonald, John. Strategy in Poker, Business and War.
Osborne, Martin. An Introduction to Game Theory. New York: Oxford University Press, Raiffa, Howard. The Art and Science of Negotiation. Cambridge: Harvard University Press, Riker, William. But we can imagine the case where both prisoners are genuinely disinterested activists, and each wants to leave prison as soon as possible because they sincerely believe they will do the most good in the world by furthering the respective cause they are committed to.
The negotiations currently taking place between Greece and its creditors are a prime place to deploy game theory - not least because of Varoufakis's past as a theorist in the field. Not everybody agrees. Sean Hargreaves Heap, a professor of political economy at King's College London, who co-authored a critical introduction to game theory in the s, believes that game theory is of little use to Greece's financial negotiations.
That's useful, but game theory merely tells you there are three different things you should expect in such a game of chicken," he says. Game theory is a useful way of characterising the problem, but in terms of telling you what someone is going to do in a game of chicken, it's completely hopeless.
Hargreaves Heap wrote his book on game theory with a young academic born in Athens and educated in Essex and Birmingham. His co-author's name? Yanis Varoufakis. Imagine you're buying a car from a dealership. Image source, Getty Images. Image source, Thinkstock. Thomas Schelling. One of the first to apply game theory to international relations in his book The Strategy of Conflict which analysed the nuclear arms race Argued the capability to retaliate was more useful than the ability to resist an attack and that uncertain retaliation was more credible than certain retaliation Both the US and the former Soviet Union adopted such a strategy - known as mutually assured destruction - during the Cold War.
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